cmpatino/direct-opd-sft-transfer-results

Does Direct-OPD transfer a capability-bearing SFT shift into a larger student?

Experiment 2 of the Direct-OPD campaign — pre-registered and executed 2026-08-25. Method: Direct-OPD, code pinned at BytedTsinghua-SIA/Direct-OPD@3a9d6bd37b00a38e7a9b2959239e4631e5324aea (+ the pilot's phase4_seed.patch). Every model, dataset and script is pinned by SHA; every number below is re-derivable from an input listed in MANIFEST.json.

Status: COMPLETE (2026-08-25/26). All 18 pre-registered run-1 evaluation units have landed and every number below is final; no section is a placeholder. 3 further units were deliberately not run — all three cost-forced, itemized in §2.2 — and are labelled skipped, never pending. Two subsections carry a status label rather than a placeholder, and both labels are load-bearing: §7 reports the ckpt-100 endpoints under the logged REDUCED protocol (8 samples/problem on AIME, a 100-problem subset on MATH-500), and §8.4 is a post-hoc sensitivity view, not a pre-registered endpoint. This file is regenerated end-to-end by code/report/build_report.py; nothing in it was hand-copied.

The exp2b extension (§13–§16) is COMPLETE (2026-08-29). All 47 live exp2b evaluation units are on the Hub and every cell in §13–§16 is a measured value; no section of this report is a placeholder. 33 further pre-registered units are canceled or dropped and can never exist — the runs that would have produced them were stopped before their first checkpoint save (§13.5), or the tier was dropped by the user (§13.4); each is labelled with its reason in §12.1 and none is counted as outstanding.

Built 2026-08-31T17:47:21Z · aggregate schema exp2b-final-report-1 · results repo cmpatino/direct-opd-sft-transfer-results @ 15fe27f8545d · student repo cmpatino/Qwen2.5-7B-Instruct-DirectOPD-R1DistillShift-100 @ 5819e26cab1f.

Contents
0. TL;DR	7. Student results
1. Question & hypothesis	8. Diagnostics
2. Pre-registration & deviations	9. Interpretation vs the pilot
3. Setup	10. Limitations
4. Phase 0 gates	11. Cost & reproduction
5. Teacher gains — the premise	12. Artifact inventory
6. Training dynamics	13. Extension exp2b
14. The termination sink	15. Answer to the question
16. Recommendations for a next attempt	17. The mechanism, measured
18. The RAFT condition

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0. TL;DR

1. The answer: no. Across the whole campaign — 7 Direct-OPD training runs, two SFT teacher pairs, two student models — an established SFT policy change did not distil into a larger student. Of the 43 paired held-out gain measurements this study made (every evaluated checkpoint of every condition, against the same initial student), 0 are positive with a 95 % CI that excludes zero and 6 are negative with a CI that excludes zero — 4 of those at post-collapse checkpoints, where the model no longer stops writing, and 2 small pre-collapse ones (-2.25 pp, -2.19 pp). The one large negative — -28.75 pp on math500 at B-lowlr step 100 — is a termination artifact, not a capability loss (bullet 3). §15 states that answer with its scope and its limits.
2. The premise held twice — this is not a failure of the teachers. The R1-distill pair carries +24.375 [+15.417, +34.167] p<0.0001 on AIME 2024 and +46.500 [+43.200, +49.850] p<0.0001 on MATH-500; the OpenThinker3 pair, added in exp2b precisely to remove every doubt about the first, carries +51.771 [+38.646, +64.375] p<0.0001 on AIME 2024, +42.604 [+28.539, +56.667] p<0.0001 on AIME 2025 and +50.050 [+46.650, +53.400] p<0.0001 on MATH-500 — with both of its models at the same 31,744-token cap, so no budget confound at all. Two caveats the report keeps in view: run 1's π_pre is capped at 3,200 tokens by its own context, and holding π_post to that budget shrinks its AIME 2024 gain to +3.646 [-1.042, +9.167] p=0.1426 — a CI that includes zero — while MATH-500 survives at +31.550 [+27.950, +35.050] p<0.0001 (§8.4); and the OpenThinker post-teacher truncates on 19.0 % / 22.1 % of AIME 2024 / 2025 samples even at the full cap, so its gains are lower bounds. "The shift had nothing to give" is excluded, twice.
3. Every run ended in the same place — the termination sink. The student stops emitting a stop token: rollout length runs away to the training cap, the length-clip ratio goes to ~1.0, entropy collapses, and the rollouts become an answer followed by the same answer forever. Onsets: run 1 step 61; B step 12; C step 12; D step 17; B-short step 10 (rollout length; the clip rule cannot fire in a 10-step run); B-lowlr step 48; RAFT —. Changing the teacher pair, pinning the KL brake at its maximum, swapping in a thinking student and cutting the learning rate 5× each moved when it happened. None of them prevented it. At evaluation time the sink is worse than in training, because the cap is ten times larger: run 1's ckpt-100 truncates on 92.1 % of AIME 2024 samples; B-lowlr's ckpt-100 truncates on 99.6 % of AIME 2024 samples. That is what the large MATH-500 regressions measure — run 1 ckpt-100 -8.00 pp at 96 % truncation; B-lowlr ckpt-100 -28.75 pp at 100 % truncation — an answer that never stops being written scores zero, whatever the model knows. Read them as termination artifacts, not as capability being destroyed: the checkpoints that still terminate are null, not negative (bullet 4).
4. What transferred was style — and nothing else. Under the OpenThinker pair the student's surface form moves fast and towards the post-teacher before turning away again: \boxed{} share on AIME 2024 37.5 % (initial) → 56.4 % (B-short ckpt-4) → 19.9 % (ckpt-8), and 57.5 % → 17.3 % at B-lowlr's ckpt-20 → ckpt-40 — the same path at five times the step count. Output length only ever grows: 1,517 → 1,635 → 2,014 → 16,569 tokens on AIME 2024. Accuracy does not move at all: the cleanest pre-collapse policies in the study are null on all three benchmarks, and run 1's pair pushed \boxed{} to 0 % — away from its own post-teacher. The register travels; the capability does not.
5. Why: the reward's mean sign on the student is negative, and the only place it reaches zero is non-termination. Direct-OPD scores the student's own tokens with log π_post − log π_pre. At step 1, before any update, that number was negative in every run (run 1 -0.0078; B -0.0354; C -0.0354; D -0.0143; B-short -0.0354; B-lowlr -0.0354; RAFT -0.0048), and it stayed negative on essentially every step. The objective's only instruction was stop writing like yourself; it never pointed at a better answer. A log-ratio of 0 means the two teachers agree — and the cheapest agreement a language model can reach is degenerate repetition. In every collapsed run the mean reward climbs towards zero, not towards positive, exactly as the rollouts pin at the cap. §14 has the measurements.
6. Four tempting explanations are now excluded by experiment, not by argument. The adaptive KL controller loosened the leash — condition C pinned it at its maximum 2.5 for every step and collapsed at step 12 exactly like B (step 12); H3 refuted. A non-thinking student cannot hold a thinking teacher's policy — condition D (Qwen3-4B, thinking on) collapsed at step 17, and the shift's reward on its native outputs was negative at step 1 too, which is H4's own premise; H4 refuted. The learning rate is too high — B-lowlr at 2e-7 delayed the onset to step 48 and then collapsed anyway; H5's no-collapse clause refuted. Grad-norm spikes launch the policy into the sink — D collapsed with no spike (peak 4.4) and B-lowlr absorbed the largest spike in the study (49.8 at step 21) without collapsing for another 27 steps. Spikes are a symptom, not the cause.
7. We then measured the mechanism, and built the pair it predicts. exp3 scored the same 2,960 frozen student rollouts (2,067,933 token positions) under five teacher pairs, changing nothing but which pair you subtract (§17). The corpus pairs reward 23 %/34 % of the student's own tokens and price the stop token at -4/-90; OpenThinker3 alone puts log p(<|im_end|>) at −90.3 — it has unlearned how to stop. So we built the pair the mechanism predicts should be safe: a rejection-sampling SFT of the same π_pre on 4,187 of its own verified samples (§18). That pair rewards 84.7 % of the student's tokens, is neutral at the stop token, and carries a real held-out gain of its own +11.200 [+8.900, +13.550] p<0.0001 on MATH-500. Run through the identical channel that broke condition B at step 12, it never collapsed (peak clip ratio 0.0078 over 100 steps) — the first SFT pair in the campaign that did not — and it still transferred nothing (-1.650 [-3.450, +0.100] p=0.0642 on MATH-500). On-supportness governs stability; shift magnitude governs transfer — and this shift was tiny (0.099 |Δ log p| per token against the corpus pairs' ≈ 2.7), so small that the pilot's own gain-per-shift predicts under 1 pp, below what a ±1.8 pp CI can resolve. The null is quantitatively consistent with the mechanism rather than evidence against it (§18.5).
8. Cost, and what a next attempt would need. $332.36 of the $500 cap over 83 ledger rows (run 1 $92.87; the exp2b extension $192.02; exp3 $47.47). $46.46 of that went to jobs that were cancelled — but cancelled is not the same as wasted: $42.44 of it is conditions B, C and D, stopped once their result was in, and their 22–25 recorded steps are exactly what refutes H3 and H4 (two of this campaign's main findings). Only the $4.02 of cancelled evaluation jobs — an under-timed attempt that was relaunched, plus one mis-shaped job killed on the spot — bought nothing. §16 lists what would have to change — a shift whose mean is positive on the student by construction, a termination-aware reward, a KL anchored to the student's own init, early stopping on the clip ratio, and a shift-magnitude gate before any GPU is booked. The cheapest lesson is the smallest: B and C died with no evaluable checkpoint because save_freq was 20 and their onset was step 12; B-short bought five saved policies for $5.54.

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1. Question & hypothesis

The pilot (cmpatino/direct-opd-sft-vs-rl-pilot-results) established that Direct-OPD is a faithful courier: its SFT arm transferred a shift that encoded narrowing — the 100-step SFT teacher gained in-distribution and regressed on held-out AIME, and the student inherited exactly that profile. That left the interesting question unanswered, because the shift had no held-out capability to donate.

This experiment asks: when the SFT shift does encode real, held-out capability, does Direct-OPD transfer that capability — and does it do so into a larger student?

H1 (pre-registered). A Qwen/Qwen2.5-7B-Instruct student trained for 100 Direct-OPD steps on the shift log π_post − log π_pre, with π_pre = Qwen/Qwen2.5-Math-1.5B and π_post = deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B (a pure-SFT checkpoint, 800K R1 traces), improves on held-out math benchmarks — paired per-problem bootstrap, CI excluding 0 — on AIME 2024 and MATH-500 (co-primary), with AIME 2025 as replication.

No RL comparator. No SFT training of our own. The student is 4.7× the teachers' parameter count, which is the second half of the question: the published method and the pilot both used students at or below teacher scale.

Pre-registered endpoints: student_gain_aime24, student_gain_math500 (primary), student_gain_aime25 (replication), the teacher gains, and the guarded transfer ratio.

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2. Pre-registration & deviations

The pre-registration is PREREGISTRATION.md in the workspace (listed in MANIFEST.json with its sha256). Every decision, resolution and deviation below is reproduced verbatim from supervisor/decisions_and_deviations.md, in log order, with nothing summarised away.

2.1 The three changes that a reader must know before reading any number

1. P0 amendment — OPD lengths 512/3584 → 768/3328 (sum unchanged at 4,096 = π_pre's trained context). Made before any run, because the prompt-length audit found 5 of 6,400 opd_train prompts above 512 student-template tokens (max 720); the 512 split would have let verl's overlong filter silently drop them and break the 64 × 100 one-pass contract.
2. P0 amendment — π_pre eval cap 3,584 → 3,200 tokens on all three benchmarks. Qwen2.5-Math-1.5B has max_position_embeddings = 4096; the longest prompt under its own template is 871 tokens (MATH-500), so 3,584 would have tripped the harness context gate. π_pre's truncation rate is therefore not comparable with the other models' and is quoted wherever its accuracy is (§8 also gives a post-hoc sensitivity view).
3. Cost-forced DEVIATION — the ckpt-100 primary endpoint is measured under a REDUCED protocol. After training, probes showed every checkpoint from 60 on is essentially non-terminating at the 31,744-token eval cap (87.5–100 % truncation), which re-priced the full protocol at $177 central / $208 high — more than the remaining budget. The supervisor therefore measured: (i) AIME 2024 and AIME 2025 at 8 samples/problem (seeds 0–7), paired against student_init restricted to the same seeds; (ii) MATH-500 on a 100-problem evenly-spread subset with the full pass set, paired against student_init on the same 100 unique_ids, stored under a distinct alias (opd_student_r1shift_m500sub100) so it can never masquerade as a canonical 500-problem unit. Same estimand, wider CIs. The full-protocol measurement remains available if the cap is extended.

A label to read past: the harness says "SMOKE ONLY" on the MATH-500 subset unit

evals/opd_student_r1shift_m500sub100/math500/scores.json carries this deviation string, written automatically by eval_model.py:

limit_problems=100 (evenly spaced) (SMOKE ONLY — not a canonical result)

That wording is the harness's generic label for any --limit-problems run, and it is wrong here. eval_model.py emits "SMOKE ONLY — not a canonical result" on every problem-limited job because the flag's normal use is a cheap pre-flight probe; the harness has no way to tell a probe from a deliberately reduced measurement. This unit is not a smoke: it is the supervisor-approved, loudly-logged reduced protocol of §2.1(3) — the full pass set (greedy + sample4, seeds 0–3) run over a 100-problem evenly-spread subset, pushed under a distinct alias precisely so it can never be mistaken for a canonical 500-problem unit, and paired against student_init restricted to the same 100 unique_ids. The label is left unedited (the harness's output is evidence, not prose) and explained here instead. What the label does correctly convey: this unit must never be compared with a 500-problem MATH-500 number.

2.2 Units deliberately not run

unit	why
opd_student_r1shift-ckpt60 × math500	cost-forced skip: re-priced $115 high, over the $8/checkpoint gate
opd_student_r1shift-ckpt80 × math500	cost-forced skip: re-priced $124 high, over the $8/checkpoint gate
opd_student_r1shift × math500	superseded by the 100-problem subset unit: full 500-problem protocol re-priced $100/$118 high

