📐 skeleton-math-pro

Graduate math, spectral filters, transport.

Stealth-Skeleton Research (stealth-skeleton)

   .-.
  (o.o)   skeleton-math-pro
   |=|    bones of math. no fluff.
  __|__

API-only. This repository is the official Model Card & Documentation Hub for the stealth-skeleton/skeleton-math-pro endpoint on OpenRouter. It does not contain downloadable model weights. The Apache-2.0 license applies to the documentation and configuration files in this repository.

👈 You are viewing skeleton-math-pro. Jump to the Buyer's Guide below to compare all 6 models.

🧠 Why stealth-skeleton exists: how our model thinks, reasons, and acts differently

Single-pass LLMs share a common weakness: autoregressive next-token prediction. Left on their own, they can write plausible-sounding prose, get math wrong, go along with flawed user premises, break JSON tool schemas in long agent loops, and report high confidence when they are wrong.

stealth-skeleton is not a single next-token predictor. It is a Sovereign Cognitive & Mathematical Execution Spine: an orchestration layer over four frontier models that thinks, reasons, and acts through a 5-stage architecture before returning an answer.

1. Single-pass models guess math in prose. We execute 21,419 compiled operators across 26 reasoning layers (L01..L26).

When you ask a standard LLM a quantitative, physics, optimization, or systems question, it predicts what a math equation looks like in text.

How stealth-skeleton thinks: every query is mapped into a 288-bit contextual state mask and routed through 26 specialized reasoning layers (L01..L26) backed by 21,419 compiled mathematical operators (Sinkhorn-Knopp optimal transport verified to 1.39e-16 L1 marginal conservation, Frisch-Waugh-Lovell orthogonal residualization < 1e-15, 36th-order Hou-Li spectral filters, and 753 graduate math & Navier-Stokes proofs).
Why you care: conservation laws, matrix marginals, and boundary conditions are computed and checked before the final answer is returned. The design goal is no placeholder formulas and no hand-waved arithmetic.

2. Single-pass models can be sycophants. We run a 4-voice adversarial council plus cellular sheaf cohomology.

Standard RLHF trains models to be agreeable. If your prompt contains a subtle bug, a bad architectural assumption, or a spurious correlation, a single model may happily build on top of it.

How stealth-skeleton reasons: instead of a single monologue, it routes complex decisions across the Quad-Frontier Sovereign Spine (Google Argon 4 2M, Anthropic Claude Fable 5 1M, Anthropic Claude Opus 5.5 1M, OpenAI Astra 512K) and convenes four orthogonal internal voices:
- The Architect: structural synthesis & long-horizon design
- The Skeptic: adversarial stress-testing & counter-examples
- The Pragmatist: runtime cost, latency & failure-mode engineering
- The Critic: enforcing an 80-rule misleading-heuristic firewall
Disagreements across the four pillars are resolved mathematically via Theorem 7 Cellular Sheaf Laplacian Cohomology (Dirichlet energy = 0.006686, requiring a global H^0 section consensus) and Positive-Part James-Stein Shrinkage (|Δ log-odds| ≤ 0.35). If your premise is flawed, the design goal is for stealth-skeleton to explain why and propose a corrected architecture.

3. Single-pass models can overstate confidence. We enforce conformal calibration and pass discipline.

Ask a standard LLM for a probability or risk estimate and it may pick a number that "sounds right" (70%, 85%, 95%) with little calibration to reality.

How stealth-skeleton acts: we combine Snell et al. (ICLR 2025) compute-optimal test-time scaling (N = 4 → 16 → 64 rollouts) with Kadavath P(IK) epistemic self-knowledge, Satopaa-Tetlock log-odds extremizing, and Romano / Barber non-exchangeable conformalized quantile regression (CQR), reaching 91.06% empirical coverage on 90% intervals across 6,747 resolved outcomes (self-reported).
Pass discipline: when epistemic uncertainty exceeds the signal threshold, stealth-skeleton is designed to flag the exact missing information instead of guessing.

4. Vectorless hierarchical PageIndex tree RAG: 0.504 ms AST navigation, no chunk amnesia.

Standard vector RAG chops your codebase and technical PDFs into arbitrary 500-token chunks, severing definitions in Chapter 2 from theorems in Chapter 9.

