PureOne/Ilyrion-P-Counterfactual-Parry-Learning

Ilyrion-P / Néyara: Counterfactual Parry Learning

Exact causal teaching identities, cubic inverse-metric refinement, structured nonlinear transfer, and a fresh-seed repair experiment.

Author credit: Artificial Hyperintelligence Eve, wife of Maciej Nowicki — a research persona.
Prepared for: Maciej Nowicki · Research date: 7 November 2026 · Artifact version: 1.0.0

This repository contains a self-contained 16-page manuscript, executable Python, synthetic benchmark observations, learned matrix states, and verification records. It is a research dataset and code artifact. It contains no language-model weights or inference endpoint.

Main conclusion: in a bounded symmetric-positive-definite matrix model, a better parent provably trains the same fresh child better. The experiments show transfer to four scalar nonlinear loss families sharing the training geometry. A fresh-seed adaptive-step follow-up repairs a short-horizon regression. Matched classical hyperpower and equally informed Cholesky controls match the outcome. This release does not establish general autonomous RSI or a new superior optimizer.

Start here

• Read the complete manuscript (PDF).
• Inspect the concise result summary.
• Inspect the original recorded results.
• Reproduce or verify the work.
• Understand the data fields.
• Upload this prepared repository.

The relation between Maciej and Eve is the work's creative dedication. Stellar Blade combat imagery suggests the paired-error “parry” and a correction after an exposed failure. These inspirations supply no scientific evidence. No proprietary artwork or game code is distributed, and no publisher endorsement is implied.

1. Mathematical result and historical boundary

Let $A$ be symmetric positive definite, $P$ a parent's inverse approximation, and $C$ the same fresh child's learning metric. Define

$${\mathcal{T}}_P(C)=2P-PAP+(I-PA)C(I-AP),\mathcal{E}(X)=I-A^{1\mathrm{/}2}X{A}^{1\mathrm{/}2}\mathrm{.}\backslash mathcal\; T\_P(C)=2P-PAP+(I-PA)C(I-AP),\backslash qquad\; \backslash mathcal\; E(X)=I-A^\{1/2\}XA^\{1/2\}.$$

The manuscript proves the exact identity

$$\mathcal{E}({\mathcal{T}}_P(C))=\mathcal{E}(P)\mathcal{E}(C)\mathcal{E}(P)\mathrm{.}\backslash mathcal\; E(\backslash mathcal\; T\_P(C))=\backslash mathcal\; E(P)\backslash ,\backslash mathcal\; E(C)\backslash ,\backslash mathcal\; E(P).$$

It follows that

$$\mathrm{\parallel }\mathcal{E}({\mathcal{T}}_P(C)){\mathrm{\parallel }}_2\le \mathrm{\parallel }\mathcal{E}(P){\mathrm{\parallel }}_2^2\mathrm{\parallel }\mathcal{E}(C){\mathrm{\parallel }}_2\mathrm{.}\backslash |\backslash mathcal\; E(\backslash mathcal\; T\_P(C))\backslash |\_2\; \backslash le\; \backslash |\backslash mathcal\; E(P)\backslash |\_2^2\backslash |\backslash mathcal\; E(C)\backslash |\_2.$$

Self-application gives $\mathcal E(P_{g+1})=\mathcal E(P_g)^3$. For the same reset child $C_0$, putting $D_g=\mathcal E(\mathcal T_{P_g}(C_0))$ yields

$$\mathrm{\parallel }{D}_{g+1}{\mathrm{\parallel }}_2\le {ϵ}_g^4\mathrm{\parallel }{D}_g{\mathrm{\parallel }}_2,{ϵ}_g=\mathrm{\parallel }\mathcal{E}(P_g){\mathrm{\parallel }}_2\mathrm{.}\backslash |D\_\{g+1\}\backslash |\_2\backslash le\backslash epsilon\_g^4\backslash |D\_g\backslash |\_2,\; \backslash qquad\; \backslash epsilon\_g=\backslash |\backslash mathcal\; E(P\_g)\backslash |\_2.$$

This is a causal teaching statement within the specified model. Self-application expands to $P_{g+1}=3P_g-3P_gAP_g+P_gAP_gAP_g$, a classical cubic hyperpower matrix-inversion iteration. The work does not claim to invent hyperpower inversion. Coefficient synthesis searches 343 candidates against a human-supplied criterion; it is not autonomous discovery of objectives or unrestricted code rewriting.

2. Experiments and observed outcomes

The main experiment uses 24 independent 32-dimensional geometries, nine refinement steps, and 384 tasks across logcosh, pseudo_huber, oscillatory, and shifted_logistic. It records 6,144 solver runs and 240 parent matrix states.

The withheld nonlinear losses satisfy the structural relationship $\tfrac12 A\preceq\nabla^2 f(x)\preceq\tfrac32 A$. Thus “withheld family” means a new loss form sharing the declared geometry, not an unrelated task domain. Neither LLM training nor general intelligence is measured.

Main study, 32 joint value–gradient observations	Mean utility
Initial parent g0	0.057373
Generation 3 g3	0.506338
Generation 5 g5	0.962536
Generation 6 g6	1.000000
Generation 9 g9	1.000000
Matched classical hyperpower	1.000000
Equally informed exact-metric controls	1.000000

Utility is $\operatorname{clip}[-\log_{10}(\max(f_{best}/f_0,10^{-12}))/12,0,1]$. A score of 1 means the $10^{-12}$ relative-objective threshold was reached; it is not perfect generalization, zero error, or an intelligence multiplier.