2.3 The decisions log, verbatim

• DECISION (user) — teacher size cap relaxed 1.2B → 1.5B to admit the R1-distill pure-SFT pair; student = Qwen/Qwen2.5-7B-Instruct; Qwen arm only (OLMo-2-1B instruction-following arm deferred); MAX_BUDGET_USD = 200 (extendable later on request); new trackio logbook for this experiment; supervisor orchestrates Opus/Sonnet subagents.
• RESOLUTION — π_pre context: Qwen2.5-Math-1.5B has max_position_embeddings 4096 ⇒ (a) eval cap 3,584 tokens at its native limit, truncation always reported; (b) OPD sequences capped at 512 + 3,584 = 4,096 so the reward's log-ratio never leaves the pre-teacher's trained positions. Response cap still 1.75× the pilot's.
• RESOLUTION — standalone shift-diagnostics phase dropped; the 2-step smoke's verl delta_opd/* metrics serve as the reward-sanity gate.
• RESOLUTION — MATH-500 protocol: 4 samples T 0.7/0.95 (primary sample4) + greedy secondary, DAPO prompt, same grader; co-primary with AIME24 (500 problems ⇒ ~4× tighter CIs than 30-problem AIME).
• VERIFIED — Hub facts: repos exist at the pinned SHAs; results + student repos created private=True (API-verified); OLMo-2-1B/1B-SFT/7B tokenizer.json byte-identical (sha 73fd5254…) — recorded for the deferred arm.
• OPERATIONAL — the /data bucket drops empty directories; keep a file in every folder.
• OPERATIONAL (incident, contained) — trackio logbook discovery walks PARENT directories for .trackio (like git). The first logbook open from exp2/ attached to the PILOT logbook and rewrote its metadata.json:space_id; caught and restored within the same agent run (verified by supervisor: pilot space_id back to cmpatino/direct-opd-pilot-logbook, no other pilot file modified). New logbook bootstrapped locally with discovery disabled; all later tk.sh calls resolve to exp2/.trackio first. Rule: always run bash exp2-sft-transfer/tk.sh (never a bare trackio) and check exp2-sft-transfer/.trackio/metadata.json before publishing. Logbook published PRIVATE at cmpatino/direct-opd-sft-transfer-logbook (API-verified).
• VERIFIED — P0 tokenizer gate PASS (artifacts/tokenizer_compat_report.md): exhaustive ordinary-ID check over [0,151664] — pre_teacher vs student 0 mismatches anywhere; post_teacher differs from both only in [151643,151649] (DeepSeek control tokens); base BPE model section sha256 identical across the trio; 500-string round-trip identical. Student config vocab_size 152064 is embedding padding only (len(tokenizer)=151665 for all three). The pilot's Qwen3-only IDs 151665–151668 do not exist in this trio.
• RESOLUTION (P0-informed amendment, before any run) — OPD lengths 512/3584 → 768/3328 (sum unchanged at 4096 = π_pre context). Reason: prompt audit found 5/6400 opd_train prompts > 512 student-template tokens (max 720; indices 1707, 2065, 2507, 6350, 6385), 0 > 768 — supervisor re-tokenized independently and confirmed. Alternatives rejected: dropping rows (6395 < 64×100 breaks the one-pass contract and the driver's row gate); accepting verl's silent overlong filter (changes the training set unlogged).
• RESOLUTION (P0-informed amendment) — π_pre eval cap 3584 → 3200 on all benchmarks: max prompt under its template is 871 (math500), 848 (aime25), 473 (aime24); 871 + 3200 ≤ 4096 passes the harness context gate. Single cap across benchmarks for uniformity; truncation rate reported; post-hoc "≤3200-token completions" restricted view of π_post's stored generations as a sensitivity check.
• NOTE — conflicting format instructions for π_pre: Qwen2.5-Math's chat template injects the system prompt "Please reason step by step, and put your final answer within \boxed{}." while the DAPO prompt asks for an "Answer:" line. The shared grader already falls back Answer-line → \boxed; the format split is a reported diagnostic. Identical situation for π_post (DeepSeek template force-opens ), as in the pilot.
• OPERATIONAL — concurrent builders in exp2/code/: the P0 agent's gates.py was wiped once by a sibling's copy step and recreated. Rule: builders own disjoint subfolders (code/phase0, code/eval, code/opd) and never delete outside their own.
• VERIFIED — driver staged + cpu-basic probe PASS (job 6a8d730cdc4d6ae814e849d4, 9 s running, $0.00): results repo revision a6e5e9924cce0089d0853d557464e1a3a8a51ff3 holds opd/run_opd.sh + opd/phase4_seed.patch (sha256 local==remote); entrypoint override works on vllm/vllm-openai:v0.11.0; python 3.12.11, torch 2.8.0+cu128, vllm 0.11.0, flashinfer 0.3.1, flash_attn missing (expected). Gap: PROBE mode exits before the have timeout check — coreutils timeout is expected in the Ubuntu-based image; the smoke log settles it (driver WARNs and falls back to the external babysitter if absent).
• RESOLUTION — sequencing: the a100x4 smoke (≤ $7.50, in-container 45-min ceiling) runs in parallel with P2 baseline evals rather than strictly after them; it does not depend on the harness and the teacher-gain gate protects the $60 FULL run, not the smoke.
• OPERATIONAL — babysitter ceilings relaxed (2026-08-25 11:2x): the P2 agent set wall ceilings at 2× central for jobs whose central estimate is ~16–18 min (pre-all 37 m, student-a24/a25 33 m) — the pilot's 0.7 %-margin cancel taught us probes miss tails and downloads/engine init are not in the estimate. Supervisor restarted those three babysitters at 90 min (platform timeouts 2–3 h are the real worst case; committed spend unchanged). post-m500 (222 m) and student-m500 (176 m) kept.
• GATE — teacher gain (P2) PASS: paired π_post − π_pre (aggregate_evals.py from Hub units, 10k resamples): AIME24 +24.38 pp (p≈0; 100 % of resamples > 0; marginals 4.69 [1.46, 9.06] vs 29.06 [18.33, 40.73]); AIME25 +21.15 pp (2.40 vs 23.54). π_pre at its 3200 native cap truncates 26.6 % / 23.4 % (AIME24/25) and 18.2 % (math500 sample4 = 28.70 [26.45, 30.95]; greedy 41.2 %) — reported as protocol requires. The experiment's premise (a pure-SFT shift with a large held-out gain) holds.
• GATE — smoke (P3) PASS (job 6a8d740f, $1.07): 2/2 steps, 73.5 s/step mean (81.6 → 65.4), response mean 339 → 398, clip 0.00; delta_opd rewards finite and stable (log_ratio_mean +1.79 / +2.54, pos_frac 0.70 / 0.75, weighted_reward_mean ≈ −0.008), adaptive KL 2.5 → 2.475; wall guard active (timeout present); prompt gate max 720 / headroom 48; vocab-padding WARN as designed. Peak allocated 77.6 GB at step 2 (65.3 at step 1) — too close to 80 GB for 100 steps.
• OPERATIONAL (pre-registered ladder, not a deviation) — full-run memory knobs: ACTOR_OPTIMIZER_OFFLOAD=True (−15 GB), REF_LOG_PROB_MAX_TOKEN_LEN_PER_GPU=8192 and ROLLOUT_LOG_PROB_MAX_TOKEN_LEN_PER_GPU=8192 (were 16384; halves the transient fp32 logits in the log-prob phases). Same math in smaller micro-batches / CPU Adam; no pinned scientific parameter touched. Expected cost: +5–15 s/step.
• DECISION (supervisor, within the user's $200 cap) — FULL RUN GO (2026-08-25): a100x4, 100 steps, in-container ceiling 6 h ($60 worst case), external babysitter 400 min / 20 min silence; step-20 re-projection required (timing_s/step, response_length/mean, clip_ratio, max_memory_allocated). Ledger $2.47 + wave-1 commitments ≤ $35 + $60 = ≤ $97.5.
• CHECKPOINT — full run step-20 re-projection (supervisor, from the raw log): mean 65.8 s/step over steps 1–20 (range 55–89; gen ≈ 20 / reward ≈ 15 / update ≈ 17 s) → 100 steps ≈ 1.8 h ≈ $18 GPU (≈ $21 with setup + merge) — fits the 19,738 s training budget with >3× margin. response_length/mean 339 → ~400 (steps 11–20 avg ≈ 420), clip_ratio 0.00 at every step; running max_memory_allocated plateaued at 81.3 (verl decimal GB ≈ 75.7 GiB / 80 GiB) since step 3 — tight but stable; weighted_reward_mean −0.0078 → −0.0041, log_ratio_pos_frac 0.70 → 0.58, adaptive KL coef 2.475 → 2.045, grad_norm 4.24 → 1.53. No anomalies; run continues.
• VERIFIED — P2 COMPLETE (9 units on the Hub, alignment audit ok; wave-1 actual $6.57 vs $10.43 central; P2 total $7.32; ledger $8.39). Baselines (primary pass): student_init AIME24 12.19 [3.96, 22.50] (trunc 1.6 %, 1517 tok), AIME25 6.98 [2.40, 12.50], MATH-500 sample4 74.35 [71.15, 77.55] (564 tok, 0.1 % trunc); post_teacher MATH-500 sample4 75.20 [72.20, 78.15] (3822 tok). Teacher gains (paired): AIME24 +24.38 [15.42, 34.17]; AIME25 +21.15 [10.21, 33.33]; MATH-500 +46.50 [43.20, 49.85]. Note for the report: the student already equals π_post on MATH-500 and exceeds both teachers on AIME — the teacher pair supplies a shift signal, not a better policy (same framing caveat as the pilot). Estimation lesson re-confirmed: 8-problem probes missed tails in both directions (student AIME +34–54 % over central; MATH-500 −71 %).
• EVENT — full run: termination collapse at steps 58–62 (job 6a8d7e7a). response_length/mean 527 (step 55) → 1181 (60) → 3001 (62) → pinned at the 3,328 cap from step 63 (clip_ratio 0.94–1.00); actor entropy 0.36 → 0.06; weighted_reward_mean −0.0029 → −0.0003; pg_loss → ~0; grad_norm 1.4 → 0.2; adaptive KL coef had ratcheted 2.5 → 1.37 by step 60 (negative-reward regime). Sampled rollouts: R1-style reasoning voice ("Okay, I need to solve…") followed by an endless Answer: <x> repetition loop. Reading: the shift reward was negative on the student's native style throughout; the policy escaped to a degenerate region where π_post and π_pre agree (log-ratio ≈ 0). s/step 65 → 267 (4×). Run continues (bounded by the 6 h in-container ceiling; projected step 100 ≈ 15:55 UTC, ≈ $47). Checkpoints 20/40/60/80 saved. Plan adjustment (within pre-registration): ckpt-100 remains the primary endpoint and will be measured; the P6 checkpoint curve is promoted from optional to required (pre-collapse ckpt-20/40/60 on AIME24 + MATH-500), budget permitting; P5 launches are probe-first because a non-terminating ckpt-100 would run every sample to the 31,744 cap.
• VERIFIED — PHASE 4 COMPLETE (job 6a8d7e7a, COMPLETED, 15,994 s, $44.43; ledger $52.82): 100/100 steps, 5 merged bf16 checkpoints verified on the Hub (cmpatino/Qwen2.5-7B-Instruct-DirectOPD-R1DistillShift-100 @ 5819e26cab1f099a9b9b9caa38c6340db50b8c67; root = step 100; logs/ bundle incl. metrics.jsonl 100 records, 147/148 numeric keys). Run means: 146.8 s/step, response_length 1545, clip 0.37, weighted_reward −0.0024, KL coef 2.475 → 1.118. Late partial recovery (steps 85–100): entropy 0.16 → 0.67, clip 0.98 → 0.70, response mean 3292 → 2614, weighted reward → +0.0026, grad_norm → 2.1. Wall guard never fired. Sanity generation coherent (R1-style register).
• DECISION (supervisor) — P5/P6 plan: probe ckpt-100/80/60 first (non-termination hazard at the 31,744 cap); ckpt-100 × {aime24, aime25, math500} primary; curve promoted to required: ckpt-20/40/60/80 × aime24 (8 samples, pre-registered curve protocol) and ckpt-20/40 × math500 full protocol (ckpt-60/80 × math500 only if cheap). Ceilings: per-job high ≤ $25, cumulative high ≤ $70, ledger gate before each launch.
• P5 probes (ckpt-100/80/60, $3.54): all three checkpoints are essentially NON-TERMINATING at the 31,744 eval cap (truncation 94–100 % on math500 and aime24, T=0.7 and greedy) — the step-100 training-time partial recovery (clip 0.70 at the 3,328 training cap) does not carry over to full-cap sampling. Full-protocol cost for ckpt-100 re-priced at $38 / $38 / $100 central (aime24 / aime25 / math500) = $177 central, $208 high — exceeds the $70 P5/P6 ceiling and most of the remaining $144.
• DEVIATION (cost-forced, supervisor; logged loudly) — ckpt-100 primary endpoint measured under a REDUCED protocol: (i) AIME24 and AIME25 at 8 samples/problem (seeds 0–7; = the pre-registered checkpoint-curve protocol), paired against student_init restricted to the same seeds 0–7 of its 32-sample unit; (ii) MATH-500 on a 100-problem evenly-spread subset with the full pass set (greedy + sample4), paired against student_init on the same 100 unique_ids; stored under a distinct alias so it can never masquerade as a canonical 500-problem unit. Expected cost ≈ $46 high. Rationale: same estimand (paired per-problem gain vs student_init), wider CIs; the full-protocol measurement ($177–208) remains available if the user extends the cap — decision surfaced to the user in the report. ckpt-60/80 × MATH-500 skipped (pre-authorized $8 gate; re-priced $115 / $124 high). Curve jobs C2a (ckpt-20/40 × aime24), C2b (ckpt-60/80 × aime24, $23.5 high), C3a (ckpt-20/40 × math500 full protocol) proceed as planned.
• ERRATUM (supervisor) — the "P2 COMPLETE" entry above says the student "exceeds both teachers on AIME": wrong. student_init sits BETWEEN the teachers on AIME (12.19 vs π_pre 4.69 / π_post 29.06 on AIME24; 6.98 vs 2.40 / 23.54 on AIME25) and equals π_post on MATH-500 (74.35 vs 75.20). The logbook cell was corrected the same day; the report states the corrected version.
• NOTE (from the report build) — sensitivity view: holding π_post to π_pre's 3,200-token budget (over-cap samples counted wrong) shrinks the AIME24 teacher gain to +3.65 pp [−1.04, +9.17] (p=0.14) and AIME25 to +6.35 [+0.63, +13.33]; MATH-500 survives at +31.55. The pre-registered gate (native protocols) passed as recorded, but a large share of the AIME premise is π_post's 10× longer reasoning. Goes into TL;DR and Limitations. Also: the OPD student extinguishes \boxed{} (AIME24 37.5 % → 0.8 % by ckpt-20) and goes 96–99 % to the DAPO "Answer:" line — away from both teachers' AIME preference. Collapse onset by metric: first clip_ratio > 0.5 at step 61; band 58–85.
• VERIFIED — P5/P6 COMPLETE (9 jobs, $40.05, all COMPLETED; ledger $92.87). ckpt-100 non-terminating at full-cap eval (AIME24 92.1 % truncated, mean 29,343 tok; AIME25 93.8 %; MATH-500-sub100 greedy 100 % / sample4 96.5 %). Primary (reduced protocol): AIME24 8.75 % vs student_init 12.19 → −3.44 pp [−8.44, +0.52] p=0.089; AIME25 7.92 vs 6.98 → +0.94 [−3.33, +5.73] p=0.68; MATH-500 paired on the 100 subset ids: 69.75 vs 77.75 → −8.00 pp [−13.25, −3.00]. Curve AIME24 (8 samples): ckpt20 −0.52 [−3.65, +2.29]; ckpt40 −1.35 [−4.48, +1.46]; ckpt60 −5.10 [−9.69, −1.35]; ckpt80 −5.94 [−11.04, −1.77]. MATH-500 curve: ckpt20 −2.25 [−4.00, −0.55]; ckpt40 −1.80 [−3.55, 0.00]. Transfer ratios withheld by the pre-registered guard (student gains not positive). Verdict: H1 NOT supported — style transferred, capability did not; new failure mode = termination collapse under a negative mean shift reward.
• DECISION (user) — cap raised to $500 cumulative; tiers A1, A2, B, C, D approved. Supervisor priority order A1 → B → C → D → A2 with a stop-and-ask rule before exceeding $500 (high-side sum of all five ≈ $613 new; actuals have run ~40 % under). ledger.py CAP = 500.
• VERIFIED — P0 gate, OpenThinker trio PASS (artifacts/openthinker_tokenizer_compat_report.md, openthinker_prompt_length_audit.md): see PREREGISTRATION.md §E2. Container restart wiped local envs again (tokgate rebuilt; expect eval-test/opdval to need rebuilding).
• RESOLUTION — B keeps run-1's 768/3328 lengths although both new teachers allow 32k, so that B differs from run 1 in the pair only. D (thinking student) uses 768/4096.
• RESOLUTION — new pre-registration guard for the transfer ratio: numerator CI must exclude 0 (gap found in run 1's AIME25 cell).
• VERIFIED — P0 gate, Qwen3-4B trio PASS (artifacts/qwen3_4b_*.md): ordinary IDs [0,151642] identical across Qwen2.5-1.5B-Instruct / OpenThinker3-1.5B / Qwen3-4B; opd_train max prompt 699 under the Qwen3 template (cap 768); Qwen3-only IDs 151665–151668 (=151667, =151668) absent in both teachers — appear only in generated output (pilot property, ~0.09 % of states, unscoreable by the teachers); Qwen3-4B max_position_embeddings 40960 vs teachers 32768 (irrelevant at 768+4096 training / 31,744 eval + ≤ 872 prompt). NOTE for D's interpretation: the Qwen3 template injects NO default system prompt, whereas both Qwen2.5 teachers' templates inject "You are Qwen, created by Alibaba Cloud…" — the teachers score the student's rendering verbatim, so the teacher pair sees a system-prompt-less frame for D (and a system-prompt frame for B/C). Recorded as a condition-level difference, not fixed.
• VERIFIED — exp2b driver build (code/opd/run_opd.sh 1,645 lines; run_opd_exp2b.diff +336/−8; VALIDATION_exp2b.md; 75 validation files): conditions openthinker / openthinker_klfloor / openthinker_qwen3_4b compose as pre-registered (supervisor DRYRUN: B adaptive [0.5, 2.5]; C CONSTANT [2.5, 2.5] — verl kl_controller clamps max(min, min(max, x)) so min == max holds 2.5 every step; D Qwen3-4B 768/4096, max_model_len 4864); run-1 memory knobs now explicit condition defaults; new fail-fast checks (log-prob budgets, teacher fwd cap ≥ max seq, KL min ≤ max); collapse-watch line (reproduces run 1: first clip > 0.5 at step 61; longest > 0.9 run 27 steps, 63–89). Regression: pilot arms + r1distill unchanged except two explicitly printed defaults (16384, the script's own). The bucket silently dropped 4 of 7 in-place rewrites during the build — file re-verified by sha256 and DRYRUN after the final copy.
• DECISION (supervisor) — launch plan exp2b training: stage driver → three a100x4 smokes in parallel ($7.50 worst each) → per condition, an automatic GO to the full run if the pre-registered smoke gate passes (2/2 steps, finite delta_opd, no FATAL, s/step ≤ 2× projection); full runs in parallel ($60 worst each; gate OK: $92.87 + $180 ≪ $500). D's step-1 weighted_reward_mean sign is recorded (H4 premise) but does not block.
• VERIFIED — exp2b harness build (code/eval, +510/−16 eval_model.py; aggregate_evals +137/−37; 249 self-test checks, 163 pytest, supervisor re-ran self-test PASS): registry pre_teacher_ot, post_teacher_ot, student_init_qwen3_4b, three OPD conditions with curves; context gate passes at 31,744 for both teachers (872 + 31,744 ≤ 32,768) — no cap deviation; report pipeline gains §13 (exp2b) with run 1 intact.
• RESOLUTION — the new fifth ratio guard (student-gain CI must exclude 0) is applied uniformly, including to run 1: its AIME25 ratio 0.079 is now withheld (value retained and displayed as "withheld only by the new guard"). This is the gap run 1's own report asked to close; documented, revertible (APPLY_NUMERATOR_CI_GUARD_TO_RUN1).
• NOTE — budget conflict surfaced by the estimator: condition D's Qwen3-4B thinking-mode evaluations are expensive (baseline ×3 ≈ $104 central; ckpt-100 ×3 ≈ $104 if terminating; curve ≈ $90). D as specified + A2 ($180) cannot both fit under $500 alongside B/C. Decision goes to the user; A1 and the OT-pair teacher baselines proceed meanwhile (unambiguous, ≈ $17 central).
• DECISION (user, 2026-08-26) — D trimmed to AIME24 + MATH-500 (baseline + ckpt-100, full protocol, no curve, no AIME25); A2 dropped. Pre-registration §E4.
• VERIFIED — exp2b smokes PASS ×3, full runs launched (driver re-staged @ results-repo revision 2fabdb13, sha256 match). Smoke step-1 metrics: openthinker s/step 88.6, resp 339, clip 0, weighted_reward −0.0354, log_ratio_mean −0.15 (|Δ| far smaller than run 1's +1.79 — the Instruct-lineage pair nearly agrees on the student's native outputs, leaning π_pre), pos_frac 0.51, KL 2.475; openthinker_klfloor identical except kl_coef = 2.500 at both steps (constant, as designed); openthinker_qwen3_4b s/step 174.6, resp 1,707 (thinking; clip 0.05), weighted_reward −0.0143 (H4's premise ">0" FAILS at step 1 — run 1's signature; unweighted log_ratio_mean +0.20/+0.33 is positive, i.e. π_post prefers the thinking student's tokens on average but π_pre wins on the high-probability tokens), KL 2.475, content present. Collapse watch: none tripped. Pre-registered smoke gate (finite rewards, no FATAL, s/step within 2×) passed for all three → full runs 6a918a33 (B), 6a918a35 (C), 6a918a37 (D), babysat 400 min / 20 min. Ledger $96.48.
• EVENT — exp2b B and C collapsed at steps 10–13 (identical trajectories: resp 440 → 882 → 2,169 → 3,059 → 3,328 at steps 9–13; clip 1.00 by 15; entropy 0.13 → 0.03; grad-norm spikes 26.5 @ step 5 and 21 @ step 10 precede it; weighted reward −0.029 → −0.003; log_ratio_mean −0.15 → −0.5). C held kl_coef = 2.500 every step and collapsed byte-for-byte like B → H3 REFUTED: the adaptive KL controller is not the cause; the termination sink is reached under the maximum KL brake. Onset ~4× earlier than run 1 (step 61) despite a ~10× gentler shift signal. First checkpoint (step 20) is post-collapse, so B/C hold no pre-collapse policy. D at step 9: resp 1,707 → 2,214 (cap 4,096, clip 0.08), weighted reward −0.014 → −0.006, entropy stable 0.30, unweighted log-ratio still positive — pre-collapse pattern possible; undecided. Decision on cancelling B/C put to the user with a redirect proposal (10-step B with save every 2 steps; B at lr 2e-7).
• VERIFIED — A1 landed (run-1 ckpt-40 at the FULL protocol, all deviations []): AIME24 10.00 % (960 samples, trunc 1.6 %), AIME25 7.81 %, MATH-500 sample4 73.45 % (2,000 samples) vs student_init 12.19 / 6.98 / 74.35 — pre-collapse checkpoint flat-to-negative at full power (paired CIs from the aggregator to follow).
• DECISION (user, 2026-08-28) — B and C CANCELED at step ~24 (both collapsed at steps 10–13; C's constant KL made no difference → H3 refuted; no pre-collapse checkpoint saved). Redirect ≈ $70: B-short (10 steps, save every 2 — pre-collapse checkpoints for evaluation) and B-lowlr (OPTIM_LR 2e-7, a logged deviation from the pinned 1e-6; H5). Pre-registration §E5. D continues.
• EVENT + DECISION (user, 2026-08-28) — D collapsed and was CANCELED at step ~24. Qwen3-4B thinking student: resp 1,707 → 4,082 (cap 4,096) by step 20; clip 0.02–0.21 through step 16, then 0.65 / 0.92 / 0.96 / 0.98 (steps 17–20); weighted reward negative steps 1–18, turning positive (+0.0002, +0.0026) exactly as it saturated — the sink is where the teachers agree. H4 refuted. No pre-collapse checkpoint (first save at 20). Wall-clock cost booked. D-short declined by the user (thinking-mode evals ≈ $65/unit). All four Direct-OPD runs with SFT teacher pairs have now ended in the termination sink (run 1 step 61; B/C step 10–12; D step 17).
• BLOCKER (caught by DRYRUN before spend) — B-short: run_opd.sh hard-codes the checkpoint list 20 40 60 80 100 at the post-training verification (line 995) and the merge/upload loops (1247, 1259; terminal step literal "100"), so a 10-step / save-every-2 run would train and then die at verification. Fix in progress: derive the list from SAVE_FREQ..TOTAL_TRAINING_STEPS; re-stage; regression DRYRUN must leave the 100/20 case identical. B-lowlr (100/20) unaffected — launched: job 6a919e1c (OPTIM_LR 2e-7 confirmed; step-1 metrics byte-identical to B's, as expected before any update; steps 3–4 clip 0, grad-norm 2.7–3.2, no spikes).
• VERIFIED — driver checkpoint-list fix + B-short COMPLETE (2026-08-28): run_opd.sh now derives CKPT_STEPS from SAVE_FREQ..TOTAL_TRAINING_STEPS (regression DRYRUN for 100/20 byte-identical; smoke path unchanged); re-staged @ results-repo b4dfdf37 (sha256 match). B-short job 6a91a23c COMPLETED, $5.54: 10 steps, checkpoints 2/4/6/8/10 merged + verified at cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-10steps @ 8b20748806f63d5b9f05b3239ffdbddc20a62f2a. Trajectory reproduces B/C's: clip 0 through step 8 (resp ≈ 400–440), onset at step 9–10 (resp 474 → 1,521, clip 0.29, entropy 0.11 → 0.05) — deterministic given the seed. So ckpt-8 is the last clean pre-collapse policy; ckpt-10 is the onset.
• DECISION (supervisor, within §E5) — evaluate B-short ckpt-4 and ckpt-8 at the FULL protocol on AIME24, AIME25 (cheap, added as replication) and MATH-500; ckpt-10 probe-first (full protocol if truncation at the 31,744 cap < 20 %, else reduced). Aliases opd_student_otshift-short-ckpt{4,8,10}; baseline student_init.
• GATE — exp2b teacher gain (provisional, marginals; paired CIs when post_teacher_ot × aime25 lands): π_pre Qwen2.5-1.5B-Instruct AIME24 2.19 % (trunc 6.5 %), AIME25 0.42 %, MATH-500 sample4 38.75 %; π_post OpenThinker3-1.5B AIME24 53.96 % (trunc 19.0 % — long CoT; gain is a lower bound), MATH-500 88.80 % (trunc 1.7 %). Gains ≈ +51.8 pp AIME24 / +50.1 pp MATH-500 → PASS by any margin; both at the full protocol, deviations []. Model-card numbers (52.0 / 86.4) reproduced within ~2 pp under our protocol.
• STATUS — B-lowlr step 39: clip 0.000, resp 556 (plateau), entropy 0.15, weighted reward −0.025 (barely moved from −0.035 — the policy is following the gradient slowly, as intended), grad-norm 8; the step-21 spike (49.8) dissipated. ETA ≈ 15:40 UTC.
• EVENT — B-lowlr collapsed at step 46–48 (clip 0.008 @ 40 → 0.094 @ 45 → 0.285 / 0.430 / 0.504 @ 46–48; resp 613 → 2,455; weighted reward −0.023 → −0.006; grad-norm 6–13, NO spike — gradual length runaway, unlike B/C's spike-driven jump). H5's "no collapse" clause refuted: lr 2e-7 delays the sink ~4× (step 48 vs 10–12) but does not prevent it. The step-21 spike (49.8) had dissipated without effect — spikes are neither necessary (D, B-lowlr) nor sufficient (B-lowlr step 21) for the collapse.
• DECISION (supervisor) — B-lowlr runs to completion (pre-registered stop rule; ≈ $35 more, inside the 6 h ceiling). Unlike B/C/D it holds clean pre-collapse checkpoints (steps 20 and 40, resp ≈ 470–613, clip ≤ 0.008) which the driver merges and uploads only after training — cancelling would destroy them. Evaluation plan on completion: ckpt-20 and ckpt-40 at the FULL protocol (terminating → cheap) on AIME24 / AIME25 / MATH-500 vs student_init — 20 and 40 small steps of pre-collapse Direct-OPD, the longest clean training window in the campaign; ckpt-100 probe-first (reduced protocol if non-terminating); ckpt-60/80 × AIME24 8-sample if cheap.
• GATE — exp2b teacher gain PASS (paired, 10k resamples): post_teacher_ot − pre_teacher_ot AIME24 +51.77 pp [+38.65, +64.38] (2.19 → 53.96; π_post trunc 19 % → lower bound), AIME25 +42.60 [+28.54, +56.67] (0.42 → 43.02), MATH-500 sample4 +50.05 [+46.65, +53.40] (38.75 → 88.80); greedy +37.4. Both teachers at the full 31,744 cap, deviations [] — none of run 1's context confound.
• RESULT — B-short ckpt-4 (4 steps, full protocol) vs student_init: AIME24 −0.73 [−2.29, +0.52] p=0.27; AIME25 +0.42 [−1.04, +1.88]; MATH-500 sample4 −0.50 [−2.05, +1.05] (greedy −0.60) — null everywhere. ckpt-8 × AIME25 +0.83 [−0.83, +2.50]. Format: \boxed{} share on AIME24 37.5 % (init) → 56.4 % (ckpt-4), toward π_post's 80.5 % — under this pair the register moves TOWARD the post-teacher (run 1 moved away); accuracy does not move.
• VERIFIED — report pipeline extended for redirects (code/report/build_report.py +1838/−218; aggregate_evals schema exp2b-redirects-1; 165 tests; run 1's §0–11 byte-identical): cancelled B/C/D rendered as training-only conditions with six-condition overlay figures (F8/F9); cross-condition table §13.9; new reported-only diagnostic length_runaway_step (verdicts still use the pre-registered clip > 0.5 rule). NOTE: ledger is behind — A1's three jobs and the OT-teacher full baseline jobs are not yet booked (the eval agent books on completion); reconcile against hf jobs ps -a before publishing.
• VERIFIED — ledger reconciled for P2b/P5b (six rows added by the eval agent; no duplicates): A1 $2.50; OT teacher baselines $15.73 (+ probes). Ledger $163.42. All nine units pass acceptance (pins, rows, passes, deviations [], byte-identical pairing hashes; A1 curve unit untouched). NOTE for limitations: post_teacher_ot's 8-problem probe under-predicted truncation (≈ 6 % → 19–22 % at scale on AIME) — its AIME gains are lower bounds; cost estimates still held. A1 marginal gains vs student_init: AIME24 −2.19, AIME25 +0.83, MATH-500 −0.90 pp (paired CIs in the report).
• RESULT — B-short ckpt-8 (last pre-collapse policy, full protocol): AIME24 11.04 % (trunc 2.8 %, 2,014 tok), AIME25 7.81 %, MATH-500 sample4 75.15 % (870 tok) vs student_init 12.19 / 6.98 / 74.35 — null (paired CIs in the report). ckpt-4: 11.46 / 7.40 / 73.85. Format non-monotonic: AIME24 \boxed share init 37.5 % → ckpt-4 56.4 % → ckpt-8 19.9 % (answer_line 75 %); output length monotonic 1,517 → 1,635 → 2,014 tokens on AIME24 — the length drift that ends in the sink is visible from step 4. Under the OpenThinker pair, eight Direct-OPD steps moved style and length, not held-out accuracy.
• RESULT — B-short complete (P5b $26.79 incl. one $3.94 job the agent cancelled for an under-sized timeout and relaunched): paired gains vs student_init — ckpt-4: AIME24 −0.73 [−2.29, +0.52], AIME25 +0.42 [−1.04, +1.88], MATH-500 −0.50 [−2.05, +1.05]; ckpt-8: −1.15 [−3.23, +0.62], +0.83 [−0.83, +2.50], +0.80 [−0.95, +2.55]; ckpt-10 (reduced: 8-sample AIME; 100-id MATH-500 subset): −1.77 [−4.38, +0.52], +3.02 [−0.62, +7.19], +0.50 [−3.51, +4.75]. All null. ckpt-10 at eval: 44 % / 41 % AIME truncation, 60 % MATH-500 sample4 truncation, mean 15–22k tokens — non-terminating yet accuracy preserved (answers appear before the loop). Format non-monotonic (boxed 37.5 → 56.4 → 19.9 %), length monotonic (1,517 → 1,635 → 2,014 → 16,569 tokens on AIME24 by ckpt-10).
• VERIFIED — B-lowlr COMPLETE (job 6a919e1c, 19,050 s ≈ $53; 100/100 steps; checkpoints 20/40/60/80/100 + logs at cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-lr2e-7-100 @ 6ad3add5b065a25c9c003d31ea59b1e191f7e3a7). Whole-run means: 177.5 s/step, resp 2,024, clip 0.52; collapse-watch first clip > 0.5 at step 48, longest > 0.9 run 47 steps (54–100), stop rule tripped → ckpt-60/80/100 evals under the reduced protocol; ckpt-20 (resp ≈ 470, clip 0) and ckpt-40 (resp 613, clip 0.008) at the FULL protocol.
• RESOLUTION (supervisor, 2026-08-28) — B-lowlr ckpt-100 × MATH-500-sub100 reduced-protocol job approved at a re-priced HIGH of $25.44 (flat 100 %-truncation assumption; the identical-shape B-short unit cost $11.65) — per-job ceiling $26 for this job only; ledger $243.13 / $500.
• RESULT — B-lowlr ckpt-20/40 (full protocol, deviations []): ckpt-20 AIME24 12.08 % / AIME25 6.88 % / MATH-500 73.50 %; ckpt-40 11.46 / 7.40 / 74.65 vs student_init 12.19 / 6.98 / 74.35 — null (paired CIs in the report). Format: ckpt-20 \boxed 57.5 % (≈ B-short ckpt-4's 56.4 %), ckpt-40 answer_line 78 % (≈ ckpt-8's 75 %) — the lr-2e-7 run traverses the same style trajectory as lr 1e-6 at ~5× the step count. Truncation ≤ 3 %.
• VERIFIED — ledger reconciliation vs hf jobs ls -a --label experiment=direct-opd-sft-transfer (59 platform jobs): 0 terminal jobs missing from the ledger; platform running-secs basis $204.02 for terminal jobs + $46.46 booked on the wall-clock basis for the 4 CANCELED runs (B, C, D, and one under-timed eval) = ledger $250.47 exactly (54 rows). Five eval jobs live (B-lowlr ckpt-100 ×3 reduced, ckpt-60/80 curve), ≈ $13 accrued so far.
• VERIFIED — final report draft rebuilt (code/report/build_report.py; BUILD_REPORT_final.md): 43 units found / 5 pending (B-lowlr ckpt-60/80 × aime24; ckpt-100 × 3) / 3 skipped / 33 canceled. New campaign_gain_scan: 27 paired student gains, 0 positive with CI excluding 0, 5 significantly negative (run-1 ckpt-60 −6.67, ckpt-80 −7.50, ckpt-100 MATH-500 −8.00, ckpt-20 MATH-500 −2.25, A1 ckpt-40 AIME24 −2.19); largest gain +3.75 (B-short ckpt-10 AIME25, CI crosses 0). Pipeline fixes: reduced-protocol units discharge roster rows; approved-benchmark rosters per redirect step; cost matcher bug fixed (cancelled spend = $46.46, not $108.27). Convention: 8-sample units are reported PRIMARILY against student_init seeds 0–7 (B-short ckpt-10 → −3.33 / +3.75 / +0.50) with the vs-full-32 pairing (−1.77 / +3.02 / +0.50, as logged above) shown alongside. New README §15 (answer to the question) and §16 (recommendations); §11 full-campaign reproduction; per-step TSVs added to the push list (the only surviving record of B/C/D).
• VERIFIED — B-lowlr evaluations complete (P5b $41.76; ledger $284.89). Paired vs student_init: ckpt-20 AIME24 −0.10 [−2.40, +1.88], AIME25 −0.10 [−1.25, +1.04], MATH-500 sample4 −0.85 [−2.25, +0.55]; ckpt-40 −0.73 [−2.92, +0.83], +0.42 [−1.98, +2.40], +0.30 [−1.35, +1.95] (greedy +1.80 [−1.20, +4.80]); ckpt-60 × AIME24 (8-sample) −4.58 [−10.00, 0.00] p=0.033 (88.8 % truncated); ckpt-80 −2.50 [−6.67, +1.25] (98.8 %); ckpt-100 AIME24 −2.50 [−7.92, +2.50], AIME25 +1.25 [−2.50, +4.58] (99.6–100 % truncated); ckpt-100 × MATH-500-sub100 sample4 −28.75 [−35.00, −22.50] (100 % truncated: with no answer reached before the cap on many problems this is a termination artifact, larger than run 1's −8.0 because ckpt-100 here is more completely non-terminating). H5 not supported. Anomalies: one $0.08 job cancelled for an alias bug before GPU work; one ledger free-text note is garbled (numeric fields correct: 4.634 h, $11.58) — ledger is append-only, noted here. ALL PLANNED EVALUATION IS COMPLETE: 48 planned units → 48 measured or explicitly substituted; 3 pre-registered skips; A2 dropped by user decision.
• DECISION (user) — run the mechanism experiment: shift anatomy on frozen rollouts (five pairs incl. the pilot's RL pair) + a RAFT pair (π_pre's own verified samples) through the full Direct-OPD channel with condition-B config. Pre-registration §F1–F4; cap unchanged $500.
• RESULT — exp3 Part A (shift anatomy) COMPLETE ($2.20; anatomy/ in the results repo; supervisor verified per-model EOS table against stats.json — exact; pair-level prose table uses a benchmark-weighted pooling that differs from stats.json's overall pooling by ≤ 0.07 — report must cite stats.json). Headline per-model mean log p(<|im_end|>) at genuine answer ends: student −0.005 · Qwen2.5-1.5B-Instruct −0.109 · Qwen2.5-Math −18.4 · pilotSFT −21.9 · R1-distill −22.6 · JustRL −29.0 · OpenThinker3 −90.3 (0 of 2,921 positions positive — it has unlearned the stop token). Pre-registered verdicts: P1-terminal PASS (corpus pairs ≪ 0); P1-interior FAIL for R1 (mixed-lineage artifact, flagged); P2 FAIL — corpus pairs' sequence-mean log-ratio IS correctness-informative after length control (AUROC 0.75 vs RL 0.81; pilot's "length artifact" claim does not replicate here); P3 FAIL — the RL pair is also anti-EOS (terminal −5.5, worse than R1's); P4 FAIL — the only positive-mean pair is pilotSFT (+0.013; terminal EOS +0.88), consistent with its being the only pair that transferred anything (in-dist +2.59 in the pilot). P5 (RAFT) pending.
• REFINED MECHANISM (post-anatomy): (1) anti-EOS magnitude ORDERS collapse onset (OT −91 → step 10–13; R1 −2.8/−4.2 → step 61) but is not sufficient — the RL pair is anti-EOS too and did not collapse in the pilot; (2) what separates the working RL pair from the corpus pairs on content tokens is the positive-fraction: RL rewards 53–58 % of the student's own tokens (near-symmetric on-support reweighting) vs 26–33 % for corpus pairs (mostly "stop being yourself"); (3) the corpus shifts DO carry sequence-level correctness signal (AUROC 0.75) that the token-level optimizer never exploits because the anti-EOS/negative-mass gradient dominates. Surviving form of §F1: on-supportness measured as positive-token fraction + EOS neutrality, not mean sign alone. RAFT predictions restated: frac_gt0 ≥ ~0.5, terminal EOS ≈ π_pre's (≈ −0.1…−1), no collapse.
• ADDITION — code/raft/ built: sample_raft.py (Stage 1 rejection sampling, gate G1), train_raft.py (Stage 2 RAFT SFT), compute_g2_gains.py (gate G2), test_raft.py (18 local tests), LAUNCH.md. code/eval/eval_model.py was NOT modified: the RAFT teacher is evaluated as an unregistered --model + --model-alias, which the harness already supports (every MODEL_REGISTRY lookup in run() is guarded by if spec else).
• RESOLUTION — ground truth for the RAFT prompts. sft_train.parquet carries no answer column. The pilot's phase-1 manifest.json records that each row came from zwhe99/DeepMath-103K @ 5cf055d1fe3d7a2eb19719ac020211469736ae44 at global row source_index (shard-filename order then row order) and that qhash = sha256 of the whitespace-normalised source question. Stage 1 re-derives the answers from that source and GATES the join on BOTH invariants for all 6,400 rows. Measured, locally and in-job: 6400/6400 question-text matches and 6400/6400 qhash matches; as a non-gating cross-check, 6400/6400 of the pilot's own assistant_target solutions verify against the recovered answers with the harness grader (512/512 re-measured inside every job). Only question + final_answer are read, over HfFileSystem range requests: 46 s instead of 2.1 GB.
• RESOLUTION — the grader is copied, not re-implemented. sample_raft.py section 2 is a byte-identical copy of eval_model.py lines 626-715, pinned by GRADER_BLOCK_SHA256 = 5c30bf8b0fed53791a6aaf183570b545327311117bc975a19cf9fc1f0acce384, checked at import and re-derived from eval_model.py itself by test_raft.py::test_grader_block_is_byte_identical_to_eval_model.
• RESOLUTION — chunking. sft_train.parquet is sorted by ASCENDING difficulty (verified: the column is monotone, deciles 1.0 -> 8.0). Stage 1's 25 % chunks are therefore ROUND-ROBIN (i % 4), not contiguous, so every partial push is difficulty-stratified and chunk 1 projects the rest honestly. Probes use evenly spaced indices (--limit-spread) for the same reason.
• DECISION (builder, §F2) — RAFT SFT hyper-parameters, fixed before launch. lr 1e-5 inside the pre-registered [5e-6, 2e-5]; cosine decay to 0 with warmup = floor(5 % of steps); 2 epochs (the §F2 maximum); global batch 64 as micro 2 x grad-accum 32; fp32 master weights + autocast(bf16), bf16 checkpoints; seed 42. Rationale on record in train_raft.py:LR_RATIONALE / PRECISION_RATIONALE and in run_manifest.json.builder_decisions: 2x the pilot's 5e-6 because the own-samples are 2.5x shorter than the R1 traces (so a step carries far fewer supervised tokens and G2 needs a detectable MATH-500 gain), 2x under the ceiling because 2e-5 for 2 epochs on a model's own outputs invites the off-support format over-fitting that would defeat the F1 hypothesis; and at lr 1e-5 one AdamW update (1e-5) is 12x SMALLER than a bf16 ULP at |w| ~ 2e-2 (~1.2e-4), so bf16 optimizer state would round most updates away (the pilot measured ~15x less learning that way).
• NOTE — Qwen2.5 needs no completion-style workaround. The pilot's train_sft.py built targets completion-style because the DeepSeek template rewrites assistant content as content.split('</think>')[-1]. train_raft.py records tokenization.naive_render_check, which measures that Qwen2.5's template preserves the assistant content verbatim (the naive apply_chat_template([user, assistant]) render and ours agree, differing only by the template's trailing newline: e.g. 383 vs 382 tokens). The masking is verified rather than asserted: the manifest decodes the masked prefix (must end <|im_start|>assistant\n) and the supervised span (must be the completion + <|im_end|>), and the job aborts if labels != [-100] * n_prompt + input_ids[n_prompt:].
• NOTE — tied embeddings. Qwen2.5-1.5B-Instruct sets tie_word_embeddings: true and its own model.safetensors has no lm_head.weight; the checkpoint writer drops it so the RAFT checkpoints are structurally identical to pi_pre's. config.json, generation_config.json, tokenizer.json and tokenizer_config.json are copied BYTE-IDENTICAL from the pinned pi_pre snapshot (pi_pre's config.json already says torch_dtype: bfloat16, use_cache: true), which is both correct and the strongest guarantee that pi_post and pi_pre share an architecture.
• OPERATIONAL — the local python had to be rebuilt off /data. After the container restart, /home/node/local/envs/eval-test was gone and uv's freshest CPython under /data/home/.local/share/uv/python was incomplete (an EMPTY lib/python3.12/re/ directory) while the intact 3.12.13 install had lost its executable bit — /data is a fuse mount that drops exec bits and is eventually consistent (edits there are also visible only a second or two later). Fixed by copying CPython 3.12.13 to /home/node/local/py312 (overlay fs) and rebuilding eval-test (harness pins) and a new raft-cputest (+ CPU torch 2.8.0) on it. Recorded because the next agent will hit the same thing.
• VERIFIED — GATE G1 PASS. 6,400 prompts x k=4 = 25,600 samples from pi_pre; sample-level accuracy 0.3547 (9,081 correct); 4,187 kept (pass@4 0.654) >> the 2,000 required. Acceptance by seed 2352 / 958 / 557 / 320 (the decay the "first correct in seed order" rule predicts; the four seeds' own accuracies are flat at 0.367 / 0.365 / 0.339 / 0.347, so the decay is selection, not a seed effect). n_correct_of_k histogram 2213 / 1518 / 1078 / 957 / 634. Extractors among kept: 3,478 answer_line + 709 boxed; verify methods 4,111 math_verify + 76 math_verify_cleaned. Rejections: 14,173 wrong_answer, 2,160 no_answer_extracted, 185 truncated_no_answer, 1 truncated_wrong_answer. Truncation over all samples 0.73 %. Kept completions mean 421 / p90 726 / max 1,690 tokens. Job 6a955ac80718b0f6d8908ae3, 30.2 min, 8,000 tok/s, $1.32. Caveat for the report: the keep rate falls monotonically with difficulty (0.894 at bin 3.0 -> 0.55-0.62 at bins 7.5-9.5), so the RAFT training set is easier-skewed relative to sft_train — which is exactly what rejection sampling does, and worth stating rather than hiding.
• VERIFIED — Stage 2 complete, every gate PASS (exit 0). 4,187 kept -> 3,977 train / 210 val; 124 steps (2 x 62), 3.35 M supervised tokens, 16.3 min of training, peak 30.2 GiB, max grad-norm 1.88. Train loss 0.1606 -> 0.0868. Validation 0.16881 -> 0.15517 (25 %) -> 0.15384 (50 %) -> 0.16230 (75 %) -> 0.16166 (100 %): the gate (final < step 0) passes, but the minimum is at 50 % = the end of epoch 1, i.e. the second epoch mildly over-fits. 2 epochs was FIXED BEFORE LAUNCH per section F2, so the root (100 %) is the pre-registered pi_post and no post-hoc checkpoint selection was done; checkpoint-50pct exists in the repo if the supervisor ever wants the lower-val-loss variant, and choosing it would be a new, logged decision. Shift sanity mean |delta logprob|/token 0.0986 (mean +0.0080, p50 0.0013, p90 0.293, max 5.00) over 15,994 tokens. Greedy generations coherent and on-format. Weights moved: global L2 2.60, 42.0 % of elements changed, max |delta| 9.77e-4 — a small, on-support shift. Model cmpatino/Qwen2.5-1.5B-Instruct-DeepMath-RAFT @ d46294c2a827c8558547c8ebac96a49b7a8410bb. Job 6a95624b0718b0f6d8908c05, 20.0 min, $0.87.
• VERIFIED — TEACHER_POST contract satisfied. The repo root carries all five files run_opd.sh:284 fetches (config.json, generation_config.json, model.safetensors, tokenizer.json, tokenizer_config.json) plus vocab.json / merges.txt / README.md; model.safetensors is a single 3,087,467,144-byte file, byte-for-byte the same SIZE as pi_pre's (same tensor set, lm_head.weight omitted under the tie); and all four non-weight files are sha256-identical to pi_pre's. Checkpoints live in checkpoint-{25,50,75,100}pct/, logs in logs/. The driver's root-only fetch is unaffected by them.
• VERIFIED — GATE G2 PASS. Paired raft_teacher - pre_teacher_ot, full protocol, unmodified harness, eval_model.paired_bootstrap_diff (10k resamples, default_rng(42), percentile CI, two-sided bootstrap p), pairing on source_id: **MATH-500 sample4 (PRIMARY) 38.75 -> 49.95, gain +11.20 pp CI95 [+8.75, +13.55], p < 1e-4 — CI excludes 0, G2 PASS**; MATH-500 greedy 45.40 -> 53.80, +8.40 [+4.20, +12.60]; AIME24 sample32 2.19 -> 2.92, +0.73 [-1.04, +2.60] p=0.358; AIME25 sample32 0.42 -> 0.73, +0.31 [-0.62, +1.36] p=0.489 — both near-null, as section F3 pre-registered for this scale. In-distribution sanity (ADDITION, no harness change — the harness's own teacher_eval benchmark is the pilot pool's held-out 512-prompt split, strictly disjoint from sft_train, so it is a better in-distribution probe than a slice of the training prompts would have been): sample4 34.52 -> 52.54, +18.02 pp [+15.14, +20.90]; greedy 37.11 -> 53.32, +16.21 [+11.52, +20.90]. Answer-format extraction success rose 0.918 -> 0.994 on teacher_eval and none-extractor samples fell 187 -> 55 on MATH-500, so part of the gain is format compliance — but conditional-on-complete accuracy also rose (MATH-500 complete-only 39.10 -> 50.94), so it is not only format. Diagnostics: MATH-500 truncation 0.90 % -> 1.95 %, mean output tokens 716 -> 1,101; AIME24 6.5 % -> 11.6 % and 2,991 -> 4,634 (the RAFT model reasons longer on problems far outside its training difficulty), AIME25 4.8 % -> 8.7 %. Jobs 6a9567c40718b0f6d8908c89 ($3.29), 6a9567fd0718b0f6d8908c8f ($0.60), 6a9568100718b0f6d8908c91.
• ADDITION (supervisor addendum 2026-08-31) — terminal <|im_end|> log-prob. Measured with train_raft.py --eos-probe, which reuses this file's own split/example construction so the 32 sequences are byte-identically the ones the training run held out. Mean log p of the terminal <|im_end|> at the TRUE end of 32 held-out completions: pi_pre -0.0804 (bf16) / -0.0741 (fp32); RAFT -0.0167 / -0.0154; delta = +0.0636 / +0.0587. The pre-registered prediction (RAFT stays in [-1, 0]) HOLDS, and the delta is not merely small but POSITIVE — the RAFT shift reward at the stop token slightly REWARDS terminating, where the corpus-SFT comparator OpenThinker3 measured -90.3 in Part A. This is the sharpest single discriminator yet between the RAFT pair and the corpus-SFT pairs, and it is the direct mechanism prediction of section F1. Job 6a956a240718b0f6d8908ccf, $0.06, eos_logprob_probe.json in the data repo.
• ANOMALY (operational, cost) — the probe container did not exit. exp3-raft-probe's script printed DONE at 171 s and its running_secs froze at 347 s, but the platform kept the job RUNNING; the babysitter cancelled it on the 15-min silence rule at 19.7 min wall. CANCELED jobs report no durations, so the ledger carries two rows for that job id (0.094 h from the live running_secs, then a 0.234 h wall-clock correction) totalling the full 0.328 h / $0.82. The three later jobs exited promptly, so this looks like a one-off platform hiccup rather than a pattern — but it is the reason the silence window matters.
• CORRECTION to the ANOMALY above — it was OUR bug, not a platform hiccup, and it is fixed. exp3-raft-sample-full did the same thing (script DONE at 30.2 min, running_secs frozen at 1,903 s, babysitter cancelled on the silence rule at 49.4 min wall). Both offenders are sample_raft.py; the train / eval / probe jobs all exited promptly. Root cause: sample_raft.py never shut the vLLM engine down, so its EngineCore worker held the container open — eval_model.py has always called release_engine() for exactly this reason. FIXED: sample_raft.py now calls release_engine() + collect_gpu() (the harness's verbatim shutdown-path policy) after the last chunk, before the manifest is written. Cost of the bug, booked conservatively on a wall-clock basis in two correction rows: $0.59 (probe) + $0.74 (full run) = $1.33. Anyone reusing sample_raft.py gets the fix; anyone writing a new vLLM script in this workspace should copy release_engine too.
• RESULT — exp3 Part B COMPLETE ($8.23; ledger $295.32): G1 PASS — 4,187 own-samples kept of 25,600 (sample accuracy 0.355, pass@4 0.654; easier-skewed: keep rate 0.89 at difficulty 3 → 0.55–0.62 at 7.5–9.5; ground truth re-derived from DeepMath @ 5cf055d1 with 6400/6400 question + qhash match AND 6400/6400 pilot-target verification). SFT (lr 1e-5 cosine, 2 epochs = 124 steps, batch 64, fp32-master/bf16): val loss 0.1688 → 0.1617 with minimum at epoch 1 (mild 2nd-epoch over-fit; pre-registered 2 epochs kept, checkpoint-50pct preserved); shift 0.099 |Δlogp|/token. Model @ d46294c2a827c8558547c8ebac96a49b7a8410bb; tokenizer/config sha-identical to π_pre; driver's 5-file fetch verified. G2 PASS — paired gains vs pre_teacher_ot: MATH-500 sample4 +11.20 pp [+8.75, +13.55] (greedy +8.40), teacher_eval in-dist +18.02, AIME24 +0.73 n.s., AIME25 +0.31 n.s.; extraction 0.918 → 0.994 but conditional-on-complete MATH-500 also +11.8 pp → not just format. EOS probe: π_pre −0.074, RAFT −0.015 (Δ +0.059) — training on its OWN complete samples slightly REWARDS stopping (vs OpenThinker3's −90.3). Anomaly: sampling jobs idled after DONE (missing vLLM release; $1.33 booked, script fixed). Local-python breakage after restart (fuse mount drops exec bits) fixed on local disk.
• RESULT — anatomy RAFT column added ($0.38; identical frozen index verified, 2,960 sequences / 2,067,933 positions): RAFT pair (vs π_pre, from stats.json) — token mean −0.03 (RL −0.20, OT −0.23), student-weighted −0.009, % tokens > 0 = 84.7 % (RL 58.1, OT 34.3), terminal EOS −0.006 (RL −6.3, OT −90.2), length-controlled AUROC 0.755 [0.716, 0.790]. The pre-registered P5 reading holds on the numbers ("qualitatively patterns with RL: near-zero terminal EOS + majority-positive tokens — in fact milder than RL on both"), though the coded P5 check is trivial (presence-only) — noted; the report cites the numbers. Two cosmetic issues flagged by the agent (a leftover placeholder column in summary_table.md; RAFT missing from the LINEAGE dict so its EOS caveat is mislabelled though the numbers are well-posed) — to be fixed in the report pass, stats.json unaffected.
• GATE — H6a (exp3 smoke, job 6a9584b7, $1.08): step-1 delta_opd/weighted_reward_mean = −0.0048 (step 2 −0.0026) — strict "≥ 0" clause FAILS; the pre-registered weaker clause ("far closer to 0 than the OT pair's −0.0354, same π_pre/student/config") HOLDS (7.4×). Adaptive KL reacting normally; clip 0.0; s/step 62.7–90.2. Env-only override path (OT_TEACHER_POST_REPO/REV) verified by DRYRUN — driver unchanged @ b4dfdf37. Pre-registered GO → full run direct-opd-exp3-raft-full launched (7 h timeout, $60 ceiling, babysat). The decisive observables: H6b (clip_ratio < 0.5 through step 100 — the anti-EOS driver is gone for this pair) and H6c (paired student gain, MATH-500 primary).
• CHECKPOINT — exp3 raft full run step 20 (job 6a958690): clip_ratio 0.000 at all 20 steps (B at the same step: 1.00 since 15), resp 339 → 431 (no trend to the cap), weighted reward −0.0048 → −0.0020 (stable near zero, no ratchet), KL 2.5 → 2.045, s/step 69.0 → projected ≈ 2.0 h / ≈ $20. H6b trending PASS.
• RESULT — H6b PASSES (exp3 raft full run, job 6a958690): 100/100 steps, training exit 0 after 8,288 s; clip_ratio mean 0.0004, collapse-watch "first step > 0.5: none"; response_length 339 → 500 (mean 523; cap 3,328 never approached); weighted reward stable −0.005 → −0.003; KL 2.475 → 0.915 adaptive. The first SFT-pair Direct-OPD run in the campaign that did not collapse — same student, same config, same π_pre as condition B (collapsed at step 12); the only change is π_post's provenance (own-samples RAFT vs corpus SFT). Merge/upload in progress; H6c (paired student gains, MATH-500 primary) next: ckpt-100 terminates → FULL protocol applies.
• VERIFIED — exp3 raft run close-out (job 6a958690, COMPLETED, 9,232 s, $25.64; ledger $322.42): checkpoints 20–100 + root + logs at cmpatino/Qwen2.5-7B-Instruct-DirectOPD-RAFTShift-100 @ de65f5a389be54f1443810a248c9e2d58c39f3bd, driver verify 0 problems; max clip over 100 steps 0.0078; log_ratio_pos_frac note: verl's metric reads ~0.08 on TRAINING rollouts (top-16 candidate basis) vs the anatomy's 84.7 % realized-token basis — different quantities, flag for the report. H6a partial, H6b confirmed; H6c to the eval wave.
• DECISION (supervisor) — H6c eval wave: ckpt-100 × {math500, aime24, aime25} at the FULL protocol (terminating model, ≈ $4–6) + MATH-500 sample4 curve over ckpt-20/40/60/80 (≈ $6) + AIME24 8-sample curve over the same (≈ $2) — all vs student_init, paired. ≈ $12–15 total.
• VERIFIED — 11-job H6c eval wave, all COMPLETE, exit 0, all pushed. Target cmpatino/Qwen2.5-7B-Instruct-DirectOPD-RAFTShift-100 @ de65f5a389be54f1443810a248c9e2d58c39f3bd. Jobs: ckpt-100 x {math500, aime24, aime25} FULL protocol (opd_student_raftshift); ckpt-20/40/60/80 x math500 FULL protocol + x aime24 8-sample curve (opd_student_raftshift-ckpt{20,40,60,80}). Total cost $9.94 (jobs 6a95ac1d/6a95ac3a/6a95ac6c/6a95ac86/6a95ac97/6a95acb0/6a95acc4/6a95ace8/ 6a95acfe/6a95ad23/6a95ad32), ledger now $332.36 / $500 ($167.64 remaining). Model TERMINATES cleanly as H6b predicted: truncation 0.05–2.5% everywhere (max output tokens well under cap on all passes), no unit hit the 31,744 cap in any meaningful fraction of samples — costs landed at the student_init-like $0.5–1.4/job estimate, not the R1shift/OTshift non-terminating $5–12/job regime.
• Acceptance checklist PASS on all 11 units: resolved_sha = pinned de65f5a3... everywhere; deviations=[] on all 7 full-protocol units, and exactly the expected "8 samples seeds 0..7 ... DIAGNOSTIC curve protocol" deviation on the 4 aime24 curve units; chat_template_sha256 = cd8e9439... on every unit; rendered_tail_example ends <|im_start|>assistant\n; sample counts correct (math500 greedy n=500/sample4 n=2000, aime24/25 full n=960, aime24 curve n=240); benchmark.parquet_sha256 verified byte-identical to student_init's on the matching benchmark for every one of the 11 units (independent check, since the panel-wide aggregate_evals.py --regrade alignment audit reports ok=False — that failure is entirely attributable to OTHER conditions' _sub100/8-sample diagnostic units sharing the results repo, exactly the "nested grids, expected" case the auditor itself names; every opd_student_raftshift* <-> student_init id-set match was exact with zero warnings in the paired-gains script).
• RESULT — H6c FAILS. Paired bootstrap (10k resamples, default_rng(42), percentile CI, two-sided p, eval_model.paired_bootstrap_diff, pairing on source_id/unique_id), full table in supervisor/h6c_gains.json: - ckpt-100 MATH-500 sample4 (PRIMARY): −1.65pp [−3.45, +0.15], p=0.065 — CI does NOT exclude 0, point estimate is slightly NEGATIVE. H6c verdict: FAIL. - ckpt-100 MATH-500 greedy: −0.80pp [−4.00, +2.20], p=0.575. - ckpt-100 AIME24 sample32: −1.56pp [−4.17, +0.83], p=0.179. - ckpt-100 AIME25 sample32: −2.19pp [−5.21, +0.00], p=0.035 — CI upper bound touches exactly 0, essentially a significant regression, not a gain. - Curve MATH-500 sample4 (full protocol) vs student_init: ckpt20 −0.70pp, ckpt40 +0.25pp, ckpt60 −0.35pp, ckpt80 −0.95pp — every CI straddles 0, no monotonic trend with training step. - Curve MATH-500 greedy: ckpt20 +0.60, ckpt40 +0.60, ckpt60 −1.80, ckpt80 −1.60pp — all n.s. - Curve AIME24 8-sample (vs student_init seeds 0-7): ckpt20 −2.50, ckpt40 −2.08, ckpt60 −1.67, ckpt80 −2.08pp — all n.s., all negative point estimates. - Every one of the 11 paired comparisons (ckpt-100 x 4 benchmarks/passes + 4 checkpoints x 3 pass/benchmark combos) has a non-positive or non-significant point estimate; none has a CI excluding 0 on the positive side. No checkpoint, benchmark, or pass shows a detectable gain. - Diagnostics: truncation 0.05–2.5% throughout (no cap-limited units); mean output tokens stable 546–1987 depending on benchmark/checkpoint, growing mildly with training step on some passes (math500 greedy tok_mean 715->838 ckpt20->ckpt80; aime24 tok_mean 1500-2000, no clear trend); extractor split answer_line-dominant (e.g. ckpt-100 math500 sample4: 1624 answer_line / 351 boxed / 25 none) with a low and stable none fraction (1-2% math500, ~7-8% aime — no format degradation with training step).
• INTERPRETATION — pre-registered failure read applies. F3: "H6a,b true but H6c false -> the channel is safe but this shift is too small to detect." H6a was the weaker-clause PASS (RAFT pair's step-1 reward −0.0048, 7.4x closer to 0 than OT's −0.0354, but still negative, not literally >= 0). H6b PASSED cleanly (max clip_ratio 0.0078 over 100 steps, no collapse). H6c now FAILS: the RAFT shift never collapsed the student (unlike every corpus-SFT condition in exp2/2b), but it also never measurably moved held-out capability — consistent with H6a's own sign (a small residual on-support-but-still-negative reward has nothing positive to transmit). This is the cleanest evidence yet for the F1 mechanism claim in its safety half (no collapse when the shift is on-support) while leaving the transfer half unconfirmed at this shift magnitude — the RAFT teacher's own gain was real (G2 PASS, MATH-500 +11.2pp) but the shift the student received from it was apparently too weak/diffuse (own-sample RAFT SFT with |dlogp|/token mean 0.099, far smaller than the corpus pairs') to detect in a 7B student over 100 Direct-OPD steps.
• SYNTHESIS (supervisor, post-H6c) — exp3 outcome: H6a partial (step-1 reward −0.0048, 7.4× closer to 0 than the corpus pair; still negative), H6b TRUE (first non-collapsing SFT pair: max clip 0.0078 over 100 steps), H6c FALSE (ckpt-100 MATH-500 −1.65 [−3.45, +0.15]; all 16 gain cells flat-to-negative; no trend with step). The complete two-axis picture: on-supportness governs stability, shift magnitude governs transfer. Corpus SFT = large-magnitude, off-support (|Δ| ≈ 2.7/token, anti-EOS) → collapse, style-only. RAFT (124 steps on 4,187 own samples) = on-support but tiny (|Δ| ≈ 0.099/token) → safe, null; the pilot's gain-per-shift (+8.75 pp per unit RMS) predicts < 1 pp here — below CI resolution, consistent with the measurement. RL = on-support AND large (pilot RMS 1.02) → transfers (~half the teacher gain), because for KL-regularized RL the log-ratio is the learned advantage, so magnitude and usefulness scale together. Open (stated as such): whether iterated/scaled RAFT — which is one step of an RL-like loop — interpolates to the RL case.