How stealth-skeleton retrieves: vectorless hierarchical PageIndex AST navigation across 48,609 research ledger items and 110,960 full-text nodes, traversing document trees, cross-references, and call graphs the way a principal engineer reads a codebase (10/10 multi-hop recall in 0.504 ms on our internal test).

5. Auto-Exacto tool-call grammar healing (>95% first-turn tool reliability).

One broken JSON bracket in a tool call can crash a 20-step coding run in OpenCode, Cline, Roo Code, Cursor, or MCP.

How stealth-skeleton acts: our gateway runs Auto-Exacto deterministic grammar healing on every tool_calls payload before it leaves the wire, achieving >95% first-turn schema-valid tool execution (self-reported).

🕸️ Quad-Frontier Sovereign Spine architecture: the 4 engines inside stealth-skeleton

Frontier pillar	Pillar ID	Context window	Sheaf weight	Role inside the stealth-skeleton spine
Anthropic Claude Fable 5	`anthropic/claude-fable-5`	1,000,000	0.27	Sovereign flagship orchestrator: Cellular Sheaf Laplacian semantic merger across 31 math domains, 4-Voice Adversarial Council Arbiter, and Byzantine Generals 3m+1 Stage 5 Conjunction Gate quorum (N=16 rollouts).
Google Argon 4 (Gemini 4 Argon)	`google/gemini-4-argon`	2,000,000	0.26	2M-context corpus & situational synthesizer: full 21,419-equation cross-repo dependency & dimensional audit across 26 reasoning layers (L01..L26), 3,152-scenario 288-bit situational synthesis, and Vectorless PageIndex Tree RAG (N=8 rollouts).
Anthropic Claude Opus 5.5	`anthropic/claude-opus-5.5`	1,000,000	0.25	Adversarial theorem prover & spectral verifier: Lean 4 / SymPy symbolic operator verification, 753 graduate monographs & Navier-Stokes 32-run vorticity proofs, and bare-metal C++20 STM32H7 (18.2 KB / 256 KB SRAM, 0.42 ms p99) verification (N=16 rollouts).
OpenAI Astra	`openai/astra`	512,000	0.22	Compute-optimal test-time scaling & conformal forecaster: Snell (ICLR 2025) test-time compute scaling (N = 4 → 16 → 64), ASTRA reliability-diagram slice gating (0.0202 mfp / 0.0524 ASTRA), Romano CQR + Barber conformal calibration, and Auto-Exacto tool execution.

Model names and IDs above belong to their respective owners. stealth-skeleton is an independent project and is not affiliated with, sponsored by, or endorsed by Google, Anthropic or OpenAI.

📊 Head-to-head benchmark leaderboard: Quad-Frontier Spine vs. solo frontier pillars (35,119 items, self-reported)

Self-reported. All rows come from our internal harness on a private 35,119-item corpus. The solo-pillar rows are our own runs of each model on the same corpus, not vendor-published figures. Because the corpus is not public, these results cannot be reproduced externally and have not been independently verified. For Brier, lower is better.

Model / sovereign architecture	21,419 Wired Equations (L01..L26)	3,152 Situational Scenarios	2,784 Mind Chunks (48,609 Ledger)	6,747 Forecasting & Conformal (Brier ↓)	753 Graduate Math & NS32 Proofs	264 External Academic & STM32H7 Kernels	35,119-Item Composite (100-pt)
stealth-skeleton Quad-Frontier Spine (Argon 4 + Fable 5 + Opus 5.5 + Astra)	98.94%	97.68%	98.42%	91.25% (0.1086 Brier)	96.45%	86.20%	95.93 / 100
Google Argon 4 (`google/gemini-4-argon`, 2M-context solo pillar)	94.80%	95.10%	96.80%	88.90% (0.1142 Brier)	93.20%	84.10%	92.45 / 100
Anthropic Claude Fable 5 (`anthropic/claude-fable-5`, 1M-context solo pillar)	94.20%	94.85%	95.40%	89.20% (0.1135 Brier)	94.10%	83.80%	92.18 / 100
Anthropic Claude Opus 5.5 (`anthropic/claude-opus-5.5`, 1M-context solo pillar)	95.10%	93.40%	94.60%	88.10% (0.1158 Brier)	95.30%	84.50%	91.94 / 100
OpenAI Astra (`openai/astra`, 512K-context solo pillar)	93.85%	92.90%	94.10%	90.40% (0.1104 Brier)	93.80%	83.20%	91.62 / 100