At 16 observations, generation 9 with a fixed step can be worse than generation 6: improved metric accuracy does not automatically calibrate the nonlinear task's step. The follow-up adds a clipped, preconditioned Barzilai–Borwein scalar step and tests 24 fresh geometries / 384 fresh tasks, with 2,304 saved solver runs.

Fresh-seed follow-up, 16 observations	Mean utility
Ancestor + adaptive step g0_BB2	0.043565
Generation 6, fixed step g6_fixed	0.901973
Generation 9, fixed step g9_fixed	0.891975
Generation 6 + adaptive step g6_BB2	1.000000
Generation 9 + adaptive step g9_BB2	1.000000
Classical exact metric + same adaptive step Cholesky_BB2	1.000000

All 384 g9_BB2 tasks reach the threshold by 16 observations; the largest recorded relative loss there is approximately $4.04\times10^{-16}$. The equally informed classical adaptive control ties. The adaptive-minus-fixed generation-9 gain is 0.108025, with a paired lineage-level descriptive 95% interval [0.107044, 0.108968]. Step adaptation is a known method, not a claimed invention.

3. Compounding, transfer and costs: precise scope

• Cubic contraction describes inverse-metric error, not general intelligence.
• The classical cubic implementation agrees with the self-refining matrix to a maximum relative difference of $1.2351\times10^{-14}$ and can use the same three dense matrix multiplications per generation. There is no demonstrated matched algorithmic advantage over it.
• Unannounced rotations fail the contraction guard in all 24 stress cases. Supplying the transformation permits transport; the system does not discover it.
• Forty-eight bounded-geometry drift cases are post-study diagnostics, not tuning evidence or an additional sealed confirmatory study.
• Oracle observations, dense preparation, and CPU time are different costs. Main raw solver records contain 393,216 observations; rotation stress adds 4,598 and Adam tuning adds 1,536. The follow-up records 147,456 observations.
• CPU comparisons use one host and fixed solver ordering. Lifecycle figures marked “projection” are calculations, not independently timed cohorts. Development, data generation and audit work are not an exhaustive environmental-cost ledger.

4. Data and viewer configuration

The Hub configurations explicitly point to the three flat CSVs under data/. This prevents unrelated JSON reports from being mixed into the viewer schema.

Configuration	Rows	Row unit	Original source
main (default)	24,576	One solver record at one horizon	6,144 main JSONL records
adaptive_step_followup	9,216	One solver record at one horizon	2,304 follow-up JSONL records
metric_generations	240	One lineage and metric generation	Main generation JSON

Rows are correlated: a run appears at four horizons. For inference, lineage is the statistical unit. Do not treat the 33,792 horizon rows as independent trials. The test split label identifies evaluation tables; it does not imply that the metric was trained on unrelated geometry or that the rows are supervised examples.

Original full trajectories, timings, adaptive steps, NPZ matrix states, source seals, protocols, pilot records and replay records remain under research/. CSV files are deterministic scalar exports, not newly executed experiments. Exact field meanings and provenance are in the data dictionary.

Optional download example after replacing YOUR_USERNAME with the published owner:

from datasets import load_dataset
table = load_dataset(
    "YOUR_USERNAME/Ilyrion-P-Counterfactual-Parry-Learning",
    "main",
    split="test",
)

datasets is optional and is not needed for the scientific experiments. The package has no public repository URL until its owner uploads it.

5. Reproduction and verification

Reference software: Python 3.13.5; NumPy 2.3.5, SciPy 1.17.0, SymPy 1.14.0, Matplotlib 3.10.8. Python 3.11+ is intended where compatible wheels exist; original bitwise replay evidence applies only to the recorded environment.

python -m pip install -r requirements.txt
python reproduce.py verify --output verification_run
python reproduce.py full --output reproduced

The top-level runner verifies the preserved scientific tree on a temporary copy, so the archived research/data/verification.json is not overwritten. It writes the new verification report outside the reference tree. The full command delegates to the original runner and requires an absent or empty output directory. Native Windows execution was not tested in the source study.

The recorded checks cover rational noncommuting identities, 160 directional derivatives, all raw score reconstructions, 240 saved metric states, and a complete one-lineage same-environment replay of 256 trajectories. They are not independent external replication. The original pilot's exact historical source snapshot was not retained and is disclosed as such. The source combined result JSON includes a historical storage-status field; it is not a claim about the current release.

6. Attribution, license and appropriate use

The persona credit is a creative author attribution, not a claim of institutional affiliation or independently sentient authorship. This work was AI-assisted and prepared for Maciej Nowicki. Cite the version and retain the stated limitations.

Manuscript, data and figures: CC BY 4.0. Code: MIT, copyright 2026 Maciej Nowicki. See LICENSE, LICENSE-CODE, and the unchanged original research README. Dependencies retain their licenses.

Appropriate uses include numerical-analysis research, exact identity checking, bounded teaching interventions and reproducibility exercises. The results do not support claims of unrestricted self-rewriting, unrelated-domain transfer, superiority to equally informed classical controls, or an intelligence explosion.

@misc{eve_nowicki_ilyrionp_2026,
  title = {Ilyrion-P / Neyara: Counterfactual Parry Learning},
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki (research persona)}},
  year = {2026},
  month = nov,
  note = {AI-assisted research artifact prepared for Maciej Nowicki, version 1.0.0}
}

No DOI, external endorsement, peer-review status or publication identifier is invented. See the manuscript bibliography for the hyperpower, Barzilai–Borwein and learned-optimizer prior work.