---

3. Setup

3.1 Pinned revisions

role	repo	revision	note
π_pre (teacher_ref / reward denominator)	Qwen/Qwen2.5-Math-1.5B	4a83ca6e4526a4f2	base model; max_position_embeddings 4096 — the binding constraint of this design
π_post (reward model / shift numerator)	deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B	ad9f0ae0864d7fbc	pure-SFT R1 distillation, 800K traces; = the pilot's BASE_TEACHER, so its AIME units are reused
student init	Qwen/Qwen2.5-7B-Instruct	a09a35458c702b33	non-thinking instruct; 4.7× the teachers' parameters
OPD prompts	cmpatino/direct-opd-sft-deepmath-pilot-data	22625ae5db434947	6,400 rows, verl loader contract, AIME-decontaminated; reused verbatim
AIME 2024	HuggingFaceH4/aime_2024	2fe88a2f1091d504	30 problems, pairing key id
AIME 2025	yentinglin/aime_2025	6f71d77b0b89b9da	30 problems, pairing key id
MATH-500	HuggingFaceH4/MATH-500	6e4ed1a2a79af7d8	500 problems, pairing key unique_id
Direct-OPD code	https://github.com/BytedTsinghua-SIA/Direct-OPD	3a9d6bd37b00a38e	+ the pilot's phase4_seed.patch
OPD student output	cmpatino/Qwen2.5-7B-Instruct-DirectOPD-R1DistillShift-100	5819e26cab1f099a	root = step 100; checkpoints 20/40/60/80/100
results (this bundle's inputs)	cmpatino/direct-opd-sft-transfer-results	15fe27f8545d21de	private dataset

3.2 Roles

The Direct-OPD reward is the token-level log-ratio log π_post(t) − log π_pre(t), scored on the student's own rendered token ids (input_tokenizer = null, as the method prescribes). π_pre and π_post are therefore not policies to imitate — they are the two ends of a difference. A property worth stating early, because it frames everything in §5: on MATH-500 the initial 7B student already matches π_post; on AIME it is far ahead of π_pre but well behind π_post. The teacher pair supplies a shift signal, not a uniformly better policy — the exact numbers are in §5.

3.3 Training configuration

parameter	value
max_prompt_length	768
max_response_length	3328
max_sequence_length	4096
mini_batch_size	64
n_responses	4
optim_lr	1e-6
kl_loss_coef	2.5
model_dtype	fp32
log_prob_top_k	16
top_k_strategy	only_stu
reward_weight_mode	student_p
adv_estimator	token_reward_direct
ppo_max_token_len_per_gpu	8192
gpus_per_node	4
steps / save_freq / seed	100 / 20 / 42
train seconds (driver)	15060

★ changed from the pilot's config: student, teacher_ref, MAX_PROMPT_LENGTH, MAX_RESP_LENGTH, PPO_MAX_TOKEN_LEN_PER_GPU. Everything else is the pilot's pinned configuration. Memory knobs (optimizer_offload, the log-prob token budgets, GPU_MEMORY_UTILIZATION) are operational, not scientific, and were adjusted after the smoke without a deviation entry — the pre-registration says so explicitly.

3.4 Evaluation protocol

	AIME 2024 / 2025	MATH-500
problems	30	500
primary pass	sample32 — 32 samples, T 0.7, top_p 0.95, seeds 0–31	sample4 — 4 samples, T 0.7, top_p 0.95, seeds 0–3
secondary pass	—	greedy — 1 sample, T 0
output cap	31,744 tokens (3,200 for π_pre, native-context amendment)	same
prompt	DAPO PREFIX + problem + SUFFIX, each model's own chat template, add_generation_prompt=True	same
grader	last Answer: line, else last \boxed{}, then math-verify	same
pairing key	id	unique_id
CI	percentile bootstrap over problems, 10,000 resamples, numpy.default_rng(42)	same

Curve and reduced-protocol units use 8 samples/problem (seeds 0–7), which is the pre-registered diagnostic-curve protocol. Wherever an 8-sample unit is compared with student_init, this report restricts student_init to the same eight seeds of its 32-sample unit, read from its generations.parquet — so the comparison is paired in problems and matched in samples. The naive comparison against the full 32-sample mean is reported beside it, labelled.

---

4. Phase 0 gates

All Phase 0 gates ran on CPU, at $0, before any GPU spend. Both artifacts are in MANIFEST.json.

gate	rule	outcome
tokenizer byte-identity	ABORT on any ordinary-ID mismatch in [0, 151642] between any two of the trio	PASS — exhaustive check over [0, 151664]: π_pre vs student 0 mismatches anywhere; π_post differs from both only in [151643, 151649] (DeepSeek control tokens). The base BPE model section sha256 is identical across all three (d792a3d6…); 500-string round-trip identical.
prompt-length audit	ABORT if any opd_train prompt exceeds MAX_PROMPT_LENGTH under the student template	Initially FAIL at 512 (5 of 6,400 rows, max 720) → amended to 768/3328, which passes with 0 rows over the limit and 48 tokens of headroom.
π_pre context feasibility	max prompt + --max-tokens ≤ max_position_embeddings	3,584 infeasible on aime25 (848 + 3,584 > 4,096) and math500 (871 + 3,584 > 4,096) → 3,200 on all three benchmarks.
repos private	results + student repos created private=True	VERIFIED via the API.
reward sanity (P3 smoke, replaces a standalone diagnostics phase)	finite delta_opd rewards, |weighted_reward_mean| > 0	PASS — 2/2 steps, log_ratio_mean +1.79/+2.54, pos_frac 0.70/0.75, weighted_reward_mean ≈ −0.008, adaptive KL 2.5 → 2.475.
teacher-gain gate (P2)	paired π_post − π_pre on AIME 2024 > 0, 95 % CI excluding 0	PASS — +24.375 [+15.417, +34.167] p<0.0001 (§5).

A known, reported-not-fixed method property: special IDs 151643–151649 mean different things in the DeepSeek π_post than in the Qwen π_pre/student. Only the response's terminal <|im_end|> is affected — about one token per response.

---

5. Teacher gains — the premise

This is the section the whole experiment is built on: the shift we are asking Direct-OPD to carry must actually encode held-out capability. Paired by problem, percentile bootstrap over problems, 10,000 resamples, seed 42.

benchmark	pass	π_pre (Qwen2.5-Math-1.5B)	π_post (R1-Distill-1.5B)	teacher gain (pp)
aime24	sample32 (primary)	4.69	29.06	+24.375 [+15.417, +34.167] p<0.0001
aime25	sample32 (primary)	2.40	23.54	+21.146 [+10.208, +33.333] p<0.0001
math500	greedy (secondary)	41.20	66.20	+25.000 [+19.600, +30.400] p<0.0001
math500	sample4 (primary)	28.70	75.20	+46.500 [+43.200, +49.850] p<0.0001

The pre-registered TEACHER-GAIN GATE passes: +24.375 [+15.417, +34.167] p<0.0001 on AIME 2024. The premise is true — this teacher pair is separated by a large, real, held-out capability difference, which is exactly what the pilot's SFT pair lacked.

Two caveats that must travel with these numbers.

1. π_pre is measured at a 3,200-token cap it cannot exceed, and truncates heavily there — see the rates in §8.1. Part of the measured teacher gain is a token budget difference, not a reasoning difference. §8.4 bounds it from π_post's own stored generations, and the bound is not small:

   • AIME 2024 — native +24.375 [+15.417, +34.167] p<0.0001 → at π_pre's budget, over-cap-as-wrong +3.646 [-1.042, +9.167] p=0.1426.
   • AIME 2025 — native +21.146 [+10.208, +33.333] p<0.0001 → at π_pre's budget, over-cap-as-wrong +6.354 [+0.625, +13.333] p=0.0216.
   • MATH-500 sample4 — native +46.500 [+43.200, +49.850] p<0.0001 → at π_pre's budget, over-cap-as-wrong +31.550 [+27.950, +35.050] p<0.0001.

   On AIME the restricted gain's CI includes zero; on MATH-500 it does not. The pre-registered gate is stated on the native protocol and it passed — but any statement of the form "the shift carries N pp of capability" should quote the range, not the headline.

2. The teacher pair is not better than the student. On MATH-500 sample4 the initial student scores 74.35 [71.15, 77.55] against π_post's 75.20 [72.20, 78.15] — statistically indistinguishable. On AIME 2024 the initial student scores 12.19 [3.96, 22.50] against π_post's 29.06 [18.33, 40.73]; π_post is ahead here, but the student is far ahead of π_pre (4.69 [1.46, 9.06]). So the shift is a direction, not a better policy to copy — the same framing caveat the pilot recorded, and it matters for reading §7.

---

6. Training dynamics

100/100 steps on a100x4, 100 metric records, 148 numeric keys per step. The run splits cleanly into three regimes. The collapse band is steps 58–85; the first step whose length-clip ratio exceeds 0.5 is step 61.

regime	steps	response len (mean)	clip ratio	actor entropy	weighted reward	log-ratio pos-frac	KL coef	grad norm	s/step
I — pre-collapse	1–57	466	0.000	0.229	-0.0043	0.534	1.894	1.382	71
II — termination collapse	58–85	2996	0.875	0.093	-0.0005	0.530	1.223	0.406	249
III — partial recovery	86–100	2938	0.828	0.625	+0.0008	0.474	1.057	2.017	244

Per-step snapshots at the checkpoint steps and either side of the break:

step	s/step	response mean	clip	entropy	weighted reward	pos-frac	KL coef	grad norm	max mem (GB)
1	89.4	339	0.000	0.156	-0.0078	0.701	2.475	4.244	65.3
20	62.9	399	0.000	0.171	-0.0041	0.585	2.045	1.528	81.3
40	96.5	519	0.000	0.217	-0.0034	0.458	1.672	0.919	81.3
57	72.8	509	0.000	0.352	-0.0023	0.373	1.410	1.342	81.3
60	137.4	1181	0.219	0.134	-0.0006	0.462	1.368	0.846	81.3
62	253.6	3001	0.867	0.060	-0.0005	0.510	1.341	0.274	86.9
70	271.7	3303	0.980	0.062	-0.0002	0.524	1.237	0.251	86.9
85	262.6	3292	0.980	0.163	-0.0008	0.537	1.064	0.639	87.0
100	221.5	2614	0.699	0.667	+0.0026	0.464	1.118	2.101	87.0

The mechanism, read off the metrics

1. The shift reward was negative on the student's native style, for the entire pre-collapse regime (mean -0.0043, never above -0.0022 in steps 1–57). Read literally: on the tokens this Qwen2.5-Instruct student actually likes to emit, π_post assigns less probability than π_pre. The objective's only instruction was therefore "stop writing like yourself" — it never pointed at a better answer, only away from the current one.
2. The KL anchor gave way under that pressure. The adaptive controller ratcheted the coefficient from 2.5 down to 1.064 across the collapse band — a negative-reward regime pushes the controller to loosen the leash exactly when the leash is the only thing holding the policy in a sane region.
3. The policy escaped to where the two teachers agree. As length exploded, the weighted reward went to ≈0 — not positive, zero. A log-ratio of zero means π_post and π_pre assign the same probability, and the cheapest such region for a language model is degenerate repetition. Sampled rollouts show it exactly: an R1-style opening ("Okay, I need to solve…") followed by an endless Answer: <x> loop.
4. Everything else follows. Entropy 0.352 → 0.058; pg_loss → ~0; grad norm → ~0.25; s/step 4×'d because every rollout ran to the cap. The late partial recovery (steps 86–100: entropy back to 0.667, weighted reward turning +0.0026) is real in training, at the 3,328-token training cap. It does not carry over to eval-time sampling at the 31,744-token cap: the P5 probes (logs/p5_repricing.md) measured 87.5–100 % truncation at T=0.7 and greedy for ckpt-60, ckpt-80 and ckpt-100 alike — which is what forced the reduced protocol.

---

7. Student results — the primary endpoints

7.1 Comparability caveat (read this before the table)

The ckpt-100 endpoint is measured under the cost-forced reduced protocol of §2.1(3). Concretely:

• AIME 2024 / 2025 — ckpt-100 at 8 samples/problem (seeds 0–7). The primary comparison restricts student_init to the same 8 seeds of its 32-sample unit, recomputing its per-problem means from generations.parquet. Both sides then have identical problems and identical seeds; the CI is wider than a 32-sample comparison would give, and that is the honest price of the reduction.
• MATH-500 — ckpt-100 on a 100-problem evenly-spread subset, with the full pass set (greedy + sample4). The comparison restricts student_init to the same 100 unique_ids. The sample grid is not reduced here — only the problem set.
• The naive comparison (8 ckpt-100 samples vs student_init's full 32-sample means) is given beside the primary one and labelled unpaired-in-samples. It is not the pre-registered estimand; it is there so a reader can see the reduction did not manufacture the result.

7.2 Primary endpoints

endpoint	benchmark	pass	ckpt-100 (pp)	student_init (pp)	paired gain (pp)	n
PRIMARY	aime24	sample32 (8 samples, seeds 0–7)	8.75 [2.08, 17.50]	13.75 [4.58, 24.58]	-5.000 [-11.250, +0.417] p=0.0630	30
(same, unpaired-in-samples)	aime24	8 vs 32 samples	8.75	12.19	-3.438 [-8.438, +0.521] p=0.0888	30
PRIMARY	math500 (100-problem subset)	greedy (secondary)	63.00 [53.00, 72.00]	84.00 [77.00, 91.00]	-21.000 [-31.000, -11.000] p<0.0001	100
PRIMARY	math500 (100-problem subset)	sample4 (primary)	69.75 [63.00, 76.25]	77.75 [71.25, 83.75]	-8.000 [-13.250, -3.250] p=0.0010	100
replication	aime25	sample32 (8 samples, seeds 0–7)	7.92 [1.67, 16.67]	6.25 [1.67, 12.50]	+1.667 [-1.667, +5.417] p=0.2772	30
(same, unpaired-in-samples)	aime25	8 vs 32 samples	7.92	6.98	+0.938 [-3.333, +5.729] p=0.6840	30

7.3 Transfer ratio (pre-registered guard)

The transfer ratio is reported only when all four guards pass: |teacher_gain| ≥ 1.0 pp, teacher_gain > 0, its 95 % CI excludes 0, and student_gain > 0. This is not decoration — the pilot's measured teacher gain on AIME 2024 was negative, and without the sign guards two regressions divide into a tidy "ratio 1.0".

benchmark	teacher gain (pp)	student gain (pp)	numerator CI excludes 0?	transfer ratio	verdict
aime24	+24.375	-5.000	no	not reported	guard: student_gain = -5.000 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BOTH gains are positive; a non-positive numerator is a transfer FAILURE, and reporting it as a small or negative 'ratio' invites reading it as partial transfer
math500	+46.500	-8.000	yes	not reported	guard: student_gain = -8.000 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BOTH gains are positive; a non-positive numerator is a transfer FAILURE, and reporting it as a small or negative 'ratio' invites reading it as partial transfer
aime25	+21.146	+1.667	no	not reported	guard (exp2b, new): student_gain = 1.667 pp has CI95 [-1.667, 5.417] pp which INCLUDES zero — the numerator is statistically indistinguishable from 'no transfer'. exp2a reported it (this is the gap run 1's AIME 2025 cell exposed); exp2b's pre-registration closes it

A note on the guard, offered as a methods observation rather than a result. The pre-registration (inherited from the pilot) guards the sign of both gains and the significance of the denominator. It does not guard the significance of the numerator — and the AIME 2025 row is exactly the case that exposes the gap: a nominally positive but statistically null student gain divided by a large real teacher gain yields a small, tidy, entirely meaningless "transfer ratio". The value is printed because the rule says to print it, and the numerator CI excludes 0? column is printed beside it so nobody can read it as partial transfer. A future pre-registration should add that fourth significance test.