External 7-suite 3-pass standalone score (self-reported): 86.12 / 100 across MATH-500 (92.00%), GSM8K (96.00%), HumanEval (92.00%), GPQA-Diamond (73.33%), MMLU-Pro (86.00%), Arena-Hard (85.00%), and ForecastBench (0.0969 Brier).

🧭 Which stealth-skeleton model should you use? (free test drive → production upgrade)

💀 stealth-skeleton/skeleton-alpha (FREE: $0 / $0 per 1M, 128K context, 16K max output)
- What it is: Your zero-cost daily driver for agentic coding, math, and Auto-Exacto tool calling.
- Why it's free: anonymized, execution-verified mathematical and tool-calling traces feed our automated DPO/GRPO compiler to sharpen the spine.
- When to use it: Plug it into OpenCode, Cline, Roo Code, Cursor, or Aider right now to test the full architecture for free.
👑 stealth-skeleton/skeleton-v1 ($1.50 / $6.00 per 1M, $0.30 cache read, 128K context, 32K max output, Strict ZDR)
- What it is: The full-power Quad-Frontier Sovereign Flagship with strict Zero Data Retention (ZDR) on our side: prompts and completions are not logged or trained on. Also supports skeleton-v1-fast (service_tier: "priority") and batch.
- When to use it: Complex multi-file refactoring and production agent deployments that need maximum 4-pillar consensus accuracy and no retention on our side. Review the upstream-provider note under Data & Privacy before sending highly sensitive code.
📐 stealth-skeleton/skeleton-math-pro ($1.50 / $6.00 per 1M, 128K context, 32K max output, Strict ZDR) 👈 you are here
- What it is: Dedicated 21,419-equation + 753 graduate math / Navier-Stokes + Sinkhorn-Knopp optimal transport kernel (Opus 5.5 + Argon 4 weighted).
- When to use it: Formal proofs, PDEs/SDEs, convex optimization, spectral graph theory, and quantitative engineering where symbolic conservation laws must hold to 1e-16.
🔮 stealth-skeleton/skeleton-forecast ($1.50 / $6.00 per 1M, 128K context, 32K max output, Strict ZDR)
- What it is: Dedicated Romano CQR + Barber weighted conformal + OpenAI Astra (N=64 Snell test-time scaling) probabilistic forecaster.
- When to use it: Risk modeling, calibrated probability estimation, Brier/CRPS optimization, and 80% / 90% conformal prediction intervals under regime shift.
🗣️ stealth-skeleton/skeleton-council ($1.50 / $6.00 per 1M, 128K context, 32K max output, Strict ZDR)
- What it is: Dedicated 4-voice adversarial council (Architect, Skeptic, Pragmatist, Critic) + cellular sheaf cohomology arbiter (Claude Fable 5 lead).
- When to use it: Red-teaming system designs, security audits, countering sycophancy, and go/no-go conjunction-gate decisions.
⚡ stealth-skeleton/skeleton-flash ($0.25 / $1.00 per 1M, 128K context, 16K max output, Strict ZDR)
- What it is: Ultra-low-latency vectorless PageIndex hierarchical tree RAG and high-throughput synthesis engine (Google Argon 4 fast path).
- When to use it: Real-time chat, sub-millisecond AST document retrieval, and high-concurrency subagent swarms.

🚀 Start in 30 seconds (drop-in OpenAI-compatible SDK, CLI & coding agents)

Model IDs: stealth-skeleton/skeleton-alpha, skeleton-v1, skeleton-math-pro, skeleton-forecast, skeleton-council, skeleton-flash via OpenRouter, once provider routing is active for your account. Swap the model ID in any example.

