---
language:
- en
license: apache-2.0
library_name: openai-compatible
pipeline_tag: text-generation
tags:
- stealth-skeleton
- mathematical-reasoning
- conformal-prediction
- optimal-transport
- tool-calling
- code-generation
- livebench
inference: false
---
# 📐 skeleton-math-pro
### Graduate math, spectral filters, transport.
    
**Stealth-Skeleton Research (`stealth-skeleton`)**
```text
.-.
(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)
1. 💀 **`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.
2. 👑 **`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.
3. 📐 **`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.
4. 🔮 **`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.
5. 🗣️ **`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.
6. ⚡ **`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)
```python
from openai import OpenAI
client = OpenAI(
base_url="https://openrouter.ai/api/v1",
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)
```python
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
```typescript
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
```bash
curl https://openrouter.ai/api/v1/chat/completions \
-H "Content-Type: application/json" \
-H "Authorization: Bearer " \
-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)
```json
{
"$schema": "https://opencode.ai/config.json",
"provider": {
"openrouter": {
"options": { "apiKey": "" },
"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
```bash
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.