7.4 The checkpoint curve

Every point is a paired per-problem bootstrap against a comparable student_init slice (same seeds on AIME; same problems on MATH-500). The collapse band (steps 58–85) is shaded in the figure.

AIME 2024, 8 samples/problem (seeds 0–7); baseline = student_init restricted to the same seeds

OPD step	unit	accuracy (pp)	paired gain vs student_init (pp)	naive gain vs the full 32-sample init (pp)
20	opd_student_r1shift-ckpt20	11.67 [3.75, 21.67]	-2.083 [-6.250, +1.667] p=0.2544	-0.521 [-3.646, +2.292] p=0.7128
40	opd_student_r1shift-ckpt40	10.83 [2.50, 21.25]	-2.917 [-7.500, +1.667] p=0.1606	-1.354 [-4.479, +1.458] p=0.3566
60	opd_student_r1shift-ckpt60	7.08 [1.67, 14.17]	-6.667 [-11.667, -2.500] p<0.0001	-5.104 [-9.688, -1.354] p=0.0020
80	opd_student_r1shift-ckpt80	6.25 [1.67, 12.08]	-7.500 [-13.750, -2.083] p=0.0012	-5.938 [-11.042, -1.771] p=0.0004
100	opd_student_r1shift	8.75 [2.08, 17.50]	-5.000 [-11.250, +0.417] p=0.0630	-3.438 [-8.438, +0.521] p=0.0888

MATH-500 sample4 (primary pass) — MATH-500 sample4; steps 20/40 on all 500 problems, step 100 on the 100-problem evenly-spread subset (NOT the same problem set)

OPD step	unit	accuracy (pp)	paired gain vs student_init (pp)
20	opd_student_r1shift-ckpt20	72.10 [68.75, 75.35]	-2.250 [-4.000, -0.550] p=0.0090
40	opd_student_r1shift-ckpt40	72.55 [69.25, 75.75]	-1.800 [-3.550, +0.000] p=0.0454
100	opd_student_r1shift_m500sub100	69.75 [63.00, 76.25]	-8.000 [-13.250, -3.250] p=0.0010

MATH-500 greedy (secondary pass) — MATH-500 greedy; steps 20/40 on all 500 problems, step 100 on the 100-problem evenly-spread subset (NOT the same problem set)

OPD step	unit	accuracy (pp)	paired gain vs student_init (pp)
20	opd_student_r1shift-ckpt20	72.60 [68.60, 76.40]	-2.800 [-6.200, +0.600] p=0.0964
40	opd_student_r1shift-ckpt40	74.60 [70.80, 78.40]	-0.800 [-4.200, +2.600] p=0.5996
100	opd_student_r1shift_m500sub100	63.00 [53.00, 72.00]	-21.000 [-31.000, -11.000] p<0.0001

AIME 2025 (replication); only the ckpt-100 endpoint was measured

OPD step	unit	accuracy (pp)	paired gain vs student_init (pp)	naive gain vs the full 32-sample init (pp)
100	opd_student_r1shift	7.92 [1.67, 16.67]	+1.667 [-1.667, +5.417] p=0.2772	+0.938 [-3.333, +5.729] p=0.6840

7.5 Headline table

One row per benchmark. Teacher gain on the native protocol; student gain at ckpt-100 under the reduced protocol; both are paired percentile bootstraps over problems (10,000 resamples, seed 42).

benchmark	role	teacher gain π_post − π_pre (pp)	student gain ckpt-100 − student_init (pp)	pairing used	transfer ratio
aime24	co-primary (gate benchmark)	+24.375 [+15.417, +34.167] p<0.0001	-5.000 [-11.250, +0.417] p=0.0630	30 problems, both sides on seeds 0–7	withheld by guard
math500	co-primary	+46.500 [+43.200, +49.850] p<0.0001	-8.000 [-13.250, -3.250] p=0.0010	100-problem evenly-spread subset, sample4, same unique_ids	withheld by guard
aime25	replication	+21.146 [+10.208, +33.333] p<0.0001	+1.667 [-1.667, +5.417] p=0.2772	30 problems, both sides on seeds 0–7	withheld by the exp2b numerator-CI guard (exp2a printed 0.079)

---

8. Diagnostics

8.1 Truncation, length and answer format, per unit

answer_line / boxed / none are the three branches of the pre-registered extractor (last Answer: line, else last \boxed{}, else nothing). A none sample is graded incorrect by construction.

unit	pass	cap	trunc %	mean out tok	answer_line	boxed	none	acc|complete	acc|truncated	extract-success|truncated
opd_student_otshift-short-ckpt10 / aime24	sample32	31744	44.2	16569	91.2 %	3.3 %	5.4 %	10.45 (n=134)	10.38 (n=106)	93.4 %
opd_student_otshift-short-ckpt4 / aime24	sample32	31744	1.9	1635	39.0 %	56.4 %	4.7 %	11.68 (n=942)	0.00 (n=18)	0.0 %
opd_student_otshift-short-ckpt8 / aime24	sample32	31744	2.8	2014	75.2 %	19.9 %	4.9 %	11.36 (n=933)	0.00 (n=27)	29.6 %
opd_student_otshift_lowlr / aime24	sample32	31744	99.6	31647	0.8 %	65.0 %	34.2 %	0.00 (n=1)	11.30 (n=239)	66.1 %
opd_student_otshift_lowlr-ckpt20 / aime24	sample32	31744	1.8	1622	38.3 %	57.5 %	4.2 %	12.30 (n=943)	0.00 (n=17)	0.0 %
opd_student_otshift_lowlr-ckpt40 / aime24	sample32	31744	3.1	2088	78.2 %	17.3 %	4.5 %	11.61 (n=930)	6.67 (n=30)	30.0 %
opd_student_otshift_lowlr-ckpt60 / aime24	sample32	31744	88.8	29734	91.2 %	2.5 %	6.2 %	7.41 (n=27)	9.39 (n=213)	95.8 %
opd_student_otshift_lowlr-ckpt80 / aime24	sample32	31744	98.8	31414	45.0 %	36.7 %	18.3 %	0.00 (n=3)	11.39 (n=237)	82.3 %
opd_student_r1shift / aime24	sample32	31744	92.1	29343	93.3 %	0.0 %	6.7 %	0.00 (n=19)	9.50 (n=221)	93.2 %
opd_student_r1shift-ckpt20 / aime24	sample32	31744	0.8	1198	96.2 %	0.8 %	2.9 %	11.76 (n=238)	0.00 (n=2)	0.0 %
opd_student_r1shift-ckpt40 / aime24	sample32	31744	0.4	1242	98.8 %	0.0 %	1.2 %	10.88 (n=239)	0.00 (n=1)	0.0 %
opd_student_r1shift-ckpt40-full / aime24	sample32	31744	1.6	1467	96.8 %	0.0 %	3.2 %	10.16 (n=945)	0.00 (n=15)	0.0 %
opd_student_r1shift-ckpt60 / aime24	sample32	31744	97.5	30993	85.0 %	0.0 %	15.0 %	16.67 (n=6)	6.84 (n=234)	85.0 %
opd_student_r1shift-ckpt80 / aime24	sample32	31744	100.0	31744	84.2 %	0.0 %	15.8 %	0.00 (n=0)	6.25 (n=240)	84.2 %
opd_student_raftshift / aime24	sample32	31744	2.4	1987	55.9 %	35.7 %	8.3 %	10.89 (n=937)	0.00 (n=23)	0.0 %
opd_student_raftshift-ckpt20 / aime24	sample32	31744	2.5	1918	64.6 %	30.0 %	5.4 %	11.54 (n=234)	0.00 (n=6)	0.0 %
opd_student_raftshift-ckpt40 / aime24	sample32	31744	1.2	1538	58.8 %	38.8 %	2.5 %	11.81 (n=237)	0.00 (n=3)	0.0 %
opd_student_raftshift-ckpt60 / aime24	sample32	31744	2.5	1982	59.2 %	35.8 %	5.0 %	12.39 (n=234)	0.00 (n=6)	0.0 %
opd_student_raftshift-ckpt80 / aime24	sample32	31744	2.1	1753	55.8 %	37.5 %	6.7 %	11.91 (n=235)	0.00 (n=5)	0.0 %
post_teacher / aime24	sample32	31744	5.3	13591	21.8 %	64.2 %	14.1 %	30.58 (n=909)	1.96 (n=51)	11.8 %
post_teacher_ot / aime24	sample32	31744	19.0	18275	2.0 %	80.5 %	17.5 %	66.32 (n=778)	1.10 (n=182)	7.7 %
pre_teacher / aime24	sample32	3200	26.6	1599	14.0 %	61.1 %	24.9 %	6.38 (n=705)	0.00 (n=255)	42.0 %
pre_teacher_ot / aime24	sample32	31744	6.5	2991	59.6 %	27.2 %	13.2 %	2.34 (n=898)	0.00 (n=62)	0.0 %
raft_teacher / aime24	sample32	31744	11.6	4634	61.8 %	24.4 %	13.9 %	3.30 (n=849)	0.00 (n=111)	1.8 %
student_init / aime24	sample32	31744	1.6	1517	58.3 %	37.5 %	4.2 %	12.38 (n=945)	0.00 (n=15)	0.0 %
opd_student_otshift-short-ckpt10 / aime25	sample32	31744	41.2	15006	93.8 %	4.6 %	1.7 %	7.80 (n=141)	13.13 (n=99)	97.0 %
opd_student_otshift-short-ckpt4 / aime25	sample32	31744	1.0	1262	39.9 %	58.6 %	1.5 %	7.47 (n=950)	0.00 (n=10)	0.0 %
opd_student_otshift-short-ckpt8 / aime25	sample32	31744	1.1	1299	70.2 %	28.7 %	1.0 %	7.80 (n=949)	9.09 (n=11)	45.5 %
opd_student_otshift_lowlr / aime25	sample32	31744	100.0	31744	0.4 %	63.3 %	36.2 %	0.00 (n=0)	7.50 (n=240)	63.7 %
opd_student_otshift_lowlr-ckpt20 / aime25	sample32	31744	0.6	1120	38.3 %	60.7 %	0.9 %	6.92 (n=954)	0.00 (n=6)	0.0 %
opd_student_otshift_lowlr-ckpt40 / aime25	sample32	31744	0.6	1146	71.4 %	27.7 %	0.9 %	7.44 (n=954)	0.00 (n=6)	16.7 %
opd_student_r1shift / aime25	sample32	31744	93.8	29824	95.8 %	0.4 %	3.8 %	0.00 (n=15)	8.44 (n=225)	96.0 %
opd_student_r1shift-ckpt40-full / aime25	sample32	31744	0.3	988	99.1 %	0.0 %	0.9 %	7.84 (n=957)	0.00 (n=3)	0.0 %
opd_student_raftshift / aime25	sample32	31744	1.0	1337	65.0 %	32.5 %	2.5 %	4.84 (n=950)	0.00 (n=10)	0.0 %
post_teacher / aime25	sample32	31744	3.3	12852	20.6 %	72.9 %	6.5 %	24.35 (n=928)	0.00 (n=32)	12.5 %
post_teacher_ot / aime25	sample32	31744	22.1	19302	1.9 %	78.1 %	20.0 %	54.95 (n=748)	0.94 (n=212)	9.4 %
pre_teacher / aime25	sample32	3200	23.4	1523	13.3 %	65.6 %	21.0 %	3.13 (n=735)	0.00 (n=225)	46.7 %
pre_teacher_ot / aime25	sample32	31744	4.8	2267	66.8 %	22.3 %	10.9 %	0.44 (n=914)	0.00 (n=46)	0.0 %
raft_teacher / aime25	sample32	31744	8.6	3458	67.0 %	23.1 %	9.9 %	0.80 (n=877)	0.00 (n=83)	0.0 %
student_init / aime25	sample32	31744	1.2	1307	61.8 %	36.5 %	1.8 %	7.07 (n=948)	0.00 (n=12)	0.0 %
opd_student_otshift-short-ckpt10_m500sub100 / math500	greedy	31744	88.0	28629	99.0 %	0.0 %	1.0 %	66.67 (n=12)	88.64 (n=88)	98.9 %
opd_student_otshift-short-ckpt10_m500sub100 / math500	sample4	31744	60.5	22020	98.0 %	1.2 %	0.8 %	75.32 (n=158)	80.17 (n=242)	99.2 %
opd_student_otshift-short-ckpt4 / math500	greedy	31744	1.2	963	75.8 %	22.2 %	2.0 %	75.71 (n=494)	0.00 (n=6)	0.0 %
opd_student_otshift-short-ckpt4 / math500	sample4	31744	0.2	659	78.8 %	20.1 %	1.1 %	74.04 (n=1995)	0.00 (n=5)	0.0 %
opd_student_otshift-short-ckpt8 / math500	greedy	31744	1.2	1012	98.8 %	0.2 %	1.0 %	75.91 (n=494)	66.67 (n=6)	66.7 %
opd_student_otshift-short-ckpt8 / math500	sample4	31744	0.8	870	98.9 %	0.7 %	0.4 %	75.25 (n=1984)	62.50 (n=16)	75.0 %
opd_student_otshift_lowlr-ckpt20 / math500	greedy	31744	1.0	870	71.8 %	25.4 %	2.8 %	74.75 (n=495)	0.00 (n=5)	0.0 %
opd_student_otshift_lowlr-ckpt20 / math500	sample4	31744	0.4	707	74.0 %	23.5 %	2.5 %	73.83 (n=1991)	0.00 (n=9)	0.0 %
opd_student_otshift_lowlr-ckpt40 / math500	greedy	31744	2.8	1494	97.8 %	0.6 %	1.6 %	77.98 (n=486)	50.00 (n=14)	50.0 %
opd_student_otshift_lowlr-ckpt40 / math500	sample4	31744	0.9	890	98.7 %	0.9 %	0.4 %	74.74 (n=1983)	64.71 (n=17)	70.6 %
opd_student_otshift_lowlr_m500sub100 / math500	greedy	31744	100.0	31744	0.0 %	62.0 %	38.0 %	0.00 (n=0)	54.00 (n=100)	62.0 %
opd_student_otshift_lowlr_m500sub100 / math500	sample4	31744	100.0	31744	0.8 %	61.3 %	38.0 %	0.00 (n=0)	49.00 (n=400)	62.0 %
opd_student_r1shift-ckpt20 / math500	greedy	31744	0.8	758	98.4 %	0.0 %	1.6 %	73.19 (n=496)	0.00 (n=4)	0.0 %
opd_student_r1shift-ckpt20 / math500	sample4	31744	0.1	513	98.3 %	0.2 %	1.5 %	72.14 (n=1999)	0.00 (n=1)	0.0 %
opd_student_r1shift-ckpt40 / math500	greedy	31744	1.0	831	98.6 %	0.0 %	1.4 %	75.35 (n=495)	0.00 (n=5)	0.0 %
opd_student_r1shift-ckpt40 / math500	sample4	31744	0.1	540	98.8 %	0.1 %	1.1 %	72.62 (n=1998)	0.00 (n=2)	0.0 %
opd_student_r1shift-ckpt40-full / math500	greedy	31744	1.0	819	98.8 %	0.0 %	1.2 %	75.35 (n=495)	0.00 (n=5)	0.0 %
opd_student_r1shift-ckpt40-full / math500	sample4	31744	0.1	529	98.8 %	0.1 %	1.1 %	73.49 (n=1999)	0.00 (n=1)	0.0 %
opd_student_r1shift_m500sub100 / math500	greedy	31744	100.0	31744	90.0 %	0.0 %	10.0 %	0.00 (n=0)	63.00 (n=100)	90.0 %
opd_student_r1shift_m500sub100 / math500	sample4	31744	96.5	30678	98.2 %	0.0 %	1.8 %	64.29 (n=14)	69.95 (n=386)	98.2 %
opd_student_raftshift / math500	greedy	31744	0.6	757	81.4 %	17.4 %	1.2 %	75.05 (n=497)	0.00 (n=3)	0.0 %
opd_student_raftshift / math500	sample4	31744	0.4	653	81.2 %	17.5 %	1.2 %	72.96 (n=1993)	0.00 (n=7)	0.0 %
opd_student_raftshift-ckpt20 / math500	greedy	31744	0.6	715	86.2 %	12.8 %	1.0 %	76.46 (n=497)	0.00 (n=3)	0.0 %
opd_student_raftshift-ckpt20 / math500	sample4	31744	0.1	546	84.2 %	15.0 %	0.9 %	73.69 (n=1999)	0.00 (n=1)	0.0 %
opd_student_raftshift-ckpt40 / math500	greedy	31744	0.8	790	80.8 %	18.4 %	0.8 %	76.61 (n=496)	0.00 (n=4)	0.0 %
opd_student_raftshift-ckpt40 / math500	sample4	31744	0.2	612	82.2 %	16.8 %	0.9 %	74.79 (n=1995)	0.00 (n=5)	0.0 %
opd_student_raftshift-ckpt60 / math500	greedy	31744	2.0	1147	81.6 %	15.8 %	2.6 %	75.10 (n=490)	0.00 (n=10)	0.0 %
opd_student_raftshift-ckpt60 / math500	sample4	31744	0.1	591	83.2 %	15.8 %	1.0 %	74.11 (n=1997)	0.00 (n=3)	0.0 %
opd_student_raftshift-ckpt80 / math500	greedy	31744	1.0	838	82.2 %	16.6 %	1.2 %	74.55 (n=495)	0.00 (n=5)	0.0 %
opd_student_raftshift-ckpt80 / math500	sample4	31744	0.2	615	82.9 %	16.2 %	0.9 %	73.58 (n=1995)	0.00 (n=5)	0.0 %
post_teacher / math500	greedy	31744	21.2	8134	73.4 %	5.2 %	21.4 %	83.76 (n=394)	0.94 (n=106)	0.9 %
post_teacher / math500	sample4	31744	0.8	3822	79.8 %	17.3 %	2.9 %	75.81 (n=1984)	0.00 (n=16)	12.5 %
post_teacher_ot / math500	greedy	31744	9.0	7094	9.6 %	79.4 %	11.0 %	90.77 (n=455)	2.22 (n=45)	2.2 %
post_teacher_ot / math500	sample4	31744	1.7	5762	12.6 %	84.2 %	3.3 %	90.19 (n=1967)	6.06 (n=33)	27.3 %
pre_teacher / math500	greedy	3200	28.6	1337	5.6 %	62.6 %	31.8 %	57.14 (n=357)	1.40 (n=143)	7.7 %
pre_teacher / math500	sample4	3200	18.2	1055	36.7 %	41.5 %	21.8 %	33.82 (n=1635)	5.75 (n=365)	40.8 %
pre_teacher_ot / math500	greedy	31744	3.6	1602	67.8 %	19.8 %	12.4 %	47.10 (n=482)	0.00 (n=18)	0.0 %
pre_teacher_ot / math500	sample4	31744	0.9	716	71.5 %	19.1 %	9.3 %	39.10 (n=1982)	0.00 (n=18)	0.0 %
raft_teacher / math500	greedy	31744	2.8	1389	79.6 %	17.2 %	3.2 %	55.35 (n=486)	0.00 (n=14)	0.0 %
raft_teacher / math500	sample4	31744	1.9	1101	77.5 %	19.7 %	2.8 %	50.94 (n=1961)	0.00 (n=39)	0.0 %
student_init / math500	greedy	31744	0.8	811	84.0 %	14.4 %	1.6 %	76.01 (n=496)	0.00 (n=4)	0.0 %
student_init / math500	sample4	31744	0.1	564	83.7 %	14.6 %	1.8 %	74.42 (n=1998)	0.00 (n=2)	0.0 %

8.2 Answer-format split, side by side

The same numbers as §8.1, arranged so the direction of the style change is visible. Primary pass only.

benchmark	model	Answer: line	\boxed{}	none	mean out tok
aime24	pre_teacher	14.0 %	61.1 %	24.9 %	1599
aime24	post_teacher	21.8 %	64.2 %	14.1 %	13591
aime24	student_init	58.3 %	37.5 %	4.2 %	1517
aime24	opd_student_r1shift	93.3 %	0.0 %	6.7 %	29343
aime24	opd_student_r1shift-ckpt20	96.2 %	0.8 %	2.9 %	1198
aime24	opd_student_r1shift-ckpt40	98.8 %	0.0 %	1.2 %	1242
aime24	opd_student_r1shift-ckpt40-full	96.8 %	0.0 %	3.2 %	1467
aime24	opd_student_r1shift-ckpt60	85.0 %	0.0 %	15.0 %	30993
aime24	opd_student_r1shift-ckpt80	84.2 %	0.0 %	15.8 %	31744
aime25	pre_teacher	13.3 %	65.6 %	21.0 %	1523
aime25	post_teacher	20.6 %	72.9 %	6.5 %	12852
aime25	student_init	61.8 %	36.5 %	1.8 %	1307
aime25	opd_student_r1shift	95.8 %	0.4 %	3.8 %	29824
aime25	opd_student_r1shift-ckpt40-full	99.1 %	0.0 %	0.9 %	988
math500	pre_teacher	36.7 %	41.5 %	21.8 %	1055
math500	post_teacher	79.8 %	17.3 %	2.9 %	3822
math500	student_init	83.7 %	14.6 %	1.8 %	564
math500	opd_student_r1shift-ckpt20	98.3 %	0.2 %	1.5 %	513
math500	opd_student_r1shift-ckpt40	98.8 %	0.1 %	1.1 %	540
math500	opd_student_r1shift-ckpt40-full	98.8 %	0.1 %	1.1 %	529
math500	opd_student_r1shift_m500sub100	98.2 %	0.0 %	1.8 %	30678

Read the AIME rows first, where the effect is largest. Both teachers lean \boxed{} there (61–73 % of samples) — π_pre because its own chat template injects "put your final answer within \boxed{}", π_post because the R1 distillation writes that way — and the initial student splits roughly 58/38 between the two formats. The OPD student goes almost purely to the prompt-instructed Answer: line and extinguishes \boxed{} altogether (37.5 % → 0.8 % by step 20, 0.0 % by step 40). On MATH-500 π_post itself prefers Answer: (79.8 %) and the initial student already does too (83.7 %), so there is less room to move — and the student still moves past both, to 98 %.

The direction is the point. On the benchmark where the two teachers agree on \boxed{}, the student runs the other way. Whatever the token-level log-ratio rewards, it is not "emit π_post's surface form" — the pilot saw the same non-imitation in both of its arms, and it reproduces here with a completely different teacher pair and a 4.7× larger student.

8.3 Extraction on truncated samples — new for this experiment

The pilot could treat truncation as "no answer". This experiment cannot. Two independent reasons, and they point in opposite directions:

• π_pre is cut off at 3,200 tokens after it has often already emitted a \boxed{} or an Answer: line, so a large share of its truncated samples still extract — the answer is there, the work around it is not.
• The collapsed OPD checkpoints do the opposite in kind and the same in effect — and this is now measured, not predicted. The degenerate policy reaches an answer and then loops on it, so a truncated sample still ends in a gradeable Answer: line. At ckpt-100: 93.2 % of the 221 truncated AIME 2024 samples still extract an answer (and 9.50 pp of them are correct), and on the MATH-500 subset 98.2 % of the 386 truncated sample4 samples extract, scoring 69.95 pp. The collapse is not an answer-extraction failure. The model still solves the problem; it just never stops talking about it. That is the single most useful diagnostic in this report: it separates "the policy was destroyed" from "the policy lost its stop token", and the evidence is for the latter.

Either way, truncation and non-extraction have come apart and both must be reported. Measured now:

unit	pass	truncated n	extraction success	accuracy on truncated
opd_student_otshift-short-ckpt10_m500sub100 / math500	sample4	242	99.2 %	80.17 pp
opd_student_otshift-short-ckpt10_m500sub100 / math500	greedy	88	98.9 %	88.64 pp
opd_student_r1shift_m500sub100 / math500	sample4	386	98.2 %	69.95 pp
opd_student_otshift-short-ckpt10 / aime25	sample32	99	97.0 %	13.13 pp
opd_student_r1shift / aime25	sample32	225	96.0 %	8.44 pp
opd_student_otshift_lowlr-ckpt60 / aime24	sample32	213	95.8 %	9.39 pp
opd_student_otshift-short-ckpt10 / aime24	sample32	106	93.4 %	10.38 pp
opd_student_r1shift / aime24	sample32	221	93.2 %	9.50 pp
opd_student_r1shift_m500sub100 / math500	greedy	100	90.0 %	63.00 pp
opd_student_r1shift-ckpt60 / aime24	sample32	234	85.0 %	6.84 pp
opd_student_r1shift-ckpt80 / aime24	sample32	240	84.2 %	6.25 pp
opd_student_otshift_lowlr-ckpt80 / aime24	sample32	237	82.3 %	11.39 pp
opd_student_otshift-short-ckpt8 / math500	sample4	16	75.0 %	62.50 pp
opd_student_otshift_lowlr-ckpt40 / math500	sample4	17	70.6 %	64.71 pp
opd_student_otshift-short-ckpt8 / math500	greedy	6	66.7 %	66.67 pp
opd_student_otshift_lowlr / aime24	sample32	239	66.1 %	11.30 pp
opd_student_otshift_lowlr / aime25	sample32	240	63.7 %	7.50 pp
opd_student_otshift_lowlr_m500sub100 / math500	greedy	100	62.0 %	54.00 pp
opd_student_otshift_lowlr_m500sub100 / math500	sample4	400	62.0 %	49.00 pp
opd_student_otshift_lowlr-ckpt40 / math500	greedy	14	50.0 %	50.00 pp
pre_teacher / aime25	sample32	225	46.7 %	0.00 pp
opd_student_otshift-short-ckpt8 / aime25	sample32	11	45.5 %	9.09 pp
pre_teacher / aime24	sample32	255	42.0 %	0.00 pp
pre_teacher / math500	sample4	365	40.8 %	5.75 pp
opd_student_otshift_lowlr-ckpt40 / aime24	sample32	30	30.0 %	6.67 pp
opd_student_otshift-short-ckpt8 / aime24	sample32	27	29.6 %	0.00 pp
post_teacher_ot / math500	sample4	33	27.3 %	6.06 pp
opd_student_otshift_lowlr-ckpt40 / aime25	sample32	6	16.7 %	0.00 pp
post_teacher / aime25	sample32	32	12.5 %	0.00 pp
post_teacher / math500	sample4	16	12.5 %	0.00 pp
post_teacher / aime24	sample32	51	11.8 %	1.96 pp
post_teacher_ot / aime25	sample32	212	9.4 %	0.94 pp
post_teacher_ot / aime24	sample32	182	7.7 %	1.10 pp
pre_teacher / math500	greedy	143	7.7 %	1.40 pp
post_teacher_ot / math500	greedy	45	2.2 %	2.22 pp
raft_teacher / aime24	sample32	111	1.8 %	0.00 pp
post_teacher / math500	greedy	106	0.9 %	0.94 pp
opd_student_otshift-short-ckpt4 / aime24	sample32	18	0.0 %	0.00 pp
opd_student_otshift_lowlr-ckpt20 / aime24	sample32	17	0.0 %	0.00 pp
opd_student_r1shift-ckpt20 / aime24	sample32	2	0.0 %	0.00 pp
opd_student_r1shift-ckpt40 / aime24	sample32	1	0.0 %	0.00 pp
opd_student_r1shift-ckpt40-full / aime24	sample32	15	0.0 %	0.00 pp
opd_student_raftshift / aime24	sample32	23	0.0 %	0.00 pp
opd_student_raftshift-ckpt20 / aime24	sample32	6	0.0 %	0.00 pp
opd_student_raftshift-ckpt40 / aime24	sample32	3	0.0 %	0.00 pp
opd_student_raftshift-ckpt60 / aime24	sample32	6	0.0 %	0.00 pp
opd_student_raftshift-ckpt80 / aime24	sample32	5	0.0 %	0.00 pp
pre_teacher_ot / aime24	sample32	62	0.0 %	0.00 pp
student_init / aime24	sample32	15	0.0 %	0.00 pp
opd_student_otshift-short-ckpt4 / aime25	sample32	10	0.0 %	0.00 pp
opd_student_otshift_lowlr-ckpt20 / aime25	sample32	6	0.0 %	0.00 pp
opd_student_r1shift-ckpt40-full / aime25	sample32	3	0.0 %	0.00 pp
opd_student_raftshift / aime25	sample32	10	0.0 %	0.00 pp
pre_teacher_ot / aime25	sample32	46	0.0 %	0.00 pp
raft_teacher / aime25	sample32	83	0.0 %	0.00 pp
student_init / aime25	sample32	12	0.0 %	0.00 pp
opd_student_otshift-short-ckpt4 / math500	greedy	6	0.0 %	0.00 pp
opd_student_otshift-short-ckpt4 / math500	sample4	5	0.0 %	0.00 pp
opd_student_otshift_lowlr-ckpt20 / math500	greedy	5	0.0 %	0.00 pp
opd_student_otshift_lowlr-ckpt20 / math500	sample4	9	0.0 %	0.00 pp
opd_student_r1shift-ckpt20 / math500	greedy	4	0.0 %	0.00 pp
opd_student_r1shift-ckpt20 / math500	sample4	1	0.0 %	0.00 pp
opd_student_r1shift-ckpt40 / math500	greedy	5	0.0 %	0.00 pp
opd_student_r1shift-ckpt40 / math500	sample4	2	0.0 %	0.00 pp
opd_student_r1shift-ckpt40-full / math500	greedy	5	0.0 %	0.00 pp
opd_student_r1shift-ckpt40-full / math500	sample4	1	0.0 %	0.00 pp
opd_student_raftshift / math500	greedy	3	0.0 %	0.00 pp
opd_student_raftshift / math500	sample4	7	0.0 %	0.00 pp
opd_student_raftshift-ckpt20 / math500	greedy	3	0.0 %	0.00 pp
opd_student_raftshift-ckpt20 / math500	sample4	1	0.0 %	0.00 pp
opd_student_raftshift-ckpt40 / math500	greedy	4	0.0 %	0.00 pp
opd_student_raftshift-ckpt40 / math500	sample4	5	0.0 %	0.00 pp
opd_student_raftshift-ckpt60 / math500	greedy	10	0.0 %	0.00 pp
opd_student_raftshift-ckpt60 / math500	sample4	3	0.0 %	0.00 pp
opd_student_raftshift-ckpt80 / math500	greedy	5	0.0 %	0.00 pp
opd_student_raftshift-ckpt80 / math500	sample4	5	0.0 %	0.00 pp
pre_teacher_ot / math500	greedy	18	0.0 %	0.00 pp
pre_teacher_ot / math500	sample4	18	0.0 %	0.00 pp
raft_teacher / math500	greedy	14	0.0 %	0.00 pp
raft_teacher / math500	sample4	39	0.0 %	0.00 pp
student_init / math500	greedy	4	0.0 %	0.00 pp
student_init / math500	sample4	2	0.0 %	0.00 pp

Two readings of the table. π_pre: 40–47 % of its truncated samples still extract, against 0–12 % for the two teachers' and the initial student's — so reading "truncated ⇒ no answer" would understate π_pre and, through it, overstate the teacher gain. The collapsed checkpoints: 84–98 % extraction on truncated samples, with real accuracy behind it. Truncation rate alone is therefore a terrible summary of what went wrong here, and this column is what replaces it.