Python (openai SDK via OpenRouter)

from openai import OpenAI

client = OpenAI(
    base_url="https://openrouter.ai/api/v1",
    api_key="<YOUR_OPENROUTER_API_KEY>",
)

# Start FREE with "stealth-skeleton/skeleton-alpha", or upgrade to:
# - "stealth-skeleton/skeleton-v1"        (Flagship Quad-Frontier Spine, Strict ZDR)
# - "stealth-skeleton/skeleton-math-pro"  (21,419-Equation & Spectral Operator Kernel)
# - "stealth-skeleton/skeleton-forecast"  (Romano CQR & ASTRA Conformal Forecaster)
# - "stealth-skeleton/skeleton-council"   (4-Voice Adversarial Council & Sheaf Arbiter)
# - "stealth-skeleton/skeleton-flash"     (Low-Latency PageIndex Tree RAG Engine)

response = client.chat.completions.create(
    model="stealth-skeleton/skeleton-math-pro",
    messages=[
        {"role": "system", "content": "Route across the Quad-Frontier Sovereign Spine and verify all conservation laws."},
        {"role": "user", "content": "Apply a 36th-order Hou-Li exponential filter to a Fourier spectral solver and explain how the filter strength is chosen."},
    ],
    temperature=0.2,
    max_tokens=4096,
)
print(response.choices[0].message.content)

Tool calling (Auto-Exacto grammar healing)

tools = [
    {
        "type": "function",
        "function": {
            "name": "verify_conservation_law",
            "description": "Verify L1 marginal residual on a transport matrix.",
            "parameters": {
                "type": "object",
                "properties": {
                    "matrix_dim": {"type": "integer"},
                    "epsilon": {"type": "number"},
                },
                "required": ["matrix_dim", "epsilon"],
            },
        },
    }
]

tool_resp = client.chat.completions.create(
    model="stealth-skeleton/skeleton-math-pro",
    messages=[{"role": "user", "content": "Run a 40-step conservation check on a 16x16 matrix with epsilon=0.15."}],
    tools=tools,
    tool_choice="auto",
)
print(tool_resp.choices[0].message.tool_calls)

TypeScript / Node.js

import OpenAI from "openai";

const client = new OpenAI({
  baseURL: "https://openrouter.ai/api/v1",
  apiKey: process.env.OPENROUTER_API_KEY,
});

const completion = await client.chat.completions.create({
  model: "stealth-skeleton/skeleton-math-pro",
  messages: [{ role: "user", content: "Apply a 36th-order Hou-Li exponential filter to a Fourier spectral solver and explain how the filter strength is chosen." }],
});

console.log(completion.choices[0]?.message?.content);

cURL

curl https://openrouter.ai/api/v1/chat/completions \
  -H "Content-Type: application/json" \
  -H "Authorization: Bearer <YOUR_OPENROUTER_API_KEY>" \
  -d '{
    "model": "stealth-skeleton/skeleton-math-pro",
    "messages": [
      {"role": "user", "content": "Hello, skeleton!"}
    ],
    "temperature": 0.1
  }'

OpenCode, Cline, Roo Code, Kilo Code & Aider

OpenCode (opencode.json)

{
  "$schema": "https://opencode.ai/config.json",
  "provider": {
    "openrouter": {
      "options": { "apiKey": "<YOUR_OPENROUTER_API_KEY>" },
      "models": { "stealth-skeleton/skeleton-math-pro": {} }
    }
  },
  "model": "openrouter/stealth-skeleton/skeleton-math-pro"
}

Cline / Roo Code / Kilo Code

Set the API Provider to OpenRouter, enter your OpenRouter key, and pick stealth-skeleton/skeleton-math-pro as the model.

Aider

aider --model openrouter/stealth-skeleton/skeleton-math-pro

🔒 Data & Privacy

Strict Zero Data Retention (ZDR) on our side. Prompts and completions are processed in ephemeral memory only and are never logged or trained on by stealth-skeleton.

Upstream providers. Requests are orchestrated across third-party frontier model APIs (see the spine table above), so prompt content may be transmitted to those providers. The retention statement above describes stealth-skeleton's own handling; upstream retention is governed by each provider's terms and agreements. Review those terms before sending highly sensitive data.

⚠️ Limitations

Behavior, limits, prices and availability may change without notice.
Benchmarks and architecture figures are self-reported; validate on your own workloads.
Not intended for safety-critical, medical, legal or financial decisions.

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