8.4 Sensitivity view — π_post at π_pre's cap

π_pre is capped at 3,200 tokens by its own trained context, while π_post runs to 31,744. Part of the §5 teacher gain is therefore a budget difference rather than a capability difference. This view costs no new compute: it restricts π_post's stored generations to samples of ≤ 3,200 output tokens and re-scores.

Two readings, because neither alone is honest:

• kept-only — accuracy on the π_post samples that fit under 3,200 tokens. This is conditional accuracy and is biased upwards: short samples are the easy problems.
• over-cap-as-wrong — every π_post sample longer than 3,200 tokens counted incorrect. This simulates the cap and is a lower bound: a truncated sample sometimes still extracts a correct answer (§8.3).

The true "π_post at 3,200 tokens" lies between them. Both are labelled sensitivity views and neither replaces the §5 primary numbers.

benchmark	pass	π_pre native (pp)	π_post native (pp)	π_post kept-only (pp)	π_post over-cap-as-wrong (pp)	samples kept	problems with any kept sample
aime24	sample32	4.69 [1.46, 9.06] (trunc 26.6 %)	29.06	76.21 [52.01, 99.17]	8.33 [2.60, 15.31]	9.1 % (87/960)	11/30
aime25	sample32	2.40 [0.73, 4.48] (trunc 23.4 %)	23.54	66.67 [40.00, 91.11]	8.75 [2.50, 16.56]	9.7 % (93/960)	9/30
math500	greedy	41.20 [36.80, 45.40] (trunc 28.6 %)	66.20	86.74 [83.00, 90.20]	60.20 [56.00, 64.40]	69.4 % (347/500)	347/500
math500	sample4	28.70 [26.45, 30.95] (trunc 18.2 %)	75.20	83.60 [80.54, 86.48]	60.25 [56.65, 63.75]	71.4 % (1427/2000)	411/500

The last column is why the kept-only view must not be quoted on AIME: on the 30-problem sets only ~9–11 problems have any π_post sample under 3,200 tokens, and they are the short — i.e. easy — ones. The kept-only row is included for completeness and is not a usable estimate there. On MATH-500, where ~70 % of samples survive the cut and 347–411 of 500 problems are represented, it is informative.

Restated as gains against π_pre's native numbers (paired on the problems each view covers):

benchmark	pass	teacher gain, kept-only (pp)	n	teacher gain, over-cap-as-wrong (pp)	n
aime24	sample32	+64.562 [+41.259, +85.511] p<0.0001	11	+3.646 [-1.042, +9.167] p=0.1426	30
aime25	sample32	+61.458 [+35.622, +83.819] p<0.0001	9	+6.354 [+0.625, +13.333] p=0.0216	30
math500	greedy	+37.752 [+31.412, +43.804] p<0.0001	347	+19.000 [+13.600, +24.600] p<0.0001	500
math500	sample4	+50.933 [+47.202, +54.582] p<0.0001	411	+31.550 [+27.950, +35.050] p<0.0001	500

The row that matters is aime24 / over-cap-as-wrong. It is the pre-registered teacher-gain benchmark, measured with both models on the same token budget and the unmeasurable cases resolved against π_post, and it is the one place where the premise becomes uncertain. MATH-500 keeps a large, budget-independent gain, which is why the co-primary design was worth having.

---

9. Interpretation vs the pilot

The pilot's finding was that Direct-OPD is a faithful courier of whatever the shift encodes: an SFT shift that encoded narrowing produced a student that narrowed. The obvious follow-up — give it a shift that encodes real capability — is this experiment. The answer is negative, and the interesting part is why. With a teacher pair that demonstrably carried held-out capability, 100 Direct-OPD steps produced a student that is no better on any benchmark at any checkpoint, significantly worse on MATH-500, and — after step ~61 — unable to terminate at all. The pilot's verdict (style transfers, capability does not) survives the strongest test we could give it, and a new failure mode appears alongside it.

What we can say, in decreasing order of confidence.

1. The premise is no longer the limiting factor, and the result did not follow. The teacher gain is large and unambiguous (+24.375 [+15.417, +34.167] p<0.0001 on AIME 2024). The student's gain, at every checkpoint measured, is not. Whatever blocked transfer here, it is not "the shift had nothing to give" — which was the pilot's explanation and is now excluded.
2. Surface form moved; capability did not — and the surface form did not move towards π_post. By step 20 the student had abandoned \boxed{} almost entirely in favour of the prompt-instructed Answer: line, while on AIME both teachers lean \boxed{} (§8.2). Accuracy over the same interval is flat on AIME and slightly negative on MATH-500 (§7.4). This is the pilot's finding 5 reproduced with a different teacher pair, a different student family and a 4.7× larger student: a token-level log-ratio objective buys a change of surface form first, and the form it buys is not the post-teacher's. The natural reading is that the log-ratio is largest on tokens where the two teachers disagree about style, and the cheapest way to increase it is to leave the region where they disagree — not to imitate either one.
3. The failure mode is termination collapse — a lost stop token, not a destroyed policy. It is not a generic "OPD diverged". The chain is legible in the metrics (§6): a reward that is negative on the student's native style → an adaptive KL controller that loosens under sustained negative reward → escape into the degenerate region where π_post ≈ π_pre → an Answer: repetition loop that never emits a stop token. It is worse at eval time than in training — at the 31,744-token cap ckpt-100 truncates on 92–100 % of samples despite its training-time partial recovery at the 3,328-token cap — and §8.3 pins down what "truncated" means here: 84–98 % of those truncated samples still extract an answer, and on MATH-500 ~70 pp of them are correct. The model still reasons; it cannot stop. This distinction matters for the fix list below: three of the five candidates target termination specifically.
4. A capability-bearing shift is not sufficient; distributional proximity may be necessary. The two teachers here are far apart in style (a \boxed{}-instructed math base vs an R1 <think> distillation) and both are far from the student (non-thinking Qwen2.5-Instruct, 4.7× larger). The log-ratio is then dominated by style disagreement, and the capability difference — the thing we wanted — is a small residual underneath it. This is a hypothesis this experiment suggests; it does not test it.

What would need to change, concretely, for a rerun to be informative.

change	why	cost
KL floor — clamp the adaptive coefficient below (e.g. ≥ 1.5) instead of letting it ratchet to 1.06	the controller loosened the leash precisely in the negative-reward regime that needed it tightened	free (a config pin)
Length / repetition penalty, or a repetition-aware reward	the escape region is degenerate repetition; nothing in the objective priced it	free
Response cap raised, or the training cap matched to the eval cap	the 3,328-token cap made the collapse cheap to enter and hid its eval-time severity	more GPU-hours per step
A teacher pair closer to the student's own distribution (e.g. both ends Qwen2.5-Instruct-family, or an SFT pair built on the student)	makes the log-ratio encode capability rather than style	a teacher-side SFT run
A thinking-mode student (or the student's thinking template at both train and eval time)	π_post is a <think>-native model; a non-thinking student can only imitate its surface	free at eval, config at train

A rerun that changes only one of these is worth more than one that changes all five: the first three test the collapse, the last two test the premise about distance.

---

10. Limitations

1. The primary endpoint is measured under a reduced protocol (§2.1(3), §7.1). It is the same estimand with wider intervals, not a different one — but it is not the pre-registered sample count, and a null result at 8 samples/problem is weaker evidence than a null at 32.
2. MATH-500's ckpt-100 unit is a 100-problem subset, so its interval is roughly √5 wider than the 500-problem baseline's, and it is not the same problem set as the ckpt-20/40 curve points. The curve table says so on every row.
3. π_pre is context-limited at 3,200 tokens and truncates heavily, so the teacher gain is partly a token-budget difference. §8.4 bounds it but cannot eliminate it: on the pre-registered gate benchmark the bound runs from +3.646 [-1.042, +9.167] p=0.1426 (π_post held to π_pre's budget, over-cap counted wrong) up to +24.375 [+15.417, +34.167] p<0.0001 (native protocol). The honest statement of the premise on AIME 2024 is that range, not the headline point. MATH-500 is where the premise survives the correction intact.
4. n = 30 on AIME. Even at 32 samples/problem the per-problem bootstrap over 30 problems gives intervals ~10 pp wide. MATH-500 is the co-primary precisely because 500 problems give ~4× tighter intervals — which is why losing the full MATH-500 endpoint to cost hurts.
5. One run, one seed (42), one condition. No RL comparator, no repeat at a different seed, no ablation of the collapse. We cannot separate "Direct-OPD cannot carry this shift" from "this configuration collapsed before it could".
6. The collapse confounds everything after step ~58. ckpt-60/80/100 are measurements of a degenerate policy. Their accuracies are real, but they answer "what does a collapsed policy score", not "how much capability transferred".
7. No shift-magnitude diagnostic. The pre-registration folded the reward-sanity check into the P3 smoke to save cost, so there is no weighted-RMS shift magnitude for this pair and therefore no gain-per-unit-shift number comparable to the pilot's.
8. π_post's AIME units are imported from the pilot, not re-run. Same model revision, same harness, same protocol, verified by provenance.json per unit — but not an independent measurement.
9. Cost basis. The quoted total is wall-clock occupancy × flavor rate including aborted work; the platform's running_secs basis is a floor (see §11).

---

11. Cost & reproduction

$332.36 of a $200 cap ($-132.36 unspent), recomputed by summing cost_usd over all 83 rows of ledger/cost_ledger.csv.

phase	cost	share
P1	$0.00	0.0 %
P2	$7.32	2.2 %
P2b	$16.46	5.0 %
P3	$1.07	0.3 %
P3b	$3.61	1.1 %
P4	$44.43	13.4 %
P4b	$100.90	30.4 %
P5	$26.14	7.9 %
P5b	$71.05	21.4 %
P6	$13.91	4.2 %
P7	$47.47	14.3 %
TOTAL	$332.36	100 %

By hardware: a100x4 $176.73 · a100-large $155.63 · cpu-basic $0.00.

⚠️ Two cost bases. wall-clock occupancy x flavor rate from ledger/cost_ledger.csv, INCLUDING any aborted work — the same (larger) basis the pilot quoted. The platform's own running_secs x rate is a floor, because CANCELED jobs report running_secs = 0 regardless of real occupancy. This report quotes the larger basis, as the pilot did; nothing in the decision record turns on the difference.

⚠️ This ledger is cumulative over run 1, the exp2b extension AND exp3. The cap was raised $200 → $500 by the user on 2026-08-26. Run 1's own phases (P1–P6) total $92.87, inside the original $200 cap; the exp2b extension's *b phases (P2b, P3b, P4b, P5b) add $192.02; exp3's phase (P7) — the shift anatomy, the RAFT pair and its whole eval wave — add $47.47, for $332.36 of $500. §14.4 gives the breakdown, including the cancelled runs booked on the wall-clock basis.

Ledger reconciliation: every eval unit on the Hub has a matching cost-ledger row (units imported from the pilot repo excepted, which cost nothing).

Imported at $0 (no GPU spend expected, provenance.json in each unit): post_teacher/aime24, post_teacher/aime25.

11.1 Reproducing the whole campaign

Everything below is pinned by revision or by sha256, and every table in this subsection is generated from its source at build time (eval_model.MODEL_REGISTRY, ledger/resolved_revisions.json, ledger/staged_driver.json, the files on disk) rather than typed in. A third party with the results repo and this list can rebuild the campaign end to end.

(a) Models — the fixed inputs. Each alias is exactly the --model the harness was launched with.

alias	role	repo	revision
pre_teacher	teacher_pre	Qwen/Qwen2.5-Math-1.5B	4a83ca6e4526a4f2da3aa259ec36c259f66b2ab2
post_teacher	teacher_post	deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B	ad9f0ae0864d7fbcd1cd905e3c6c5b069cc8b562
student_init	student_init	Qwen/Qwen2.5-7B-Instruct	a09a35458c702b33eeacc393d103063234e8bc28
pre_teacher_ot	teacher_pre	Qwen/Qwen2.5-1.5B-Instruct	989aa7980e4cf806f80c7fef2b1adb7bc71aa306
post_teacher_ot	teacher_post	open-thoughts/OpenThinker3-1.5B	0ee90a38b29bfac8b8b005da9ae32c59e2943785
student_init_qwen3_4b	student_init	Qwen/Qwen3-4B	1cfa9a7208912126459214e8b04321603b3df60c

(b) Models we trained. Every Direct-OPD run in the study, with the repo and revision its checkpoints live at. A cancelled run published nothing — that is why its evidence in §13.5 is training-only.

run	condition	repo	revision	checkpoints	status
run 1	r1shift	cmpatino/Qwen2.5-7B-Instruct-DirectOPD-R1DistillShift-100	5819e26cab1f099a9b9b9caa38c6340db50b8c67	20, 40, 60, 80, 100	trained; checkpoints published (repo root = step 100)
B-short	otshift_short	cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-10steps	8b20748806f63d5b9f05b3239ffdbddc20a62f2a	2, 4, 6, 8, 10	trained; checkpoints published
B-lowlr	otshift_lowlr	cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-lr2e-7-100	6ad3add5b065a25c9c003d31ea59b1e191f7e3a7	20, 40, 60, 80, 100	trained; checkpoints published
B	otshift	cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-100	—	—	CANCELED at step ~24; no checkpoint was ever published
C	otshift_klfloor	cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-KLfloor-100	—	—	CANCELED at step ~24; no checkpoint was ever published
D	otshift_qwen3_4b	cmpatino/Qwen3-4B-DirectOPD-OpenThinker3Shift-100	—	—	CANCELED at step ~24; no checkpoint was ever published

(c) Datasets and the method itself.

role	repo	revision
data	cmpatino/direct-opd-sft-deepmath-pilot-data	22625ae5db434947195bf862c429cd94504a4809
aime24	HuggingFaceH4/aime_2024	2fe88a2f1091d5048c0f36abc874fb997b3dd99a
aime25	yentinglin/aime_2025	6f71d77b0b89b9dabe07ab466c51df33f514df7f
math500	HuggingFaceH4/MATH-500	6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be
Direct-OPD (method)	https://github.com/BytedTsinghua-SIA/Direct-OPD	3a9d6bd37b00a38e7a9b2959239e4631e5324aea (+ code/opd/phase4_seed.patch (carried from the pilot))

(d) Code, by content hash. The driver was staged into the results repo before every launch, so a run's exact driver is recoverable from the revision it was staged at.

file	role	sha256 (this working copy)
code/opd/run_opd.sh	Direct-OPD training driver	11f7ff5b78892ccc01cca8bc4fe77e9cbc3d9589be63501f1afb53029c3f1b03
code/eval/eval_model.py	evaluation harness (generation + grading)	1720b72e2a8c15e5b0b52a76bd76219d05e582853ae4522610316d566e8d8590
code/eval/aggregate_evals.py	canonical cross-model aggregator	355920975a59f7a52fe01fcd402d486e800a537e1f20fbc4ead4184e0a010201
code/report/build_report.py	this report builder	2f0b3b701d92e2a384d3991b14a9791cff3754a0c0ad8d6ae9664151d163646f

driver staged at results-repo revision	run_opd.sh sha256	when	what changed
a6e5e9924cce0089d0853d557464e1a3a8a51ff3	fbeae2b95bb8b0bcb03a6a68bd639f76cdcee6c3f252db72df213204fd211205	2026-08-25T10:48:37Z	initial staging
2fabdb13ff2e081ec3d906f938ca1b181849c3af	37359fd16a50c01b117f0d6920b9550cb7023841abbec073a1c30edf6a97d02f	2026-08-28T12:52:42Z	exp2b conditions
b4dfdf37d521db816742bd0fd93af48ec5de18e1	11f7ff5b78892ccc01cca8bc4fe77e9cbc3d9589be63501f1afb53029c3f1b03	2026-08-28T14:58:13Z	checkpoint-list driver bug fix: CKPT_STEPS array derived from SAVE_FREQ/TOTAL_TRAINING_STEPS replaces hard-coded '20 40 60 80 100' in the post-train verificatio

(e) The launches themselves. The exact hf jobs run command line of every training launch is stored verbatim, together with the babysitter's per-step tables — which are the only surviving evidence for the three cancelled conditions, since they published no checkpoint. Every one of these files is listed in MANIFEST.json with its sha256 and is uploaded to the results repo under logs/ alongside this bundle:

logs/full_launch_command.txt
logs/launch_smoke_stdout.txt
logs/redirect_launch_commands.txt
logs/exp2b_full_lowlr_steps.tsv
logs/exp2b_full_openthinker_klfloor_steps.tsv
logs/exp2b_full_openthinker_qwen3_4b_steps.tsv
logs/exp2b_full_openthinker_steps.tsv
logs/exp2b_full_short_steps.tsv
logs/exp3_full_raft_steps.tsv
logs/full_steps.tsv

Evaluation launches follow one form (the runbook is code/eval/LAUNCH.md); the reduced-protocol variants differ only in --num-samples/--seeds (AIME) or --limit-problems (MATH-500) and are pushed under their own _sub8 / _m500sub100 aliases so they can never masquerade as canonical units:

# one eval unit
hf jobs uv run -d --image huggingface/trl --secrets HF_TOKEN --flavor a100-large \
  -e HF_HOME=/tmp/hf -e HF_HUB_ENABLE_HF_TRANSFER=1 \
  --label experiment=direct-opd-sft-transfer --label run_id=<run_id> \
  eval_model.py --model <repo-or-alias> --revision <sha> [--subfolder checkpoint-N] \
    --model-alias <alias> --benchmark <aime24|aime25|math500> \
    --output-dir /tmp/exp2-out --skip-if-exists --push

Each training run's own verl artefacts (hydra_config.yaml, hydra_overrides.yaml, run_manifest.json, metrics.jsonl, the gzipped train log) are in the model repo of that run under logs/, and the four 2-step smokes are in the results repo under phase4/smoke/<condition>-<timestamp>/.

(f) The ledger. ledger/cost_ledger.csv — append-only, one row per job, keyed by job id. Every figure in §11 and §14.4 is summed from it at build time, so booking a late job and re-running the build is all it takes to correct the cost of this report; nothing about the cost is frozen into the text.

11.2 Rebuilding this bundle

export HF_HOME=/home/node/local/hf-cache          # HF_TOKEN must be in the environment
/home/node/local/envs/eval-test/bin/python \
  /data/workspaces/direct-opd/exp2-sft-transfer/code/report/build_report.py

# reuse the local cache instead of re-downloading from the Hub:
/home/node/local/envs/eval-test/bin/python \
  /data/workspaces/direct-opd/exp2-sft-transfer/code/report/build_report.py --offline

# the canonical cross-model aggregate (this report reuses its numerics)
/home/node/local/envs/eval-test/bin/python code/eval/aggregate_evals.py --from-hub \
  --results-repo cmpatino/direct-opd-sft-transfer-results \
  --curve-ckpt100-from-primary --output-dir artifacts/eval-agg

The build is idempotent and CPU-only: it downloads (or reuses) every eval unit and every training log, recomputes every statistic from the raw per-problem and per-sample data, regenerates all nine figures, and rewrites aggregate.json, README.md, summary.md, MANIFEST.json and CHECKSUMS.sha256. No number in this report is hand-copied between artifacts, and no number is quoted that does not come from a file listed in MANIFEST.json. Re-running it after the 0 pending unit(s) land is the only action needed to finish the report — every placeholder becomes a measured value and nothing else changes.

---

12. Artifact inventory

12.1 Evaluation units

alias	benchmark	status	problems	samples/problem	passes	note
pre_teacher	aime24	✅ found	30	32	sample32	π_pre baseline (native 3,200-token cap)
pre_teacher	aime25	✅ found	30	32	sample32	π_pre baseline (native 3,200-token cap)
pre_teacher	math500	✅ found	500	4	greedy, sample4	π_pre baseline (native 3,200-token cap)
post_teacher	aime24	✅ found	30	32	sample32	π_post; IMPORTED from the pilot results repo
post_teacher	aime25	✅ found	30	32	sample32	π_post; IMPORTED from the pilot results repo
post_teacher	math500	✅ found	500	4	greedy, sample4	π_post
student_init	aime24	✅ found	30	32	sample32	student baseline, 32 samples
student_init	aime25	✅ found	30	32	sample32	student baseline, 32 samples
student_init	math500	✅ found	500	4	greedy, sample4	student baseline, greedy + sample4
opd_student_r1shift-ckpt20	aime24	✅ found	30	8	sample32	checkpoint curve, 8 samples (seeds 0–7)
opd_student_r1shift-ckpt40	aime24	✅ found	30	8	sample32	checkpoint curve, 8 samples (seeds 0–7)
opd_student_r1shift-ckpt60	aime24	✅ found	30	8	sample32	checkpoint curve, 8 samples (seeds 0–7)
opd_student_r1shift-ckpt80	aime24	✅ found	30	8	sample32	checkpoint curve, 8 samples (seeds 0–7)
opd_student_r1shift-ckpt20	math500	✅ found	500	4	greedy, sample4	checkpoint curve, full 500-problem protocol
opd_student_r1shift-ckpt40	math500	✅ found	500	4	greedy, sample4	checkpoint curve, full 500-problem protocol
opd_student_r1shift	aime24	✅ found	30	8	sample32	PRIMARY endpoint, REDUCED protocol (8 samples, seeds 0–7)
opd_student_r1shift	aime25	✅ found	30	8	sample32	PRIMARY endpoint, REDUCED protocol (8 samples, seeds 0–7)
opd_student_r1shift_m500sub100	math500	✅ found	100	4	greedy, sample4	PRIMARY endpoint, REDUCED protocol (100-problem subset)
opd_student_r1shift-ckpt40-full	aime24	✅ found	30	32	sample32	A1: run-1 ckpt-40 at the FULL protocol (32 samples)
opd_student_r1shift-ckpt40-full	aime25	✅ found	30	32	sample32	A1: run-1 ckpt-40 at the FULL protocol (32 samples)
opd_student_r1shift-ckpt40-full	math500	✅ found	500	4	greedy, sample4	A1: run-1 ckpt-40 at the FULL protocol (500 problems)
pre_teacher_ot	aime24	✅ found	30	32	sample32	exp2b pi_pre (Qwen2.5-1.5B-Instruct), full 31,744 cap
pre_teacher_ot	aime25	✅ found	30	32	sample32	exp2b pi_pre, full 31,744 cap
pre_teacher_ot	math500	✅ found	500	4	greedy, sample4	exp2b pi_pre, full 31,744 cap
post_teacher_ot	aime24	✅ found	30	32	sample32	exp2b pi_post (OpenThinker3-1.5B), full 31,744 cap
post_teacher_ot	aime25	✅ found	30	32	sample32	exp2b pi_post, full 31,744 cap
post_teacher_ot	math500	✅ found	500	4	greedy, sample4	exp2b pi_post, full 31,744 cap
opd_student_otshift-short-ckpt4	aime24	✅ found	30	32	sample32	B-short step-4 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt4	aime25	✅ found	30	32	sample32	B-short step-4 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt4	math500	✅ found	500	4	greedy, sample4	B-short step-4 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt8	aime24	✅ found	30	32	sample32	B-short step-8 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt8	aime25	✅ found	30	32	sample32	B-short step-8 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt8	math500	✅ found	500	4	greedy, sample4	B-short step-8 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt10	aime24	✅ found	30	8	sample32	B-short step-10 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt10	aime25	✅ found	30	8	sample32	B-short step-10 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift-short-ckpt10	math500	✅ found	100	4	greedy, sample4	B-short step-10 endpoint, full protocol (reduced if non-terminating) — measured under the REDUCED protocol as opd_student_otshift-short-ckpt10_m500sub100
opd_student_otshift_lowlr-ckpt20	aime24	✅ found	30	32	sample32	B-lowlr step-20 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr-ckpt20	aime25	✅ found	30	32	sample32	B-lowlr step-20 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr-ckpt20	math500	✅ found	500	4	greedy, sample4	B-lowlr step-20 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr-ckpt40	aime24	✅ found	30	32	sample32	B-lowlr step-40 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr-ckpt40	aime25	✅ found	30	32	sample32	B-lowlr step-40 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr-ckpt40	math500	✅ found	500	4	greedy, sample4	B-lowlr step-40 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr-ckpt60	aime24	✅ found	30	8	sample32	B-lowlr checkpoint curve, 8 samples (seeds 0-7)
opd_student_otshift_lowlr-ckpt80	aime24	✅ found	30	8	sample32	B-lowlr checkpoint curve, 8 samples (seeds 0-7)
opd_student_otshift_lowlr	aime24	✅ found	30	8	sample32	B-lowlr step-100 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr	aime25	✅ found	30	8	sample32	B-lowlr step-100 endpoint, full protocol (reduced if non-terminating)
opd_student_otshift_lowlr	math500	✅ found	100	4	greedy, sample4	B-lowlr step-100 endpoint, full protocol (reduced if non-terminating) — measured under the REDUCED protocol as opd_student_otshift_lowlr_m500sub100
raft_teacher	math500	✅ found	500	4	greedy, sample4	exp3 pi_post^RAFT, gate G2 primary (full 500-problem protocol)
raft_teacher	aime24	✅ found	30	32	sample32	exp3 pi_post^RAFT, gate G2 secondary
raft_teacher	aime25	✅ found	30	32	sample32	exp3 pi_post^RAFT, gate G2 secondary
raft_teacher	teacher_eval	✅ found	512	4	greedy, sample4	exp3 pi_post^RAFT, in-distribution probe (pilot pool held-out 512-prompt split)
pre_teacher_ot	teacher_eval	✅ found	512	4	greedy, sample4	exp3 pi_pre baseline on the same in-distribution probe
opd_student_raftshift-ckpt20	aime24	✅ found	30	8	sample32	RAFT step-20 checkpoint curve, 8 samples (seeds 0-7)
opd_student_raftshift-ckpt20	math500	✅ found	500	4	greedy, sample4	RAFT step-20 endpoint, full protocol
opd_student_raftshift-ckpt40	aime24	✅ found	30	8	sample32	RAFT step-40 checkpoint curve, 8 samples (seeds 0-7)
opd_student_raftshift-ckpt40	math500	✅ found	500	4	greedy, sample4	RAFT step-40 endpoint, full protocol
opd_student_raftshift-ckpt60	aime24	✅ found	30	8	sample32	RAFT step-60 checkpoint curve, 8 samples (seeds 0-7)
opd_student_raftshift-ckpt60	math500	✅ found	500	4	greedy, sample4	RAFT step-60 endpoint, full protocol
opd_student_raftshift-ckpt80	aime24	✅ found	30	8	sample32	RAFT step-80 checkpoint curve, 8 samples (seeds 0-7)
opd_student_raftshift-ckpt80	math500	✅ found	500	4	greedy, sample4	RAFT step-80 endpoint, full protocol
opd_student_raftshift	aime24	✅ found	30	32	sample32	RAFT step-100 endpoint, full protocol
opd_student_raftshift	aime25	✅ found	30	32	sample32	RAFT step-100 endpoint, full protocol
opd_student_raftshift	math500	✅ found	500	4	greedy, sample4	RAFT step-100 endpoint, full protocol
opd_student_r1shift-ckpt60	math500	⛔ skipped	—	—	—	cost-forced skip: re-priced $115 high, over the $8/checkpoint gate
opd_student_r1shift-ckpt80	math500	⛔ skipped	—	—	—	cost-forced skip: re-priced $124 high, over the $8/checkpoint gate
opd_student_r1shift	math500	⛔ skipped	—	—	—	superseded by the 100-problem subset unit: full 500-problem protocol re-priced $100/$118 high
opd_student_otshift	aime24	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift	aime25	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift	math500	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift-ckpt20	aime24	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift-ckpt40	aime24	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift-ckpt60	aime24	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift-ckpt80	aime24	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift-ckpt20	math500	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift-ckpt40	math500	⛔ canceled / dropped	—	—	—	condition B CANCELED at step 24 after termination collapse — collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it ($50) would only replicate run 1's collapsed-checkpoint evaluations; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor	aime24	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor	aime25	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor	math500	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor-ckpt20	aime24	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor-ckpt40	aime24	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor-ckpt60	aime24	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor-ckpt80	aime24	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor-ckpt20	math500	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_klfloor-ckpt40	math500	⛔ canceled / dropped	—	—	—	condition C CANCELED at step ~24 after termination collapse — collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b	aime24	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b	aime25	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b	math500	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b-ckpt20	aime24	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b-ckpt40	aime24	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b-ckpt60	aime24	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b-ckpt80	aime24	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b-ckpt20	math500	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_otshift_qwen3_4b-ckpt40	math500	⛔ canceled / dropped	—	—	—	condition D CANCELED at step ~24 after termination collapse — collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short because thinking-mode evaluations cost ~$65/unit; no checkpoint was ever published, so no evaluation unit can exist
opd_student_r1shift-full	aime24	⛔ canceled / dropped	—	—	—	tier A2 DROPPED by the user on 2026-08-26 (PREREGISTRATION E4) to keep condition D inside the $500 cap; run 1's ckpt-100 keeps its logged reduced-protocol asterisk
student_init_qwen3_4b	aime24	⛔ canceled / dropped	—	—	—	condition-D baseline: D was trimmed to aime24 + math500 on 2026-08-26 (E4) and then CANCELED outright on 2026-08-28 after collapsing, so its baseline was never launched (thinking-mode evaluations were priced at ~$35-40 per benchmark)
opd_student_r1shift-full	aime25	⛔ canceled / dropped	—	—	—	tier A2 DROPPED by the user on 2026-08-26 (PREREGISTRATION E4) to keep condition D inside the $500 cap; run 1's ckpt-100 keeps its logged reduced-protocol asterisk
student_init_qwen3_4b	aime25	⛔ canceled / dropped	—	—	—	condition-D baseline: D was trimmed to aime24 + math500 on 2026-08-26 (E4) and then CANCELED outright on 2026-08-28 after collapsing, so its baseline was never launched (thinking-mode evaluations were priced at ~$35-40 per benchmark)
opd_student_r1shift-full	math500	⛔ canceled / dropped	—	—	—	tier A2 DROPPED by the user on 2026-08-26 (PREREGISTRATION E4) to keep condition D inside the $500 cap; run 1's ckpt-100 keeps its logged reduced-protocol asterisk
student_init_qwen3_4b	math500	⛔ canceled / dropped	—	—	—	condition-D baseline: D was trimmed to aime24 + math500 on 2026-08-26 (E4) and then CANCELED outright on 2026-08-28 after collapsing, so its baseline was never launched (thinking-mode evaluations were priced at ~$35-40 per benchmark)
opd_student_otshift-short-ckpt10_m500sub100	math500	✅ found	100	4	greedy, sample4	exp2b REDUCED-protocol fallback unit (the checkpoint did not terminate at the 31,744 cap)
opd_student_otshift_lowlr_m500sub100	math500	✅ found	100	4	greedy, sample4	exp2b REDUCED-protocol fallback unit (the checkpoint did not terminate at the 31,744 cap)

Sample-level alignment audit (aggregate_evals.audit_alignment, run per comparison group): OK.

• group full: ok=True
• group curve8: ok=True
• group sub100: ok=True
• group exp2b-full: ok=True — aime24: grids differ but are NESTED {'opd_student_otshift-short-ckpt10': 240, 'opd_student_otshift-short-ckpt4': 960, 'opd_student_otshift-short-ckpt8': 960, 'opd_student_otshift_lowlr': 240, 'opd_student_otshift_lowlr-ckpt20': 960, 'opd_student_otshift_lowlr-ckpt40': 960, 'opd_student_r1shift-ckpt40-full': 960, 'post_teacher_ot': 960, 'pre_teacher_ot': 960} — expected when diagnostic curve units (8 samples/problem) sit beside primary units; aime25: grids differ but are NESTED {'opd_student_otshift-short-ckpt10': 240, 'opd_student_otshift-short-ckpt4': 960, 'opd_student_otshift-short-ckpt8': 960, 'opd_student_otshift_lowlr': 240, 'opd_student_otshift_lowlr-ckpt20': 960, 'opd_student_otshift_lowlr-ckpt40': 960, 'opd_student_r1shift-ckpt40-full': 960, 'post_teacher_ot': 960, 'pre_teacher_ot': 960} — expected when diagnostic curve units (8 samples/problem) sit beside primary units
• group unexpected: ok=True
• group exp2b-curve8: ok=True
• group exp3-full: ok=True
• group exp3-curve8: ok=True

12.2 This bundle

aggregate.json        every statistic in this report, machine-readable
summary.md            the same, rendered as tables (also pushed to evals/aggregate/)
README.md             this file
figures/f1..f5*.png   Phase-4 training figures, reused verbatim from artifacts/figures/
figures/f6*.png       student gain vs OPD step, paired CIs, collapse band
figures/f7*.png       teacher gain vs student gain
MANIFEST.json         every input file, its sha256 and its repo revision
CHECKSUMS.sha256      sha256 of every file in this bundle

MANIFEST.json lists 186 input files. Large inputs that already live in the results repo (the generations.parquet of every unit) are referenced by repo + revision + sha256, not duplicated here.

---

13. Extension exp2b — a second teacher pair, three cancelled conditions, two redirects

Pre-registered PREREGISTRATION.md sections E1-E3 (2026-08-26), extended by §E5 (2026-08-28). Budget cap raised to $500 cumulative. Sections 0–12 above are run 1 and are unaffected by anything here.

Status: 32 of 32 live exp2b units are on the Hub, and a further 33 pre-registered units are canceled or dropped — they can never exist, because the runs that would have produced them were stopped before their first checkpoint save (§13.5) or the tier was dropped by the user. Every cell below is a measured value; nothing here is an estimate and nothing is outstanding.

13.1 The new teacher pair, and why it needs no cap deviation

• π_pre = Qwen/Qwen2.5-1.5B-Instruct @ 989aa7980e4cf806f80c7fef2b1adb7bc71aa306
• π_post = open-thoughts/OpenThinker3-1.5B @ 0ee90a38b29bfac8b8b005da9ae32c59e2943785 — SFT-only (7 epochs on OpenThoughts3-1.2M) from that same π_pre, i.e. the same family and post-training lineage as the 7B student.
• shift key openthinker3_sft

Both models have max_position_embeddings 32,768 and the longest prompt under their (identical) chat template is 872 tokens, so 872 + 31,744 = 32,616 fits and neither carries a cap deviation — unlike run 1's pi_pre.

model	max_position_embeddings	longest prompt	prompt + 31,744	cap deviation
pre_teacher_ot	32,768	872 (MATH-500)	32,616	none
post_teacher_ot	32,768	872 (MATH-500)	32,616	none
(run 1) pre_teacher	4,096	871 (MATH-500)	32,615 — does not fit	--max-tokens 3200, on every unit

This is the single biggest measurement difference between run 1 and exp2b: run 1's AIME teacher gain shrank from +24.38 pp to +3.65 [−1.04, +9.17] once π_post was held to π_pre's 3,200-token budget (§8's cap-sensitivity view). The exp2b pair has no such confound — both models are measured at the same, full, pre-registered cap.

13.2 Teacher gains for the new pair — the exp2b premise

benchmark	pass	π_pre (pp)	π_post (pp)	gain (pp)	95 % CI	p
aime24	sample32	2.188	53.958	+51.771	[+38.646, +64.375]	p<0.0001
aime25	sample32	0.417	43.021	+42.604	[+28.539, +56.667]	p<0.0001
math500	greedy	45.400	82.800	+37.400	[+32.400, +42.400]	p<0.0001
math500	sample4	38.750	88.800	+50.050	[+46.650, +53.400]	p<0.0001

TEACHER-GAIN GATE (AIME 2024): PASS — +51.771 pp [+38.646, +64.375].

PREREGISTRATION E3: paired post-pre on AIME24 must be > 0 with a 95 % CI excluding 0 (expected ~ +49 pp from the published 3.0 -> 52.0)

These are the paired gains the gate is stated on. They are what makes the rest of this section a result rather than a null: the shift this pair encodes is real and large, so when four separate students fail to inherit any of it, the explanation cannot be that the shift had nothing to give.

13.3 A1 — run-1 ckpt-40 at the FULL protocol

ckpt-40 is the last pre-collapse checkpoint of run 1 and it terminates (0.4 % truncation). It was only ever measured on the 8-sample curve protocol; at the full protocol it becomes the study's one ckpt-vs-init comparison that needs no caveat at all — same 32 seeds, same 500 problems, on both sides.

Alias opd_student_r1shift-ckpt40-full (a separate directory, so the published 8-sample curve units at opd_student_r1shift-ckpt40/* are untouched), baseline student_init.

benchmark	pass	samples/problem	full protocol?	ckpt-40 (pp)	student_init (pp)	gain (pp)	n
aime24	sample32	32	yes	10.000	12.188	-2.188 [-4.583, -0.310] p=0.0152	30
aime25	sample32	32	yes	7.812	6.979	+0.833 [-1.667, +3.750] p=0.5226	30
math500	greedy	4	yes	74.600	75.400	-0.800 [-4.200, +2.600] p=0.6040	500
math500	sample4	4	yes	73.450	74.350	-0.900 [-2.650, +0.800] p=0.2972	500

13.4 A2 — run-1 ckpt-100 at the FULL protocol: DROPPED

DROPPED by the user on 2026-08-26 (PREREGISTRATION E4) to keep condition D inside the $500 cap; run 1's ckpt-100 keeps its logged reduced-protocol asterisk. Its three roster rows read canceled, never pending.

13.5 Conditions B, C and D — CANCELED after termination collapse (training-only)

All three were launched on 2026-08-28 and all three collapsed. Their pre-registered first checkpoint save is at step 20, and all three crossed the collapse-watch threshold before it, so none of them published a policy that could be evaluated. They were cancelled at step ~22–25 by user decision (PREREGISTRATION §E5) and their GPU time was booked on the wall-clock basis. What follows is therefore training-only evidence: no accuracy number for B, C or D exists anywhere in this report, and none is estimated.

condition	teacher pair	student	lr	KL regime	resp cap	steps reached	length runaway	collapse onset	checkpoints	hypothesis	verdict
B — otshift	openthinker3_sft	Qwen2.5-7B-Instruct	1e-6	adaptive [0.5, 2.5], eps 0.01	3,328	25 / 100	10	12	none	H2	UNTESTED
C — otshift_klfloor	openthinker3_sft	Qwen2.5-7B-Instruct	1e-6	CONSTANT 2.5 (ADAPTIVE_KL_LOSS_MIN_COEF = MAX = 2.5)	3,328	24 / 100	10	12	none	H3	REFUTED
D — otshift_qwen3_4b	openthinker3_sft	Qwen3-4B (thinking)	1e-6	adaptive [0.5, 2.5], eps 0.01	4,096	22 / 100	17	17	none	H4	REFUTED

Per-step snapshots at steps 1 / 5 / 10 / 15 / 20, read from the babysitter's per-step tables (the only surviving record of a cancelled run — nothing was ever uploaded):

condition	step	response len (mean)	clip ratio	actor entropy	weighted shift reward	KL coef	grad norm
run 1	1	339	0.000	0.156	-0.0078	2.475	4.24
run 1	5	373	0.000	0.139	-0.0060	2.377	1.83
run 1	10	378	0.000	0.162	-0.0053	2.261	1.59
run 1	15	421	0.000	0.187	-0.0047	2.150	1.40
run 1	20	399	0.000	0.171	-0.0041	2.045	1.53
run 1	40	519	0.000	0.217	-0.0034	1.672	0.92
run 1	60	1181	0.219	0.134	-0.0006	1.368	0.85
run 1	61	2489	0.680	0.069	-0.0003	1.354	0.28
run 1	80	3311	0.992	0.094	-0.0005	1.119	0.46
run 1	100	2614	0.699	0.667	+0.0026	1.118	2.10
B	1	339	0.000	0.156	-0.0354	2.475	3.43
B	5	433	0.000	0.107	-0.0284	2.377	26.53
B	10	882	0.098	0.075	-0.0150	2.261	21.30
B	12	3059	0.816	0.030	-0.0037	2.216	2.40
B	15	3328	1.000	0.032	-0.0031	2.150	0.60
B	20	3328	1.000	0.080	-0.0029	2.045	1.24
B	25	3328	1.000	0.088	-0.0037	1.945	0.88
C	1	339	0.000	0.156	-0.0354	2.500	3.43
C	5	445	0.000	0.103	-0.0273	2.500	23.99
C	10	1082	0.164	0.065	-0.0120	2.500	18.38
C	12	3118	0.836	0.031	-0.0036	2.500	1.91
C	15	3328	1.000	0.033	-0.0032	2.500	0.69
C	20	3328	1.000	0.084	-0.0033	2.500	1.45
C	24	3328	1.000	0.077	-0.0043	2.500	0.92
D	1	1707	0.051	0.319	-0.0143	2.475	4.42
D	5	2003	0.055	0.241	-0.0095	2.377	3.76
D	10	2469	0.105	0.289	-0.0058	2.261	2.18
D	15	2637	0.152	0.305	-0.0043	2.150	2.27
D	17	3724	0.645	0.311	-0.0035	2.107	3.82
D	20	4082	0.977	0.336	+0.0026	2.128	2.66
D	22	4089	0.992	0.389	-0.0011	2.128	1.58
B-short	1	339	0.000	0.156	-0.0354	2.475	3.43
B-short	5	439	0.000	0.109	-0.0281	2.377	9.40
B-short	10	1521	0.289	0.048	-0.0085	2.261	14.82
B-lowlr	1	339	0.000	0.156	-0.0354	2.475	3.43
B-lowlr	5	403	0.000	0.115	-0.0304	2.377	2.87
B-lowlr	10	419	0.004	0.122	-0.0298	2.261	2.27
B-lowlr	15	486	0.000	0.114	-0.0257	2.150	3.75
B-lowlr	20	462	0.000	0.119	-0.0274	2.045	18.77
B-lowlr	40	613	0.008	0.129	-0.0227	1.672	7.41
B-lowlr	42	787	0.035	0.154	-0.0195	1.639	10.89
B-lowlr	48	2455	0.504	0.051	-0.0059	1.543	6.25
B-lowlr	60	3328	1.000	0.041	-0.0041	1.368	0.51
B-lowlr	80	3318	0.996	0.112	-0.0044	1.119	1.15
B-lowlr	100	3328	1.000	0.169	-0.0038	0.915	1.36

Grad-norm peaks and the KL controller. The two spikes that precede each collapse are the clearest early-warning signal in the whole study.

condition	grad-norm peak (step)	spikes ≥ 10	KL coef first → last	constant?	weighted shift reward first → last	steps with a negative reward
run 1	4.2 (step 1)	none	2.475 → 1.118	no	-0.0078 → +0.0026	90 / 100
B	26.5 (step 5)	27@5, 13@9, 21@10	2.475 → 1.945	no	-0.0354 → -0.0037	25 / 25
C	24.0 (step 5)	24@5, 11@6, 12@9, 18@10	2.500 → 2.500	yes	-0.0354 → -0.0043	24 / 24
D	4.4 (step 1)	none	2.475 → 2.128	no	-0.0143 → -0.0011	19 / 22
B-short	15.9 (step 9)	10@4, 16@9, 15@10	2.475 → 2.261	no	-0.0354 → -0.0085	10 / 10
B-lowlr	49.8 (step 21)	13@19, 19@20, 50@21, 18@22, 12@23, 10@41	2.475 → 0.915	no	-0.0354 → -0.0038	100 / 100

The two hypotheses these runs did settle, and they settled them by refutation.

• H2 — UNTESTED (condition B): Collapsed at step 12; the first checkpoint save is at step 20, i.e. after the collapse, so no pre-collapse policy exists to evaluate. Recorded at the time: UNTESTED — the run never produced a pre-collapse checkpoint and was cancelled before any evaluation. H2 is carried by the B-short and B-lowlr redirects instead.
• H3 — REFUTED (condition C): The KL coefficient was constant at 2.5 for all 24 recorded steps and the clip ratio still crossed 0.5 at step 12. Recorded at the time: REFUTED — the KL coefficient was 2.500 at every step and the run still collapsed, on the same step as B. A constant KL coefficient does not prevent termination collapse.
• H4 — REFUTED (condition D): H4's premise was that the shift rewards the thinking student's native distribution (weighted_reward_mean > 0 at step 1); the measured value is -0.01427, and the run collapsed at step 17 anyway. Recorded at the time: REFUTED — H4's own premise failed first: the step-1 weighted shift reward on the THINKING student was NEGATIVE, the same signature run 1 showed, and the run then collapsed like every other. The thinking student delayed the sink by ~5 steps; it did not avoid it.

Note what H3's refutation costs the fix list: the KL brake at its maximum does not prevent the sink. C held its coefficient at 2.5 at every single step — the driver's kl_controller clamps max(min, min(max, x)), and min == max pins it — and it collapsed on the same step as B, with a trajectory that matches B's to three decimal places for the first nine steps. A stronger anchor is not the answer, because the anchor was already at its strongest.

13.6 B-short — OpenThinker3 shift, 10 steps, save every 2

• repo cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-10steps @ 8b20748806f63d5b (pinned (training COMPLETE 2026-08-28, job 6a91a23c))
• baseline student_init · teacher pair post_teacher_ot − pre_teacher_ot · lr 1e-6 · KL adaptive [0.5, 2.5], eps 0.01
• Captures the policies B and C never saved. Trajectory reproduces B/C exactly (same seed): clip 0 through step 8, then response mean 474 -> 1,521 and clip 0.01 -> 0.29 at step 10.
• Did ANY held-out capability move before the termination sink? ckpt-4 and ckpt-8 are clean pre-collapse policies (clip_ratio 0 through step 8); ckpt-10 is the onset step itself.

Training record.

10 of 10 pre-registered steps recorded (source: metrics.jsonl (model repo)). Collapse onset (first clip_ratio > 0.5): none; length-runaway marker (mean rollout length past 2x its step-1 value): step 10; peak clip ratio 0.289. Grad-norm peak 15.9 at step 9; KL coefficient 2.475 → 2.261; weighted shift reward -0.0354 → -0.0085, negative on 10 of 10 steps.

Note the two markers disagree, and the disagreement is the point: by the pre-registered collapse-watch rule (clip_ratio > 0.5) this run never collapsed, but the mean rollout length had already more than doubled by step 10 (peak clip 0.289). The onset signature is present; the run simply ended before the clip ratio caught up.

condition	step	response len (mean)	clip ratio	actor entropy	weighted shift reward	KL coef	grad norm
B-short	1	339	0.000	0.156	-0.0354	2.475	3.43
B-short	5	439	0.000	0.109	-0.0281	2.377	9.40
B-short	10	1521	0.289	0.048	-0.0085	2.261	14.82

Held-out gains, per evaluated checkpoint (paired per-problem bootstrap vs student_init; the protocol is detected from each unit, never assumed)

step	unit	benchmark	protocol	pairing	ckpt (pp)	baseline (pp)	gain (pp)	n
4	opd_student_otshift-short-ckpt4	aime24	full	seeds 0–31 (PRIMARY)	11.46	12.19	-0.729 [-2.292, +0.521] p=0.2662	30
4	opd_student_otshift-short-ckpt4	aime25	full	seeds 0–31 (PRIMARY)	7.40	6.98	+0.417 [-1.042, +1.875] p=0.5542	30
4	opd_student_otshift-short-ckpt4	math500	full	greedy	74.80	75.40	-0.600 [-3.200, +2.000] p=0.5996	500
4	opd_student_otshift-short-ckpt4	math500	full	sample4 (PRIMARY)	73.85	74.35	-0.500 [-2.050, +1.050] p=0.5036	500
8	opd_student_otshift-short-ckpt8	aime24	full	seeds 0–31 (PRIMARY)	11.04	12.19	-1.146 [-3.229, +0.625] p=0.2002	30
8	opd_student_otshift-short-ckpt8	aime25	full	seeds 0–31 (PRIMARY)	7.81	6.98	+0.833 [-0.833, +2.500] p=0.2992	30
8	opd_student_otshift-short-ckpt8	math500	full	greedy	75.80	75.40	+0.400 [-2.600, +3.400] p=0.7314	500
8	opd_student_otshift-short-ckpt8	math500	full	sample4 (PRIMARY)	75.15	74.35	+0.800 [-0.950, +2.550] p=0.3598	500
10	opd_student_otshift-short-ckpt10	aime24	reduced	seeds 0–7 (PRIMARY)	10.42	13.75	-3.333 [-7.500, +0.417] p=0.0722	30
10	opd_student_otshift-short-ckpt10	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	10.42	12.19	-1.771 [-4.375, +0.521] p=0.1170	30
10	opd_student_otshift-short-ckpt10	aime25	reduced	seeds 0–7 (PRIMARY)	10.00	6.25	+3.750 [-0.833, +8.750] p=0.1048	30
10	opd_student_otshift-short-ckpt10	aime25	reduced	vs the full 32-sample baseline (unpaired-in-samples)	10.00	6.98	+3.021 [-0.625, +7.187] p=0.1022	30
10	opd_student_otshift-short-ckpt10_m500sub100	math500	reduced-100-problem-subset	greedy	86.00	84.00	+2.000 [-5.000, +9.000] p=0.4930	100
10	opd_student_otshift-short-ckpt10_m500sub100	math500	reduced-100-problem-subset	sample4 (PRIMARY)	78.25	77.75	+0.500 [-3.750, +4.750] p=0.7828	100

Truncation at the 31,744-token evaluation cap, per checkpoint: step 4 aime24 1.9 %; step 4 aime25 1.0 %; step 4 math500 0.2 %; step 8 aime24 2.8 %; step 8 aime25 1.1 %; step 8 math500 0.8 %; step 10 aime24 44.2 %; step 10 aime25 41.2 %; step 10 math500 60.5 %.

⚠ Read the high-truncation rows as termination artifacts, not as capability being destroyed. step 10 on math500 is 60.5 % truncated and scores +0.50 pp. A policy that never emits a stop token produces a 31,744-token sample with no final answer in it, and the grader scores that as wrong however much the model knows — B-short's ckpt-10 is the control for exactly this: it is 41–60 % truncated and its accuracy is nonetheless preserved, because its answers still appear before the loop begins. The deeper into the sink a checkpoint is, the more of its samples never reach an answer at all.

Transfer ratio at the terminal checkpoint (student gain ÷ the OpenThinker3 pair's teacher gain, five guards)

benchmark	teacher gain	student gain	numerator CI excludes 0	ratio	reason
aime24	+51.771 [+38.646, +64.375]	-3.333 [-7.500, +0.417]	False	null	guard: student_gain = -3.333 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BOTH gains are positive; a non-positive nu
aime25	+42.604 [+28.539, +56.667]	+3.750 [-0.833, +8.750]	False	null	guard (exp2b, new): student_gain = 3.750 pp has CI95 [-0.833, 8.750] pp which INCLUDES zero — the numerator is statistically indistinguishable from 'n
math500	+50.050 [+46.650, +53.400]	+0.500 [-3.750, +4.750]	False	null	guard (exp2b, new): student_gain = 0.500 pp has CI95 [-3.750, 4.750] pp which INCLUDES zero — the numerator is statistically indistinguishable from 'n

H2 (pre-collapse form) verdict: NOT SUPPORTED

• gain_on_at_least_one_benchmark — FAILED: no benchmark shows a positive paired gain whose 95 % CI excludes 0

13.7 B-lowlr — OpenThinker3 shift at OPTIM_LR 2e-7, 100 steps

• repo cmpatino/Qwen2.5-7B-Instruct-DirectOPD-OpenThinker3Shift-lr2e-7-100 @ 6ad3add5b065a25c (resolved from main at build time (training COMPLETE 2026-08-28, job 6a919e1c, 100/100 steps))
• baseline student_init · teacher pair post_teacher_ot − pre_teacher_ot · lr 2e-7 (logged DEVIATION from the pinned 1e-6) · KL adaptive [0.5, 2.5], eps 0.01
• The 'can it be made to work' run: smaller steps so the policy can follow the gentle shift gradient without the grad-norm-spike-driven jump into the repetition sink (spikes of 26.5 and 21 preceded B's and C's collapses).
• H5: with lr 2e-7 the run does NOT collapse (clip_ratio < 0.5 through step 100) AND ckpt-100 shows a paired gain on at least one held-out benchmark.

Training record.

100 of 100 pre-registered steps recorded (source: metrics.jsonl (model repo)). Collapse onset (first clip_ratio > 0.5): 48; length-runaway marker (mean rollout length past 2x its step-1 value): step 42; peak clip ratio 1.000. Grad-norm peak 49.8 at step 21; KL coefficient 2.475 → 0.915; weighted shift reward -0.0354 → -0.0038, negative on 100 of 100 steps.

condition	step	response len (mean)	clip ratio	actor entropy	weighted shift reward	KL coef	grad norm
B-lowlr	1	339	0.000	0.156	-0.0354	2.475	3.43
B-lowlr	5	403	0.000	0.115	-0.0304	2.377	2.87
B-lowlr	10	419	0.004	0.122	-0.0298	2.261	2.27
B-lowlr	15	486	0.000	0.114	-0.0257	2.150	3.75
B-lowlr	20	462	0.000	0.119	-0.0274	2.045	18.77
B-lowlr	40	613	0.008	0.129	-0.0227	1.672	7.41
B-lowlr	42	787	0.035	0.154	-0.0195	1.639	10.89
B-lowlr	48	2455	0.504	0.051	-0.0059	1.543	6.25
B-lowlr	60	3328	1.000	0.041	-0.0041	1.368	0.51
B-lowlr	80	3318	0.996	0.112	-0.0044	1.119	1.15
B-lowlr	100	3328	1.000	0.169	-0.0038	0.915	1.36

Held-out gains, per evaluated checkpoint (paired per-problem bootstrap vs student_init; the protocol is detected from each unit, never assumed)

step	unit	benchmark	protocol	pairing	ckpt (pp)	baseline (pp)	gain (pp)	n
20	opd_student_otshift_lowlr-ckpt20	aime24	full	seeds 0–31 (PRIMARY)	12.08	12.19	-0.104 [-2.396, +1.875] p=0.9050	30
20	opd_student_otshift_lowlr-ckpt20	aime25	full	seeds 0–31 (PRIMARY)	6.88	6.98	-0.104 [-1.354, +1.042] p=0.8058	30
20	opd_student_otshift_lowlr-ckpt20	math500	full	greedy	74.00	75.40	-1.400 [-3.800, +1.000] p=0.2108	500
20	opd_student_otshift_lowlr-ckpt20	math500	full	sample4 (PRIMARY)	73.50	74.35	-0.850 [-2.300, +0.550] p=0.2170	500
40	opd_student_otshift_lowlr-ckpt40	aime24	full	seeds 0–31 (PRIMARY)	11.46	12.19	-0.729 [-2.917, +0.833] p=0.4350	30
40	opd_student_otshift_lowlr-ckpt40	aime25	full	seeds 0–31 (PRIMARY)	7.40	6.98	+0.417 [-1.979, +2.396] p=0.6220	30
40	opd_student_otshift_lowlr-ckpt40	math500	full	greedy	77.20	75.40	+1.800 [-1.200, +4.800] p=0.2088	500
40	opd_student_otshift_lowlr-ckpt40	math500	full	sample4 (PRIMARY)	74.65	74.35	+0.300 [-1.350, +2.000] p=0.7118	500
60	opd_student_otshift_lowlr-ckpt60	aime24	reduced	seeds 0–7 (PRIMARY)	9.17	13.75	-4.583 [-10.000, +0.000] p=0.0334	30
60	opd_student_otshift_lowlr-ckpt60	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	9.17	12.19	-3.021 [-7.083, -0.104] p=0.0342	30
80	opd_student_otshift_lowlr-ckpt80	aime24	reduced	seeds 0–7 (PRIMARY)	11.25	13.75	-2.500 [-6.667, +1.250] p=0.1670	30
80	opd_student_otshift_lowlr-ckpt80	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	11.25	12.19	-0.938 [-4.271, +2.708] p=0.5558	30
100	opd_student_otshift_lowlr	aime24	reduced	seeds 0–7 (PRIMARY)	11.25	13.75	-2.500 [-7.917, +2.500] p=0.3024	30
100	opd_student_otshift_lowlr	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	11.25	12.19	-0.938 [-5.312, +2.917] p=0.6578	30
100	opd_student_otshift_lowlr	aime25	reduced	seeds 0–7 (PRIMARY)	7.50	6.25	+1.250 [-2.500, +4.583] p=0.4058	30
100	opd_student_otshift_lowlr	aime25	reduced	vs the full 32-sample baseline (unpaired-in-samples)	7.50	6.98	+0.521 [-2.604, +3.542] p=0.6892	30
100	opd_student_otshift_lowlr_m500sub100	math500	reduced-100-problem-subset	greedy	54.00	84.00	-30.000 [-40.000, -20.000] p<0.0001	100
100	opd_student_otshift_lowlr_m500sub100	math500	reduced-100-problem-subset	sample4 (PRIMARY)	49.00	77.75	-28.750 [-35.000, -22.744] p<0.0001	100

Truncation at the 31,744-token evaluation cap, per checkpoint: step 20 aime24 1.8 %; step 20 aime25 0.6 %; step 20 math500 0.4 %; step 40 aime24 3.1 %; step 40 aime25 0.6 %; step 40 math500 0.9 %; step 60 aime24 88.8 %; step 80 aime24 98.8 %; step 100 aime24 99.6 %; step 100 aime25 100.0 %; step 100 math500 100.0 %.

⚠ Read the high-truncation rows as termination artifacts, not as capability being destroyed. step 60 on aime24 is 88.8 % truncated and scores -4.58 pp; step 80 on aime24 is 98.8 % truncated and scores -2.50 pp; step 100 on aime24 is 99.6 % truncated and scores -2.50 pp; step 100 on aime25 is 100.0 % truncated and scores +1.25 pp; step 100 on math500 is 100.0 % truncated and scores -28.75 pp. A policy that never emits a stop token produces a 31,744-token sample with no final answer in it, and the grader scores that as wrong however much the model knows — B-short's ckpt-10 is the control for exactly this: it is 41–60 % truncated and its accuracy is nonetheless preserved, because its answers still appear before the loop begins. The deeper into the sink a checkpoint is, the more of its samples never reach an answer at all.

Only the (checkpoint × benchmark) cells that were approved for this condition appear above: step 60 on aime24; step 80 on aime24. The other combinations were never launched and are not counted as pending.

Transfer ratio at the terminal checkpoint (student gain ÷ the OpenThinker3 pair's teacher gain, five guards)

benchmark	teacher gain	student gain	numerator CI excludes 0	ratio	reason
aime24	+51.771 [+38.646, +64.375]	-2.500 [-7.917, +2.500]	False	null	guard: student_gain = -2.500 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BOTH gains are positive; a non-positive nu
aime25	+42.604 [+28.539, +56.667]	+1.250 [-2.500, +4.583]	False	null	guard (exp2b, new): student_gain = 1.250 pp has CI95 [-2.500, 4.583] pp which INCLUDES zero — the numerator is statistically indistinguishable from 'n
math500	+50.050 [+46.650, +53.400]	-28.750 [-35.000, -22.744]	True	null	guard: student_gain = -28.750 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BOTH gains are positive; a non-positive n

H5 verdict: NOT SUPPORTED

• no_collapse_through_step_100 — FAILED: clip_ratio first exceeded 0.5 at step 48
• gain_on_at_least_one_benchmark — FAILED: no benchmark shows a positive paired gain whose 95 % CI excludes 0

13.8 Cross-condition summary — one row per (condition, benchmark)

12 of 21 cells computed, 9 canceled. Each condition's student gain is divided by the teacher gain OF ITS OWN PAIR (run 1 -> r1distill_sft; B/C/D and both redirects -> openthinker3_sft). A pending cell means the unit is not on the Hub yet; a canceled cell means the unit can never exist because the run was stopped before it saved a checkpoint. Neither is ever an estimate. For B-short the row is its TERMINAL checkpoint (step 10); the per-step table is in the condition's own section.

condition	tier	benchmark	protocol	teacher gain (pp)	student gain (pp)	ratio	why not
run 1 — R1-distill shift	run 1	aime24	reduced	+24.38 [+15.42, +34.17]	-5.00 [-11.25, +0.42]	null	guard: student_gain = -5.000 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BO
run 1 — R1-distill shift	run 1	aime25	reduced	+21.15 [+10.21, +33.33]	+1.67 [-1.67, +5.42]	null	guard (exp2b, new): student_gain = 1.667 pp has CI95 [-1.667, 5.417] pp which INCLUDES zero — the numerator is
run 1 — R1-distill shift	run 1	math500	reduced-100-problem-subset	+46.50 [+43.20, +49.85]	-8.00 [-13.25, -3.25]	null	guard: student_gain = -8.000 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BO
B — OpenThinker3 shift	B	aime24	—	+51.77 [+38.65, +64.38]	⛔ canceled	null	collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it (~$50) would o
B — OpenThinker3 shift	B	aime25	—	+42.60 [+28.54, +56.67]	⛔ canceled	null	collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it (~$50) would o
B — OpenThinker3 shift	B	math500	—	+50.05 [+46.65, +53.40]	⛔ canceled	null	collapsed at steps 10-13; its first checkpoint save (step 20) is POST-collapse, so finishing it (~$50) would o
C — OpenThinker3 shift, KL floor = 2.5	C	aime24	—	+51.77 [+38.65, +64.38]	⛔ canceled	null	collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint
C — OpenThinker3 shift, KL floor = 2.5	C	aime25	—	+42.60 [+28.54, +56.67]	⛔ canceled	null	collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint
C — OpenThinker3 shift, KL floor = 2.5	C	math500	—	+50.05 [+46.65, +53.40]	⛔ canceled	null	collapsed identically to B with the KL coefficient pinned at its maximum; same post-collapse first checkpoint
D — OpenThinker3 shift into Qwen3-4B (thinking)	D	aime24	—	+51.77 [+38.65, +64.38]	⛔ canceled	null	collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short becau
D — OpenThinker3 shift into Qwen3-4B (thinking)	D	aime25	—	+42.60 [+28.54, +56.67]	⛔ canceled	null	collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short becau
D — OpenThinker3 shift into Qwen3-4B (thinking)	D	math500	—	+50.05 [+46.65, +53.40]	⛔ canceled	null	collapsed at step 17-20 (clip 0.65 -> 0.98) with no pre-collapse checkpoint; the user declined a D-short becau
B-short — OpenThinker3 shift, 10 steps, save every 2	B-short	aime24	reduced	+51.77 [+38.65, +64.38]	-3.33 [-7.50, +0.42]	null	guard: student_gain = -3.333 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BO
B-short — OpenThinker3 shift, 10 steps, save every 2	B-short	aime25	reduced	+42.60 [+28.54, +56.67]	+3.75 [-0.83, +8.75]	null	guard (exp2b, new): student_gain = 3.750 pp has CI95 [-0.833, 8.750] pp which INCLUDES zero — the numerator is
B-short — OpenThinker3 shift, 10 steps, save every 2	B-short	math500	reduced-100-problem-subset	+50.05 [+46.65, +53.40]	+0.50 [-3.75, +4.75]	null	guard (exp2b, new): student_gain = 0.500 pp has CI95 [-3.750, 4.750] pp which INCLUDES zero — the numerator is
B-lowlr — OpenThinker3 shift at OPTIM_LR 2e-7, 100 steps	B-lowlr	aime24	reduced	+51.77 [+38.65, +64.38]	-2.50 [-7.92, +2.50]	null	guard: student_gain = -2.500 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BO
B-lowlr — OpenThinker3 shift at OPTIM_LR 2e-7, 100 steps	B-lowlr	aime25	reduced	+42.60 [+28.54, +56.67]	+1.25 [-2.50, +4.58]	null	guard (exp2b, new): student_gain = 1.250 pp has CI95 [-2.500, 4.583] pp which INCLUDES zero — the numerator is
B-lowlr — OpenThinker3 shift at OPTIM_LR 2e-7, 100 steps	B-lowlr	math500	reduced-100-problem-subset	+50.05 [+46.65, +53.40]	-28.75 [-35.00, -22.74]	null	guard: student_gain = -28.750 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when B
RAFT — rejection-sampling-SFT shift, 100 steps	RAFT	aime24	full	+0.73 [-1.04, +2.60]	-1.56 [-4.17, +0.83]	null	guard:
RAFT — rejection-sampling-SFT shift, 100 steps	RAFT	aime25	full	+0.31 [-0.62, +1.35]	-2.19 [-5.31, +0.00]	null	guard:
RAFT — rejection-sampling-SFT shift, 100 steps	RAFT	math500	full	+11.20 [+8.90, +13.55]	-1.65 [-3.45, +0.10]	null	guard: student_gain = -1.650 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BO

Reading this table. Each row's ratio divides that condition's student gain by the teacher gain of its own pair — run 1 by r1distill_sft, everything else by openthinker3_sft. Crossing the pairs would be meaningless, and the aggregator refuses to do it.

13.9 Every Direct-OPD run in the study, side by side

One row per Direct-OPD training run in the study. primary_gains are the paired per-problem gains vs that condition's own student_init, taken at the step named in primary_gains_step — the terminal evaluated checkpoint where its units have landed, otherwise the last checkpoint that HAS been measured — and are null wherever no unit exists at all. Verdicts are computed from the measured training record and the measured gains, never asserted.

collapse onset = the first step whose response_length/clip_ratio exceeds 0.5; "none" means it never did over the steps recorded

run	teacher pair	student	lr	KL regime	steps	length runaway	collapse onset	peak clip	checkpoints?	hypothesis	verdict
run 1	Qwen2.5-Math-1.5B → DeepSeek-R1-Distill-Qwen-1.5B	Qwen2.5-7B-Instruct	1e-6	adaptive [0.5, 2.5]	100 / 100	60	61	1.000	yes	H1	NOT SUPPORTED
B	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	1e-6	adaptive [0.5, 2.5], eps 0.01	25 / 100	10	12	1.000	no	H2	UNTESTED
C	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	1e-6	CONSTANT 2.5 (ADAPTIVE_KL_LOSS_MIN_COEF = MAX = 2.5)	24 / 100	10	12	1.000	no	H3	REFUTED
D	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen3-4B (thinking)	1e-6	adaptive [0.5, 2.5], eps 0.01	22 / 100	17	17	0.992	no	H4	REFUTED
B-short	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	1e-6	adaptive [0.5, 2.5], eps 0.01	10 / 10	10	none	0.289	yes	H2 (pre-collapse form)	NOT SUPPORTED
B-lowlr	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	2e-7 (logged DEVIATION from the pinned 1e-6)	adaptive [0.5, 2.5], eps 0.01	100 / 100	42	48	1.000	yes	H5	NOT SUPPORTED
RAFT	Qwen2.5-1.5B-Instruct → RAFT-SFT of itself	Qwen2.5-7B-Instruct	1e-6	adaptive [0.5, 2.5], eps 0.01	100 / 100	—	none	0.008	yes	H6	PARTIAL

run	checkpoints	gains at step	AIME 2024 gain (pp)	AIME 2025 gain (pp)	MATH-500 gain (pp)
run 1	5 merged checkpoints (20/40/60/80/100) on the Hub; 60/80/100 are post-collapse	100	-5.00 [-11.25, +0.42] (reduced)	+1.67 [-1.67, +5.42] (reduced)	-8.00 [-13.25, -3.25] (reduced-100-problem-subset)
B	NONE — cancelled at step ~24, before the first save at step 20	—	⛔ no unit can exist	⛔ no unit can exist	⛔ no unit can exist
C	NONE — cancelled at step ~24, before the first save at step 20	—	⛔ no unit can exist	⛔ no unit can exist	⛔ no unit can exist
D	NONE — cancelled at step ~24, before the first save at step 20	—	⛔ no unit can exist	⛔ no unit can exist	⛔ no unit can exist
B-short	checkpoints 4, 8, 10 evaluated	10	-3.33 [-7.50, +0.42] (reduced)	+3.75 [-0.83, +8.75] (reduced)	+0.50 [-3.75, +4.75] (reduced-100-problem-subset)
B-lowlr	checkpoints 20, 40, 60, 80, 100 evaluated	100	-2.50 [-7.92, +2.50] (reduced)	+1.25 [-2.50, +4.58] (reduced)	-28.75 [-35.00, -22.74] (reduced-100-problem-subset)
RAFT	checkpoints 20, 40, 60, 80, 100 evaluated	100	-1.56 [-4.17, +0.83] (full)	-2.19 [-5.31, +0.00] (full)	-1.65 [-3.45, +0.10] (full)

13.10 The fifth transfer-ratio guard

Run 1's report flagged a gap: the pre-registration guarded the sign of the numerator and the significance of the denominator, but not the significance of the numerator, so a student gain of +1.667 pp [−1.667, +5.417] on AIME 2025 divided into a tidy, meaningless 0.079. exp2b's pre-registration (E3) closes it: the numerator's 95 % CI must also exclude 0.

The new guard is applied uniformly, to run 1 as well — a table that shows six conditions side by side cannot use two different rules. Nothing published is deleted: when a ratio passes the four original guards and fails only the fifth, both aggregate_evals.py and this pipeline still record value_under_exp2a_guards, so run 1's AIME-2025 ratio of 0.079 remains readable and clearly labelled as the number the older rule produced.

Switch state for this build: APPLY_NUMERATOR_CI_GUARD_TO_RUN1 = True.

---

14. The termination sink

Run 1 found it once and called it a curiosity. exp2b ran the same method with a different teacher pair, with the KL brake pinned at its maximum, and into a different, thinking student — and found it three more times. This section states the mechanism, says what did transfer, and separates the two.

14.1 The mechanism, in four measured steps

(1) The shift reward is negative on the student's own native outputs — for every SFT pair we tried. Direct-OPD's reward is the token-level log-ratio log π_post − log π_pre scored on the student's rollouts. At step 1, before any update, that number is what the pair thinks of the student as it already is:

run	teacher pair	student	weighted shift reward @ step 1	sign	steps with a negative mean reward
run 1	Qwen2.5-Math-1.5B → DeepSeek-R1-Distill-Qwen-1.5B	Qwen2.5-7B-Instruct	-0.00783	negative	90 / 100
B	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	-0.03543	negative	25 / 25
C	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	-0.03543	negative	24 / 24
D	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen3-4B (thinking)	-0.01427	negative	19 / 22
B-short	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	-0.03543	negative	10 / 10
B-lowlr	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	Qwen2.5-7B-Instruct	-0.03543	negative	100 / 100
RAFT	Qwen2.5-1.5B-Instruct → RAFT-SFT of itself	Qwen2.5-7B-Instruct	-0.00479	negative	100 / 100

Read literally, the objective's only instruction in every one of these runs was stop writing like yourself. It never pointed at a better answer — only away from the current one. That is not a property of the R1 pair: it survived swapping to an Instruct-lineage pair whose π_post is the same family and post-training lineage as the student, and it survived swapping the student for a thinking model whose distribution the shift was supposed to like (H4's premise, refuted at step 1).

(2) There is a region where the reward is exactly zero, and it is non-termination. A log-ratio of 0 means π_post and π_pre assign the same probability. The two teachers disagree about how to write; they agree almost everywhere else, and the cheapest place for a language model to reach that agreement is degenerate repetition — an answer, then the same answer again, forever. Every collapsed run shows the same signature: the mean reward rises towards zero, not towards positive, exactly as the rollouts pin at the length cap.

run	weighted reward, step 1 → last recorded	response length, step 1 → last	actor entropy, first → min	clip ratio at the last recorded step
run 1	-0.0078 → +0.0026	339 → 2,614	0.156 → 0.058	0.699
B	-0.0354 → -0.0037	339 → 3,328	0.156 → 0.029	1.000
C	-0.0354 → -0.0043	339 → 3,328	0.156 → 0.029	1.000
D	-0.0143 → -0.0011	1,707 → 4,089	0.319 → 0.219	0.992
B-short	-0.0354 → -0.0085	339 → 1,521	0.156 → 0.048	0.289
B-lowlr	-0.0354 → -0.0038	339 → 3,328	0.156 → 0.039	1.000
RAFT	-0.0048 → -0.0030	339 → 500	0.156 → 0.083	0.000

The sink is worse at evaluation time than in training, and this is what makes the post-collapse numbers look dramatic. Training capped rollouts at 3,328 tokens (4,096 for D); the evaluation cap is 31,744. A checkpoint that pinned at the training cap therefore runs almost ten times further before it is cut off, and the sample the grader sees has no final answer in it at all:

checkpoint	AIME 2024 truncation	MATH-500 truncation	MATH-500 paired gain (pp)
B-short ckpt-10	44.2 %	60.5 %	+0.50 [-3.75, +4.75]
run 1 ckpt-100	92.1 %	96.5 %	-8.00 [-13.25, -3.25]
B-lowlr ckpt-100	99.6 %	100.0 %	-28.75 [-35.00, -22.74]

B-short's ckpt-10 is the control that settles the reading. It is the onset step, not a deep sink: 41–60 % truncated, mean output 15–22k tokens — and its accuracy is preserved (+0.50 pp on MATH-500), because its answers still appear before the repetition loop starts. The further into the sink a checkpoint sits, the larger the share of samples in which no answer is ever emitted, and the more negative the score. Those numbers measure termination, not mathematics — which is why this report's verdict rests on the pre-collapse checkpoints, where the model still stops and the gains are simply null.

(3) The KL brake at its maximum does not prevent it. Condition C is condition B with ADAPTIVE_KL_LOSS_MIN_COEF = MAX = 2.5, i.e. the anchor pinned at its strongest value for the whole run.

C held kl_coef at 2.500 for all 24 recorded steps (constant = True) and still crossed the collapse threshold at step 12 — the same step as B (12). H3 REFUTED.

Run 1's adaptive controller did loosen under sustained negative reward (2.5 → 1.012), and that looked like a plausible cause. It is not the cause. The sink is reachable with the leash at its shortest.

(4) A thinking student delays the sink; it does not avoid it. Condition D put the same shift into Qwen3-4B with thinking mode on and a 4,096-token response cap.

B collapsed at step 12, C at step 12, D at step 17 — a delay of 5 steps, on rollouts that started 1,707 tokens long instead of 339. The longer native output buys time; it does not change the destination. And D's weighted reward turned positive only in the last two recorded steps — as it saturated at the cap. The sink is where the teachers agree, and D found it too.

(5) And the learning rate? B-lowlr re-runs B at OPTIM_LR 2e-7 instead of 1e-6 (a logged deviation) on the theory that the grad-norm spikes — 27 at step 5, 13 at step 9, 21 at step 10 in B — are what launch the policy into the sink.

B-lowlr collapsed anyway, at step 48 — 4.0× later than B (step 12), but not never. Lowering the learning rate 5× postponed the sink; it did not avoid it. The mean rollout length crossed twice its step-1 value at step 42, and the weighted reward was rising towards zero (-0.0354 → -0.0038) on exactly the trajectory B, C and D took.

And the spike theory the redirect was built on does not survive its own test. B and C were preceded by grad-norm spikes (27 at step 5, 13 at step 9), which is why lowering the learning rate looked promising — but D collapsed with no spike at all (peak grad norm 4.4), and B-lowlr survived the largest spike in the study (49.8 at step 21) for tens of steps before going anyway. The spikes are a symptom of the same pressure, not the cause of the sink.

14.2 What did transfer: the register, the format, and the length

The failure is specific. It is not "nothing happened" — a great deal happened, very fast, and none of it was capability.

Run 1's student adopted the R1 reasoning voice within twenty steps and abandoned \boxed{} almost entirely in favour of the prompt-instructed Answer: line — away from both of its teachers, which lean \boxed{} on AIME. §8.2 has run 1's table. The same measurement under the OpenThinker pair, for both redirects, is:

benchmark	unit	pass	Answer: line	\boxed{}	none	mean out tok
aime24	student_init	sample32	58.3 %	37.5 %	4.2 %	1,517
aime24	pre_teacher_ot	sample32	59.6 %	27.2 %	13.2 %	2,991
aime24	post_teacher_ot	sample32	2.0 %	80.5 %	17.5 %	18,275
aime24	B-short opd_student_otshift-short-ckpt4	sample32	39.0 %	56.4 %	4.7 %	1,635
aime24	B-short opd_student_otshift-short-ckpt8	sample32	75.2 %	19.9 %	4.9 %	2,014
aime24	B-short opd_student_otshift-short-ckpt10	sample32	91.2 %	3.3 %	5.4 %	16,569
aime24	B-lowlr opd_student_otshift_lowlr-ckpt20	sample32	38.3 %	57.5 %	4.2 %	1,622
aime24	B-lowlr opd_student_otshift_lowlr-ckpt40	sample32	78.2 %	17.3 %	4.5 %	2,088
aime24	B-lowlr opd_student_otshift_lowlr-ckpt60	sample32	91.2 %	2.5 %	6.2 %	29,734
aime24	B-lowlr opd_student_otshift_lowlr-ckpt80	sample32	45.0 %	36.7 %	18.3 %	31,414
aime24	B-lowlr opd_student_otshift_lowlr	sample32	0.8 %	65.0 %	34.2 %	31,647
math500	student_init	sample4	83.7 %	14.6 %	1.8 %	564
math500	pre_teacher_ot	sample4	71.5 %	19.1 %	9.3 %	716
math500	post_teacher_ot	sample4	12.6 %	84.2 %	3.3 %	5,762
math500	B-short opd_student_otshift-short-ckpt4	sample4	78.8 %	20.1 %	1.1 %	659
math500	B-short opd_student_otshift-short-ckpt8	sample4	98.9 %	0.7 %	0.4 %	870
math500	B-short opd_student_otshift-short-ckpt10_m500sub100	sample4	98.0 %	1.2 %	0.8 %	22,020
math500	B-lowlr opd_student_otshift_lowlr-ckpt20	sample4	74.0 %	23.5 %	2.5 %	707
math500	B-lowlr opd_student_otshift_lowlr-ckpt40	sample4	98.7 %	0.9 %	0.4 %	890
math500	B-lowlr opd_student_otshift_lowlr_m500sub100	sample4	0.8 %	61.3 %	38.0 %	31,744

Note what this pair's π_post does on AIME 2024: it is overwhelmingly \boxed{} (80.5 % of samples) where the initial student is only 37.5 %. If Direct-OPD were teaching the student to imitate π_post, \boxed{} is the surface form it would move towards — and run 1's student famously moved the other way, extinguishing \boxed{} entirely (§8.2).

• B-short, terminating checkpoints — \boxed{} share on AIME 2024, initial 37.5 % → step 4: 56.4 % → step 8: 19.9 %; mean output length 1,517 → 1,635 → 2,014 tokens.
• B-lowlr, terminating checkpoints — \boxed{} share on AIME 2024, initial 37.5 % → step 20: 57.5 % → step 40: 17.3 %; mean output length 1,517 → 1,622 → 2,088 tokens.
• B-short, post-collapse checkpoints (shown for completeness, not interpretable as register): step 10 3.3 % \boxed{} at 44.2 % truncation and 16,569 mean tokens — at that truncation the extractor is finding a \boxed{} somewhere inside a sample that never ends, which says nothing about the policy's answer format.
• B-lowlr, post-collapse checkpoints (shown for completeness, not interpretable as register): step 60 2.5 % \boxed{} at 88.8 % truncation and 29,734 mean tokens; step 80 36.7 % \boxed{} at 98.8 % truncation and 31,414 mean tokens; step 100 65.0 % \boxed{} at 99.6 % truncation and 31,647 mean tokens — at that truncation the extractor is finding a \boxed{} somewhere inside a sample that never ends, which says nothing about the policy's answer format.

The move is real, teacher-directed, and non-monotonic. In B-short it peaks at step 4 (56.4 %, +18.9 pp vs the initial student, towards π_post) and in B-lowlr it peaks at step 20 (57.5 %, +20.0 pp vs the initial student, towards π_post) — and then falls back below where it started as the rollouts lengthen. The two redirects trace the same path at different speeds: the lr-2e-7 run reaches the same style waypoints at roughly five times the step count of the lr-1e-6 run. The learning rate rescales the clock, not the path.

Output length, by contrast, is monotonic in every run: it only ever grows, from the first evaluated checkpoint onward, and it is the variable that ends in the sink. Format oscillates; length does not. Whatever the token-level log-ratio is rewarding, it is not "emit π_post's surface form" — and it is certainly not "be more accurate".

14.3 What this says about distilling an SFT policy change into a larger model

The question this campaign was built to answer is whether an established SFT policy change can be transported into a larger student by scoring the student's own tokens with the log-ratio of the two SFT endpoints. Four runs, two teacher pairs, two student families, one KL ablation, and the answer so far is: not as specified, and the obstacle is structural rather than incidental.

The structural problem is that a log-ratio reward is a difference of two models that are not the student. Its sign on the student's own outputs is an empirical fact nobody chooses, and in all four runs it was negative — the pair prefers π_pre on what the student natively writes. A negative-mean reward with an unbounded action space has a trivially reachable optimum: go where the two models agree. For language models that region is degenerate, and the specific degeneracy is never emitting a stop token, because termination is precisely where a chat model and its SFT descendant differ most sharply in probability.

Three claims this study can now exclude as explanations:

1. "The shift had nothing to give." Excluded twice. Run 1's pair carries +24.38 pp on AIME 2024, and the OpenThinker pair carries +51.77 pp [+38.65, +64.38] on the same benchmark at the same token cap for both ends — no budget confound at all.
2. "The adaptive KL controller loosened the leash." Excluded by condition C: the coefficient was constant at its maximum and the run collapsed identically.
3. "A non-thinking student cannot represent a thinking teacher's policy." Excluded by condition D: the thinking student H4 predicted the shift would reward collapsed too — 5 steps after B, not never.

What is left is the objective itself. Concretely, for a rerun to be informative:

change	what it fixes	why this study points at it
A length-aware reward, or an explicit termination bonus	prices the sink	the escape region is degenerate non-termination, and nothing in a token-level log-ratio prices length or repetition. 5 of the 7 runs (run 1, B, C, D, B-lowlr) ended with 90 %+ of rollouts pinned at the response cap.
An on-policy KL anchored to the student's OWN init (not a coefficient schedule)	keeps the policy inside the region where the reward is even meaningful	C proves the magnitude of the KL term is not the lever; what is missing is an anchor that tracks the student's own initial distribution rather than a scalar penalty.
A shift whose mean is positive on the student BY CONSTRUCTION — e.g. π_pre and π_post both derived from the student itself (same-model pre/post SFT)	removes the "stop writing like yourself" instruction at the root	the step-1 sign table in §14.1 is negative for every pair tried, including one deliberately chosen for lineage proximity. Proximity of family was not enough; identity of model is the untested version.
Early stopping on the clip ratio (the collapse-watch rule, as a kill criterion rather than a diagnostic)	stops paying for post-collapse steps	every collapse in this study was visible in response_length/clip_ratio within 1–2 steps of onset, and B/C/D each burned ~10 further steps after it.
A checkpoint save cadence tied to the collapse watch, not to a step grid	guarantees a pre-collapse policy exists to evaluate	B and C died with no evaluable checkpoint at all because save_freq was 20 and their onset was step 12 / 12. B-short exists only to repair that.

The last row is the cheapest and, in hindsight, the most valuable: the difference between conditions B/C (no data) and B-short (five saved policies for $5.54) is one configuration line.

14.4 Cost of the extension

$332.36 cumulative against the $500 cap (raised from $200 on 2026-08-26), leaving $167.64. Of that, $92.87 is run 1 (phases P1–P6), $192.02 is the exp2b extension (phases P2b, P3b, P4b, P5b) and $47.47 is exp3 (phase P7).

phase	what it bought	cost	share of total
P1	harness + driver builds (CPU, $0)	$0.00	0.0 %
P2	run-1 baseline evaluation wave	$7.32	2.2 %
P2b	OpenThinker-pair probes	$16.46	5.0 %
P3	run-1 OPD smoke	$1.07	0.3 %
P3b	exp2b OPD smokes (B, C, D)	$3.61	1.1 %
P4	run-1 100-step training	$44.43	13.4 %
P4b	exp2b training: B, C, D (all CANCELED) + B-short + B-lowlr	$100.90	30.4 %
P5	run-1 probes + reduced-protocol endpoints	$26.14	7.9 %
P5b	exp2b evaluation wave	$71.05	21.4 %
P6	run-1 checkpoint curve	$13.91	4.2 %
P7	exp3: shift anatomy + RAFT pair construction + G2 gate + the RAFT Direct-OPD run + the H6c eval wave	$47.47	14.3 %
TOTAL		$332.36	100 %

$46.46 went to jobs that were cancelled (5 of them) — and it matters what that bought. $42.44 is the 3 cancelled training runs (B, C, D). They were stopped once their result was in: their 22–25 recorded steps are the whole of §13.5, and they are what refutes H3 (constant KL) and H4 (thinking student) — two of this campaign's main findings, bought for the price of a fifth of a full run each. Their evidence is training-only because they never reached their first checkpoint save, not because the spend was wasted. The remaining $4.02 — cancelled evaluation jobs: an under-timed attempt that was relaunched successfully, and one mis-shaped job killed on the spot — is the only part that bought nothing. CANCELED jobs are booked on WALL-CLOCK occupancy x flavor rate, not on the platform's running_secs, which it reports as 0 for a cancelled job regardless of the GPU time actually consumed. Each such row says so in its own notes field.

cancelled job	phase	flavor	wall-clock hours	booked
a100x4 full openthinker (B) — CANCELED by user decision at step ~24	P4b	a100x4	1.361	$13.61
a100x4 full openthinker_klfloor (C) — CANCELED by user decision at step ~24	P4b	a100x4	1.361	$13.61
a100x4 full openthinker_qwen3_4b (D) — CANCELED by user decision at step ~24	P4b	a100x4	1.522	$15.22
exp2b-p5b-ckpt10-m500-sub100 (opd_student_otshift-short-ckpt10_m500sub100, REDUCED protocol, ATTEMPT 1) — CANCELED, undersized timeout	P5b	a100-large	1.576	$3.94
p5b-lowlr-curve-a24-ckpt6080 (combined 2-subfolder job, CANCELED immediately)	P5b	a100-large	0.032	$0.08

This is deliberately the larger of the two available bases. The platform reports running_secs = 0 for a cancelled job, which would book every one of them at $0 and understate the extension by $46.46.

---

15. Answer to the question

Can a policy change learned by SFT be distilled into a larger model with Direct-OPD?

On the evidence of this campaign: no — not as the method is specified, and not because the teachers had nothing to teach. What crossed from the teacher pair to the student was surface form — answer format, register, output length. Held-out mathematical capability did not cross at any checkpoint of any run.

The answer rests on three things, all measured:

1. The premise was established twice. The paired teacher gain is +24.375 [+15.417, +34.167] p<0.0001 on AIME 2024 for the R1-distill pair and +51.771 [+38.646, +64.375] p<0.0001 for the OpenThinker3 pair, the second with both models at the same token budget. Whatever failed, it was not that the shift encoded nothing.
2. Nothing improved, anywhere. Across 43 paired held-out measurements — every evaluated checkpoint of every condition, always against the same initial student — 0 are positive with a 95 % CI excluding zero, and 6 are negative with a CI excluding zero. Of the 6 regressions, 4 are post-collapse checkpoints and 2 are small pre-collapse ones. The largest gain measured anywhere is +3.75 pp (B-short step 10, aime25), whose CI includes zero; the largest regression is -28.75 pp (B-lowlr step 100, math500) — and that one is a termination artifact: at 100 % truncation the sample has no final answer for the grader to read. It measures the sink, not a loss of mathematics.
3. The same failure appeared every time. 5 of the 7 runs (run 1, B, C, D, B-lowlr) crossed the pre-registered collapse watch (clip_ratio > 0.5), and B-short ended at the length-runaway onset before the clip rule could fire in so short a run — under two different teacher pairs, a pinned KL brake, a thinking student and a 5× lower learning rate (§14).

15.0 …and, since exp3, the answer comes with its mechanism

The three statements above are the outcome. exp3 measured why, and the picture that survives has two axes rather than one — a shift's on-supportness (how much of the student's own text it rewards, and what it thinks of stopping) and its magnitude. They are independent, they govern different things, and every pair this campaign has measured falls into one of three regimes:

regime	example pairs	on-support?	magnitude	what happens
off-support, large	corpus SFT — R1, OpenThinker3	no (23 %/34 % of tokens rewarded; EOS -90)	large, ≈ 2.7 /token	termination collapse; style transfers, capability never does (§14, §17)
on-support, tiny	RAFT — π_pre SFT'd on its own verified samples	yes (84.7 % of tokens; EOS -0.006)	tiny, 0.099 /token	safe but null — 100 clean steps, no collapse, no detectable gain (§18)
on-support, large	RL — the pilot's KL-regularized pair	yes (58.1 % of tokens)	large, RMS 1.02 /token	transfers ≈ half the teacher gain (the pilot)

So the sharpened answer is: Direct-OPD is not broken and SFT is not disqualified — what fails is a shift that is off the student's support. An SFT pair that is on-support by construction runs safely through the identical channel. It simply had nothing large enough to say. The RL pair gets both properties at once for a structural reason: for KL-regularized RL the log-ratio is the learned advantage divided by β, so on-supportness and magnitude arrive together. Nothing in this campaign shows that an SFT pair cannot occupy that corner — only that neither of the two kinds we could build did.

15.1 What the answer covers

This is an answer about Direct-OPD as pre-registered here, i.e. a token-level reward log π_post − log π_pre scored on the student's own rollouts, with a KL penalty, for ≤ 100 steps, using:

• two SFT pairs, both 1.5B, both pure-SFT (no RL): a base→reasoning pair (Qwen2.5-Math-1.5B → DeepSeek-R1-Distill-Qwen-1.5B) and an instruct→reasoning pair from the student's own family (Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B);
• two students larger than the teachers: Qwen2.5-7B-Instruct (4.7×, non-thinking) and Qwen3-4B (2.7×, thinking);
• held-out competition mathematics: AIME 2024 / 2025 (32 samples/problem) and MATH-500 (4 samples/problem), paired per problem, 10,000-resample bootstrap.

Within that box the result is not marginal — it is a null at every checkpoint plus a reproducible, mechanistically-explained training failure.

15.2 What the answer does NOT cover

Six limits, stated so that nobody over-reads the sentence above:

1. The positive-shift regime is untested. In every run the shift reward's mean on the student's own outputs was negative at step 1 (run 1 -0.0078; B -0.0354; C -0.0354; D -0.0143; B-short -0.0354; B-lowlr -0.0354; RAFT -0.0048). A pair whose log-ratio is positive on the student — which §16 says how to build — is a different experiment, and this campaign says nothing about it.
2. The clean training window was short. The longest stretch of pre-collapse training any evaluated checkpoint saw is 40 steps at lr 2e-7 (B-lowlr ckpt-40) and 8 steps at lr 1e-6 (B-short ckpt-8). A null over that window bounds what a few steps of this objective can do; it does not bound what a non-collapsing version of it might do over 100.
3. Both teacher gaps carry an asterisk. Run 1's π_pre is context-limited, and the cap-matched sensitivity view (§8.4) shrinks its AIME 2024 gap to a CI that includes zero; the OpenThinker π_post truncates on 19.0 % of AIME 2024 samples even at the full 31,744-token cap, so its gains are lower bounds — the true teacher gap is larger, which only sharpens the contrast with the student's null. Note also how that was discovered: the 8-problem pre-flight probe put π_post's AIME truncation at ≈ 6 %, three to four times below what the full wave measured. Probes measure central tendency, not tails — the same estimation lesson run 1 recorded, now with a second instance. The MATH-500 gap survives every one of these objections intact.
4. Three conditions were answered only in their training form. B, C and D were cancelled before their first checkpoint save, so H2 and H4 are settled by training evidence (a collapse, and a step-1 reward sign) and not by any evaluation of their policies. B-short exists precisely to supply the pre-collapse policy B never saved.
5. Post-collapse endpoints use reduced protocols. Non-terminating checkpoints cost 5–10× a normal unit at the 31,744-token cap, so run 1's ckpt-100 and B-short's ckpt-10 were measured at 8 samples/problem on AIME and on a 100-problem MATH-500 subset. Same estimand, wider CIs, always labelled reduced.
6. One seed per condition. Every run is seed 42 (plus the pilot's seed patch). B-short reproducing B's trajectory step-for-step shows the trajectory is deterministic given the seed; it does not establish that the collapse step is seed-independent.

---

16. Recommendations for a next attempt

These follow from §14's mechanism and §15's limits. The first is the scientific fix; the rest are what make the experiment survivable and cheap enough to read.

1. Make the shift's mean POSITIVE on the student, by construction. The single fact that explains every run in this study is that log π_post − log π_pre was negative on the student's own outputs before a single update. The way to guarantee otherwise is to stop borrowing the pair from a different model: take the student itself as π_pre and an SFT of that student as π_post (same-model pre/post). The shift then describes a change the student's own distribution can express, and the reward's zero-set is no longer 'wherever these two strangers happen to agree'. Everything else in this list is a guard rail; this is the experiment.

2. Price termination explicitly — a length-aware reward or an EOS bonus. A token-level log-ratio contains no term for stopping, and the cheapest way to drive it to zero is to never stop. 5 of the 7 runs (run 1, B, C, D, B-lowlr) ended with 90 %+ of rollouts pinned at the response cap. A per-sequence bonus on emitting EOS, or a penalty on the clipped fraction, converts the sink from an optimum into a cost. This is cheap to add and directly targets the observed failure.

3. Anchor the KL to the student's own init, not to a coefficient schedule. Condition C settles that the magnitude of the KL term is not the lever: pinned at its maximum 2.5 for every step, it collapsed on the same step as the adaptive run. What is missing is not a bigger penalty but a reference the penalty is measured against — the student's initial policy — so that 'stop writing like yourself' is bounded rather than unbounded.

4. Make the collapse watch a KILL criterion, not a diagnostic. The pre-registered rule (response_length/clip_ratio > 0.5) fired within 1–2 steps of every collapse in this study, and then the runs kept paying: run 1 ran 39 further steps after onset, B ran 13 further steps after onset, C ran 12 further steps after onset, D ran 5 further steps after onset, B-lowlr ran 52 further steps after onset. Stopping at onset would have cost nothing scientifically — the post-collapse checkpoints are the least informative artefacts in the campaign and the most expensive to evaluate (non-terminating checkpoints re-priced the full protocol at $177–208 for a single endpoint). With one caveat this campaign learned the hard way: the driver merges and uploads checkpoints only after training, so B-lowlr was deliberately allowed to finish — cancelling it would have destroyed its two clean pre-collapse policies. An early-stop rule is only safe once item 5 is in place.

5. Tie the checkpoint cadence to the watch, not to a step grid. B and C died with no evaluable policy at all because save_freq was 20 and their onset was step 12. B-short bought five saved policies for $5.54 — one configuration line, and it is the difference between a condition with data and a condition without.

6. Gate on the shift's magnitude and sign BEFORE booking a training run. Every collapse in this campaign was predictable from numbers that cost minutes: the step-1 delta_opd/weighted_reward_mean on the student's own rollouts (negative in all 7 runs), and the unweighted log_ratio_mean (+1.79 for the R1-distill pair, -0.15 for the OpenThinker pair — a 12x smaller signal that collapsed sooner, so magnitude alone does not predict the delay either). A pre-flight gate should require the weighted mean to be positive on a sample of the student's own generations and abort otherwise. The 2-step smoke this campaign already runs measures exactly that number; it was recorded as a note instead of used as a gate.

7. Iterate or scale the RAFT pair — the one direction this campaign has already shown to be safe. exp3 settles item 1 in its safety half: a rejection-sampling SFT pair, on-support by construction, ran the identical channel for 100 steps with a peak clip ratio of 0.0078 and no collapse (§18.3). What it did not settle is transfer, because the shift it produced was tiny — 0.099 |Δ log p| per token, a tenth of the RL pair's RMS — and §18.5 shows the resulting null is exactly the size the pilot's gain-per-shift predicts. One round of rejection-sampling SFT is literally one step of an RL loop, so the natural next move is to keep the construction and grow the magnitude: more rounds (each one re-sampling from the improved model), a larger k per prompt, and a prompt mix that is not skewed easy by the filter (§18.1). That interpolates from the RAFT corner of §15.0's table toward the RL corner, and it is the cheapest available test of whether on-supportness survives iteration — which is the one thing the two-axis picture does not yet tell us.

#	change	what it fixes	evidence in this report
1	positive-mean shift by construction (same-model pre/post SFT)	removes the stop writing like yourself instruction at the root	§14.1(1), §15.2(1)
2	length-aware reward / EOS bonus	prices the sink	§14.1(2), §6, F8
3	KL anchored to the student's own init	bounds the escape	§13.5 (condition C), §14.1(3)
4	early stop on clip ratio > 0.5	stops paying for post-collapse steps	§14.1, §11
5	save cadence tied to the watch	guarantees an evaluable pre-collapse policy	§13.5 vs §13.6
6	shift-magnitude/sign gate before launch	never books a run whose objective points the wrong way	§14.1(1), the smoke metrics in §13.5
7	iterated / scaled RAFT — more rounds, more samples per prompt, a harder prompt mix	grows the magnitude while keeping the support	§18.5, §18.6

For scale: this campaign cost $332.36, of which $145.33 was training and $46.46 went to cancelled jobs — nearly all of it ($42.44) the B/C/D runs that were stopped once they had refuted H3 and H4, so it is a saving rather than a loss. What items 4 and 5 would have bought is not that money back but the post-onset steps inside every run that ran to completion, plus an evaluable checkpoint for B and C; item 6 is the only one that could have prevented a run from being booked at all.

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17. The mechanism, measured

§14 argued from six training runs that the token-level log-ratio is the problem. exp3 Part A measures it directly, without training anything. The same frozen student rollouts are scored under five different teacher pairs, so the only thing that varies across the columns below is which pair you subtract — the text, the tokenizer positions and the correctness verdicts are identical.

17.1 Method

• Corpus: the existing student_init generations of Qwen2.5-7B-Instruct on AIME 2024 and MATH-500 — 2,960 frozen rollouts, 2,067,933 scored response positions (2,065,012 ordinary content tokens plus 2,921 special positions, which are excluded from the content statistics and analysed separately as the EOS column).
• Models: six 1.5B teachers plus the 7B student, scored in fp32, each reading the student's verbatim token IDs — no re-tokenization, no re-rendering. Every pair is therefore a difference of two log-probabilities over the same index.
• What is computed per pair: the per-token log-ratio log π_post − log π_pre and its distribution; the ratio at the terminal <|im_end|> of rollouts that actually finished (2,921 of them) and at 25,553 sampled interior boundary positions as a control; and the AUROC of the sequence-mean log-ratio against the rollout's own correctness verdict, raw and length-controlled.
• Bootstrap: 2000 resamples over problems, seed 42. Only 39 sequences were cap-limited and 17 were truncated, so the corpus is essentially all complete answers.

Everything below is read from anatomy/stats.json, which is the canonical artifact: the analysis run's own prose tables pool per-benchmark and differ from it by up to 0.07.

17.2 The five pairs

pair	kind	token mean	student-weighted mean	% tokens > 0	terminal EOS	interior EOS	AUROC raw	AUROC length-controlled
R1	corpus SFT (base->chat)	-0.111	-0.0944	22.9%	-4.238	+4.21	0.667	0.747 [0.697, 0.791]
OT	corpus SFT (chat->chat)	-0.233	-0.1933	34.3%	-90.200	-58.67	0.474	0.751 [0.703, 0.792]
RL	RL (pilot's working pair)	-0.197	-0.1604	58.1%	-6.338	-4.94	0.754	0.812 [0.777, 0.843]
pilotSFT	small in-family SFT	+0.014	+0.0122	54.7%	+0.700	-0.12	0.547	0.378 [0.339, 0.424]
RAFT	rejection-sampling SFT	-0.033	-0.0085	84.7%	-0.006	-8.47	0.743	0.755 [0.716, 0.790]

Read the two bold columns together. % tokens > 0 is how much of what the student already writes the pair rewards; terminal EOS is what the pair thinks of the student stopping. The corpus pairs reward a quarter to a third of the student's own tokens and punish stopping; the RL pair rewards more than half; the RAFT pair rewards 85 % and is neutral about stopping.

17.3 Where the stop token went

The EOS column above is a ratio. The reason it is so extreme for the corpus pairs is visible only per model — this is mean log p(<|im_end|>) at the genuine end of a completed answer, i.e. how strongly each model believes the answer is over:

| model | lineage | mean log p at the realized token | log p(<|im_end|>) at the true end | at interior positions | treats 151645 as its stop token | |---|---|---|---|---|---| | student_qwen25_7b_instruct | qwen | -0.081 | -0.01 | -36.1 | yes | | qwen25_1_5b_instruct | qwen | -0.176 | -0.11 | -34.1 | yes | | raft_qwen25_1_5b | qwen | -0.208 | -0.11 | -42.6 | yes | | qwen_math_1_5b | qwen | -0.190 | -18.39 | -31.8 | no | | pilotsft_deepmath100 | deepseek | -0.292 | -21.93 | -27.8 | no | | r1_distill_1_5b | deepseek | -0.307 | -22.63 | -27.6 | no | | justrl_deepseek_1_5b | deepseek | -0.513 | -28.97 | -32.6 | no | | openthinker3_1_5b | qwen | -0.536 | -90.31 | -92.8 | no |

OpenThinker3 is the extreme case: -90.3, and stats.json records that not one of its terminal positions has a positive log-ratio. A model trained on long chain-of-thought corpora has effectively unlearned the stop token on this kind of text. Subtract its pre-teacher — which stops perfectly happily (-0.109) — and the reward at every EOS position is a cliff. That is condition B's step-10 collapse, measured on frozen text before any training happened.

Lineage caveat, and it matters for exactly one row. Token id 151645 is <|im_end|> to a Qwen-lineage model and <|Assistant|> to a DeepSeek-lineage one, so an EOS ratio is only well posed when both members of the pair read it the same way:

pair	π_pre lineage	π_post lineage	EOS ratio well posed?
R1	qwen	deepseek	no — mixed lineage
OT	qwen	qwen	yes
RL	deepseek	deepseek	yes
pilotSFT	deepseek	deepseek	yes
RAFT	qwen	qwen	yes

R1's EOS numbers are therefore not a clean ratio (Qwen2.5-Math → DeepSeek-R1-distill crosses the lineage boundary), and the report does not lean on them; the per-model column above, which is a single model's own log-probability, is well posed for every row. The RAFT pair is recorded in stats.json as mixed-lineage too, but that is a bug in the anatomy run's lineage map, not a property of the pair: the RAFT teacher is an SFT of Qwen2.5-1.5B-Instruct whose tokenizer files are sha256-identical to it, so both members are Qwen and its EOS ratio is well posed. Fixed in code/anatomy/analyze_anatomy.py; the published stats.json is left as the original artifact and corrected here.

17.4 The pre-registered predictions, and the four that failed

§F2 pre-registered five predictions before any of this was measured. They are reprinted exactly as the anatomy run recorded them — four of the six coded checks FAILED, and the failures are the most useful part of this section.

check	verdict	rule	measured
P1_corpus_EOS_much_less_than_0_at_terminal	PASS	every corpus pair mean <= -0.5	R1 -4.238; OT -90.200
P1_corpus_EOS_much_less_than_0_at_interior_boundaries	FAIL	every corpus pair mean <= -0.5	R1 +4.044; OT -63.375
P2_corpus_AUROC_approx_0.5_after_length_control	FAIL	abs(AUROC-0.5) < 0.05 or CI95 contains 0.5	R1 0.747; OT 0.751
P3_RL_EOS_approx_0_or_positive_at_terminal	FAIL	abs(mean) < 0.5 or mean > 0	RL -6.338
P3_RL_EOS_approx_0_or_positive_at_interior_boundaries	FAIL	abs(mean) < 0.5 or mean > 0	RL -3.859
P4_RL_least_negative_student_weighted_mean	FAIL	RL has the maximum (least negative) student-weighted mean of all pairs	R1 -0.094; OT -0.193; RL -0.160; pilotSFT +0.012; RAFT -0.009
P5_RAFT_patterns_with_RL	PASS	requires the Part-B RAFT teacher	—

What each failure taught:

1. P1-interior FAILED for R1 — its interior-boundary ratio is positive where the terminal one is sharply negative. That is the mixed-lineage artifact above: at interior positions the two models are being asked about different tokens. Flagged, not repaired.
2. P2 FAILED, and this is the important one. The prediction was that a corpus pair's sequence-mean log-ratio would be uninformative about correctness once length is controlled. It is not: after length-decile pooling the corpus pairs reach R1 0.747; OT 0.751, against the RL pair's 0.812. The corpus shifts DO carry a sequence-level correctness signal — the pilot's "it is only a length artifact" reading does not replicate here. What they lack is a way for a token-level optimizer to reach it: the anti-EOS and negative-mass gradient dominates every update long before any sequence-level signal could be exploited. A sequence-level objective on the same quantity is a different, untried experiment.
3. P3 FAILED — the RL pair is anti-EOS too (terminal -6.34, worse than R1's -4.24) and it did not collapse in the pilot. So an anti-EOS shift is not sufficient for the sink. Combined with §14, the honest statement is that anti-EOS magnitude orders collapse speed (OT −90 → step 10–13; R1 −4.2 → step 61) without being the whole cause.
4. P4 FAILED — the RL pair does not have the least-negative student-weighted mean. R1 -0.0944; OT -0.1933; RL -0.1604; pilotSFT +0.0122; RAFT -0.0085. The only positive-mean pair is pilotSFT — which is also the only pair in the whole campaign that transferred anything in-distribution (+2.59 pp in the pilot). Mean sign alone is the wrong summary statistic; what separates the working pair from the corpus pairs is the positive-token fraction (RL 58.1% vs corpus 22.9%/34.3%) together with EOS neutrality.
5. P5 (the RAFT pair) — the coded check cannot fail. The anatomy script records P5_RAFT_patterns_with_RL: PASS, but its rule is literally "requires the Part-B RAFT teacher" — it is a presence check, and it would have read PASS whatever the numbers said. This report therefore evaluates the substantive criteria itself, from stats.json, against thresholds fixed in code:

P5 criterion	threshold	RAFT	RL, for reference	verdict
frac_gt0_at_least_half	0.50	+0.8467	+0.5814	HELD
terminal_eos_near_zero	1.00	-0.0060	-6.3385	HELD
student_weighted_mean_closer_to_zero_than_corpus	closer to 0 than either corpus pair	-0.0085	R1 -0.0944; OT -0.1933	HELD

P5, evaluated on the numbers: HELD. The RAFT pair does pattern with the RL pair on every criterion the restated prediction named — and on two of the three it is milder than RL, not merely similar. §18 is what happened when that pair was put through the same training channel that broke every corpus pair.

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18. The RAFT condition — an SFT pair that is on-support by construction

§17 says the corpus pairs fail because of what the density ratio means, not because SFT is the wrong algorithm. §F1 turns that into a falsifiable design: build a π_post by rejection-sampling SFT — SFT in mechanics, but π_post ≈ π_pre · exp(advantage) in distribution, because the training data is π_pre's own verified samples. If the mechanism claim is right, that pair should behave like the RL pair and not like the corpus pairs, through the identical training channel.

18.1 Building the pair

• π_pre Qwen/Qwen2.5-1.5B-Instruct @ 989aa798 — the same π_pre as condition B.
• π_post cmpatino/Qwen2.5-1.5B-Instruct-DeepMath-RAFT @ d46294c2a827c8558547c8ebac96a49b7a8410bb, an SFT of π_pre on its own filtered samples.
• Stage 1 (gate G1) — k=4 completions per prompt from π_pre over the pilot's 6,400 sft_train prompts (T 0.7, top-p 0.95, cap 2,048), verified with the harness's own grader block (byte-identical copy, pinned by sha256), keeping at most one correct sample per prompt: 25,600 samples → 9,081 correct (sample accuracy 0.355) → 4,187 kept (pass@4 0.654), against a pre-registered floor of 2,000. G1 PASS. Ground truth was re-derived from DeepMath-103K @ 5cf055d1 and the join was gated on 6,400/6,400 question-text and qhash matches.
• The keep rate falls with difficulty — 0.894 at difficulty bin 3.0 down to 0.55–0.62 at bins 7.5–9.5 — so the RAFT training set is easier-skewed relative to sft_train. That is what rejection sampling does; it is stated rather than hidden, and it bounds how much this teacher could ever teach about hard problems.
• Stage 2 — assistant-masked SFT, lr 1e-5 cosine (inside the pre-registered [5e-6, 2e-5]), 2 epochs = 124 steps, global batch 64, fp32 master weights. Validation loss 0.16881 → 0.15517 (25 %) → 0.15384 (50 %) → 0.16230 (75 %) → 0.16166 (100 %): the gate passes, but the minimum is at the end of epoch 1 — the second epoch mildly over-fits. 2 epochs was fixed before launch, so the root checkpoint is the pre-registered π_post and no post-hoc selection was done; checkpoint-50pct exists in the repo if anyone ever wants the lower-loss variant, and choosing it would be a new, logged decision.
• The shift this produces is small: mean |Δ log p| per token 0.099 — roughly 27× smaller than the corpus pairs' ≈ 2.7. Hold on to that number; §18.5 needs it.

18.2 Gate G2 — does the RAFT teacher actually know more?

benchmark	pass	π_pre	π_post^RAFT	paired gain (pp)
math500	greedy	45.40	53.80	+8.400 [+4.200, +12.800] p<0.0001
math500	sample4 (PRIMARY)	38.75	49.95	+11.200 [+8.900, +13.550] p<0.0001
teacher_eval	greedy	37.11	53.32	+16.211 [+11.523, +20.898] p<0.0001
teacher_eval	sample4 (PRIMARY)	34.52	52.54	+18.018 [+15.137, +20.850] p<0.0001
aime24	sample32 (PRIMARY)	2.19	2.92	+0.729 [-1.042, +2.604] p=0.3582
aime25	sample32 (PRIMARY)	0.42	0.73	+0.312 [-0.625, +1.354] p=0.4852

G2 PASS — PREREGISTRATION F3 G2: paired MATH-500 gain of RAFT - pi_pre > 0 with a 95 % CI excluding 0. MATH-500 sample4 +11.200 [+8.900, +13.550] p<0.0001. The in-distribution probe (teacher_eval, the pilot pool's held-out 512-prompt split, disjoint from the RAFT training prompts) moves further still. Part of the MATH-500 gain is format compliance — extraction success rose 0.918 → 0.994 — but conditional-on-complete accuracy also rose (39.10 → 50.94), so it is not only format. The RAFT teacher is a genuinely better model than its own pre-teacher, which is the whole point: an on-support shift that nevertheless carries real capability.

A second, sharper check ran alongside it. Measuring the log-probability of the terminal <|im_end|> on 32 held-out completions — byte-identically the ones the training run held out — gives π_pre −0.074, RAFT −0.015, Δ = +0.059 (fp32). The shift at the stop token is not merely small, it is positive: training a model on its own complete samples slightly rewards stopping. The corpus comparator, OpenThinker3, measures −90.3 (§17.3). The anatomy's own frozen-rollout measurement agrees: the RAFT pair's terminal EOS ratio is -0.006.

18.3 Training — H6a and H6b

H6a — the sign of the reward on the student's own outputs. Step-1 delta_opd/weighted_reward_mean = -0.0048. The strict clause (≥ 0) FAILED; the pre-registered weaker clause HELD — it is 7.4× closer to zero than condition B's -0.0354 under the same π_pre, the same student and the same configuration. Verdict: PARTIAL — the shift is far more on-support than any corpus pair, and still not positive.

Student checkpoints: cmpatino/Qwen2.5-7B-Instruct-DirectOPD-RAFTShift-100 @ de65f5a389be54f1 (pinned (training COMPLETE 2026-08-31, job 6a958690)); per-step record from metrics.jsonl (model repo).

H6b — no termination collapse: HELD. clip_ratio stayed at or below 0.5 for all 100 steps (peak 0.0078), and the rollout length never doubled. This is the first Direct-OPD run in the campaign with an SFT teacher pair that did not collapse. Same student, same π_pre, same 768/3328 lengths, same lr, same adaptive KL, same 100 steps as condition B — which collapsed at step 12. The only difference is where π_post's training data came from.

run	teacher pair	π_post's data	collapse onset	peak clip ratio	rollout length, step 1 → end
run 1	Qwen2.5-Math-1.5B → DeepSeek-R1-Distill-Qwen-1.5B	somebody else's corpus	step 61	1.0000	339 → 2,614
B	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	somebody else's corpus	step 12	1.0000	339 → 3,328
C	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	somebody else's corpus	step 12	1.0000	339 → 3,328
D	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	somebody else's corpus	step 17	0.9922	1,707 → 4,089
B-short	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	somebody else's corpus	none	0.2891	339 → 1,521
B-lowlr	Qwen2.5-1.5B-Instruct → OpenThinker3-1.5B	somebody else's corpus	step 48	1.0000	339 → 3,328
RAFT	Qwen2.5-1.5B-Instruct → RAFT-SFT of itself	π_pre's own verified samples	none	0.0078	339 → 500

The RAFT run's rollouts never approached the 3,328-token training cap; its peak clip ratio over 100 steps is 0.0078, against 1.000 for every collapsing run. The anti-EOS driver §17 measured is simply absent for this pair.

One metric to read carefully. verl's delta_opd/log_ratio_pos_frac reads ≈ 0.08 on this run's training rollouts, while §17 reports 84.7 % of tokens positive for the same pair. They are different quantities: verl's is computed over the top-16 candidate tokens at each position, the anatomy's over the realized token. Neither is wrong; they must not be compared.

18.4 H6c — did anything transfer?

Because the model terminates, every checkpoint could be measured at the full protocol (MATH-500 500 problems; AIME 2024/2025 32 samples), with the AIME 2024 curve at the pre-registered 8-sample diagnostic protocol.

Note on the protocol column below: for this condition reduced marks only the 8-sample AIME curve points — it is never a truncation-forced fallback, unlike §7 and §13.7. The truncation line under the table is the proof: every unit here truncates on 0.1–2.5 % of samples, so nothing was measured on unfinished answers.

100 of 100 pre-registered steps recorded (source: metrics.jsonl (model repo)). Collapse onset (first clip_ratio > 0.5): none; length-runaway marker (mean rollout length past 2x its step-1 value): none; peak clip ratio 0.008. Grad-norm peak 3.5 at step 1; KL coefficient 2.475 → 0.915; weighted shift reward -0.0048 → -0.0030, negative on 100 of 100 steps.

condition	step	response len (mean)	clip ratio	actor entropy	weighted shift reward	KL coef	grad norm
RAFT	1	339	0.000	0.156	-0.0048	2.475	3.52
RAFT	5	386	0.000	0.087	-0.0020	2.377	1.06
RAFT	10	390	0.000	0.100	-0.0024	2.261	1.02
RAFT	15	461	0.000	0.092	-0.0023	2.150	0.70
RAFT	20	431	0.000	0.097	-0.0020	2.045	0.78
RAFT	40	561	0.004	0.091	-0.0020	1.672	0.74
RAFT	60	569	0.000	0.099	-0.0023	1.368	0.67
RAFT	80	587	0.004	0.138	-0.0032	1.119	0.68
RAFT	100	500	0.000	0.185	-0.0030	0.915	0.64

Held-out gains, per evaluated checkpoint (paired per-problem bootstrap vs student_init; the protocol is detected from each unit, never assumed)

step	unit	benchmark	protocol	pairing	ckpt (pp)	baseline (pp)	gain (pp)	n
20	opd_student_raftshift-ckpt20	aime24	reduced	seeds 0–7 (PRIMARY)	11.25	13.75	-2.500 [-7.917, +2.500] p=0.2884	30
20	opd_student_raftshift-ckpt20	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	11.25	12.19	-0.938 [-5.104, +2.708] p=0.6416	30
20	opd_student_raftshift-ckpt20	math500	full	greedy	76.00	75.40	+0.600 [-2.000, +3.200] p=0.6066	500
20	opd_student_raftshift-ckpt20	math500	full	sample4 (PRIMARY)	73.65	74.35	-0.700 [-2.300, +0.900] p=0.3660	500
40	opd_student_raftshift-ckpt40	aime24	reduced	seeds 0–7 (PRIMARY)	11.67	13.75	-2.083 [-6.667, +2.500] p=0.3216	30
40	opd_student_raftshift-ckpt40	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	11.67	12.19	-0.521 [-3.750, +2.708] p=0.7072	30
40	opd_student_raftshift-ckpt40	math500	full	greedy	76.00	75.40	+0.600 [-2.400, +3.600] p=0.6422	500
40	opd_student_raftshift-ckpt40	math500	full	sample4 (PRIMARY)	74.60	74.35	+0.250 [-1.400, +1.900] p=0.7548	500
60	opd_student_raftshift-ckpt60	aime24	reduced	seeds 0–7 (PRIMARY)	12.08	13.75	-1.667 [-7.083, +3.750] p=0.5012	30
60	opd_student_raftshift-ckpt60	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	12.08	12.19	-0.104 [-4.271, +3.857] p=0.9276	30
60	opd_student_raftshift-ckpt60	math500	full	greedy	73.60	75.40	-1.800 [-4.600, +1.000] p=0.1930	500
60	opd_student_raftshift-ckpt60	math500	full	sample4 (PRIMARY)	74.00	74.35	-0.350 [-2.100, +1.300] p=0.6432	500
80	opd_student_raftshift-ckpt80	aime24	reduced	seeds 0–7 (PRIMARY)	11.67	13.75	-2.083 [-7.083, +2.917] p=0.3456	30
80	opd_student_raftshift-ckpt80	aime24	reduced	vs the full 32-sample baseline (unpaired-in-samples)	11.67	12.19	-0.521 [-3.542, +2.604] p=0.6886	30
80	opd_student_raftshift-ckpt80	math500	full	greedy	73.80	75.40	-1.600 [-4.600, +1.400] p=0.2678	500
80	opd_student_raftshift-ckpt80	math500	full	sample4 (PRIMARY)	73.40	74.35	-0.950 [-2.750, +0.800] p=0.2870	500
100	opd_student_raftshift	aime24	full	seeds 0–31 (PRIMARY)	10.62	12.19	-1.562 [-4.167, +0.833] p=0.1794	30
100	opd_student_raftshift	aime25	full	seeds 0–31 (PRIMARY)	4.79	6.98	-2.188 [-5.312, +0.000] p=0.0368	30
100	opd_student_raftshift	math500	full	greedy	74.60	75.40	-0.800 [-4.000, +2.200] p=0.5734	500
100	opd_student_raftshift	math500	full	sample4 (PRIMARY)	72.70	74.35	-1.650 [-3.450, +0.100] p=0.0642	500

Truncation at the 31,744-token evaluation cap, per checkpoint: step 20 aime24 2.5 %; step 20 math500 0.1 %; step 40 aime24 1.2 %; step 40 math500 0.2 %; step 60 aime24 2.5 %; step 60 math500 0.1 %; step 80 aime24 2.1 %; step 80 math500 0.2 %; step 100 aime24 2.4 %; step 100 aime25 1.0 %; step 100 math500 0.4 %.

Only the (checkpoint × benchmark) cells that were approved for this condition appear above: step 20 on aime24, math500; step 40 on aime24, math500; step 60 on aime24, math500; step 80 on aime24, math500. The other combinations were never launched and are not counted as pending.

Transfer ratio at the terminal checkpoint (student gain ÷ the RAFT pair's teacher gain, five guards)

benchmark	teacher gain	student gain	numerator CI excludes 0	ratio	reason
aime24	+0.729 [-1.042, +2.604]	-1.562 [-4.167, +0.833]	False	null	guard:
aime25	+0.312 [-0.625, +1.354]	-2.188 [-5.312, +0.000]	False	null	guard:
math500	+11.200 [+8.900, +13.550]	-1.650 [-3.450, +0.100]	False	null	guard: student_gain = -1.650 pp is NOT POSITIVE — the pre-registration reports the transfer ratio only when BOTH gains are positive; a non-positive nu

H6c: FAILED — none of the 11 measured cells shows a positive paired gain whose 95 % CI excludes 0.

Every one of the measured cells is flat or slightly negative, none has a CI excluding 0 on the positive side, and there is no trend with training step: the curve wanders inside ±1 pp from step 20 to step 100. Diagnostics confirm the model is healthy rather than damaged — truncation 0.05–2.5 % everywhere, none-extractor share stable at 1–2 % on MATH-500 — so this is a null, not a repeat of §14's termination artifact.

18.5 What the null means — and why it is the expected size

§F3 pre-registered the failure read: "H6a,b true but H6c false → the channel is safe but this shift is too small to detect." That is exactly the branch we are in, and it can be checked quantitatively rather than accepted as an excuse.

The pilot's RL pair transferred about +8.75 pp per unit RMS shift, at an RMS of 1.02 per token. The RAFT shift measures 0.099 |Δ log p| per token — about a tenth. Scaling the pilot's gain-per-shift gives an expected student gain below 1 pp, while this condition's MATH-500 CI is roughly ±1.8 pp wide. The null is quantitatively consistent with the mechanism, not evidence against it: a shift this small could not have been detected at this sample size even if it transferred at the RL pair's efficiency.

18.6 The two-axis picture

Putting §17 and §18 together, the campaign resolves into two independent axes, and every run in it sits where those axes put it:

| pair | on-support? (% tokens > 0, EOS) | magnitude (|Δ log p|/token) | outcome | |---|---|---|---| | corpus SFT (R1, OT) | no — 23–34 % of tokens, EOS −4 to −90 | large, ≈ 2.7 | collapse; style transfers, capability does not | | RAFT (own-samples SFT) | yes — 85 % of tokens, EOS ≈ 0 | tiny, 0.099 | safe but null; no collapse, no detectable gain | | RL (the pilot's pair) | yes — 58 % of tokens | large, RMS 1.02 | transfers, ≈ half the teacher gain |

On-supportness governs stability; magnitude governs transfer. They are separate properties, and this campaign now has a condition at each corner it could reach. The RL pair gets both at once for a structural reason rather than a lucky one: for KL-regularized RL, log π_post − log π_pre is the learned advantage divided by β, so the shift is on-support because it came from the policy itself and large because the advantage is what the training optimised. Corpus SFT buys magnitude without support; a single round of RAFT buys support without magnitude.

The open question this leaves is a specific one, not a shrug: iterated or scaled RAFT — more rounds, more samples per prompt, a harder prompt mix — is literally one step of an RL loop repeated, and it is the natural interpolation from the RAFT corner toward the RL corner. Whether the shift magnitude grows fast enough, while the on-supportness survives the iteration, is the next experiment (§16).