Update model card

README.md

@@ -36,19 +36,19 @@ inference: false
 
 > **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.
 
-## 📐 Overview: Graduate Mathematical, Spectral Operator & PDE/Optimization Kernel
+## 📐 Overview: Mathematical & Spectral Operator Kernel
 
-Built for symbolic derivations, **Sinkhorn-Knopp optimal transport** (L1 marginal residual 1.39e-16), **Frisch-Waugh-Lovell (FWL)** orthogonal residualization (< 1e-15), **36th-order Hou-Li spectral filtering**, and Lyapunov stability proofs.
+**Opus 5.5 + Argon 4 Mathematical & Spectral Operator Kernel.** Executes all 21,419 wired equations across 26 layers (L01..L26), Sinkhorn-Knopp optimal transport (L1 residual 1.39e-16), FWL orthogonal projection (< 1e-15), Hou-Li 36th-order spectral filters, and 753 graduate math/Navier-Stokes proofs.
 
-- **36th-order Hou-Li spectral filtering** for smooth, stable spectral methods.
-- **Sinkhorn-Knopp optimal transport** and **FWL orthogonal projection** with tiny residuals.
-- **PDE / optimization kernel** with Lyapunov stability proofs.
+- **21,419 wired equations** across 26 layers.
+- **36th-order Hou-Li spectral filters**, Sinkhorn-Knopp transport and FWL projection.
+- **753 graduate math / Navier-Stokes proofs.**
 
 **Best for:**
 
-- Graduate-level mathematics, physics, quantitative finance & operations research
-- Convex optimization, optimal transport, spectral graph theory & PDE/SDE modeling
-- Verifying symbolic equations and numerical stability invariants
+- Graduate mathematics, physics, PDEs/SDEs, and quantitative optimization
+- Optimal transport, spectral graph theory, and numerical stability verification
+- Auditing symbolic derivations with zero placeholder tolerance
 
 ## 🧾 Quick facts
 
@@ -58,20 +58,33 @@ Built for symbolic derivations, **Sinkhorn-Knopp optimal transport** (L1 margina
 | Price (input / output per 1M tokens) | $1.50 / $6.00 |
 | Context window | 128K tokens |
 | Max output | 32K tokens |
-| Data policy | Strict ZDR |
+| Data policy | Strict ZDR (see Data & Privacy) |
 | Interface | OpenAI-compatible Chat Completions |
 | Weights | None: API-only |
 
-## 🦴 Stealth-Skeleton Model Family Guide: What Each Model Does & When to Use It
+## 🕸️ 1. Quad-Frontier Sovereign Spine: how stealth-skeleton works under the hood
 
-| Model | Tier, pricing & limits | Core architecture & what it does | Best use cases (when to use it) |
+Every `stealth-skeleton/*` endpoint orchestrates a 4-pillar frontier spine merged via **Theorem 7 Cellular Sheaf Laplacian Cohomology** (Dirichlet energy = 0.006686, H^0 global-section consensus) and **Stage D Positive-Part James-Stein Shrinkage** (|Δ log-odds| ≤ 0.35).
+
+| Frontier pillar | Model ID | Context window | Sheaf weight | Primary engine stages & capabilities |
+|---|---|---:|---:|---|
+| **Anthropic Claude Fable 5** | `anthropic/claude-fable-5` | 1,000,000 | 0.27 | **Sovereign flagship orchestrator:** Cellular Sheaf Cohomology semantic merger across 31 math domains, 4-Voice Adversarial Council Arbiter (Architect, Skeptic, Pragmatist, Critic), 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 context synthesis, and Vectorless PageIndex Hierarchical 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 (BK-01..BK-25 + GAP-01..08), 32-run Navier-Stokes vorticity & Hou-Li 36th-order spectral filtering, 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 et al. (ICLR 2025) test-time compute scaling (N = 4 → 16 → 64 rollouts), ASTRA learned reliability-diagram slice gating (0.0202 mfp / 0.0524 ASTRA), Romano CQR + Barber weighted conformal bounds across 6,747 resolutions, and Auto-Exacto schema-valid 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.*
+
+## 🦴 2. The 6 stealth-skeleton models: what they are, what they do & when to use them
+
+| Model | Tier, pricing & limits | What it does | When to use it |
 |---|---|---|---|
-| 💀 **[skeleton-alpha](https://huggingface.co/stealth-skeleton/skeleton-alpha)** | **Free Preview**<br>$0 / $0 (free) per 1M<br>128K context, 16K max output | Combines multi-pass reasoning with **Auto-Exacto** deterministic tool-call grammar healing (>95% schema compliance, self-reported) and symbolic conservation checks. Anonymized execution-verified traces help align future checkpoints via DPO/GRPO. | • Daily agentic coding in **OpenCode, Cline, Roo Code, Cursor, Aider**<br>• Multi-turn function/tool calling & MCP orchestration<br>• Zero-cost high-volume prototyping, unit test generation & math/code verification |
-| 👑 **[skeleton-v1](https://huggingface.co/stealth-skeleton/skeleton-v1)** | **Flagship Production**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | Full 3-pass inference stack (Pass 1 fast draft → Pass 2 chain-of-thought critique → Pass 3 operator-verified synthesis) with strict **Zero Data Retention (ZDR)**. Also supports `service_tier: "priority"` (`skeleton-v1-fast`) and `variant: "batch"`. | • Production software engineering & complex multi-file refactoring<br>• Enterprise workloads requiring strict **Zero Data Retention (ZDR)**<br>• Long-horizon system design, formal verification & deep research synthesis |
-| 📐 **[skeleton-math-pro](https://huggingface.co/stealth-skeleton/skeleton-math-pro)** | **Specialist Kernel**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | Built for symbolic derivations, **Sinkhorn-Knopp optimal transport** (L1 marginal residual 1.39e-16), **Frisch-Waugh-Lovell (FWL)** orthogonal residualization (< 1e-15), **36th-order Hou-Li spectral filtering**, and Lyapunov stability proofs. | • Graduate-level mathematics, physics, quantitative finance & operations research<br>• Convex optimization, optimal transport, spectral graph theory & PDE/SDE modeling<br>• Verifying symbolic equations and numerical stability invariants |
-| 🔮 **[skeleton-forecast](https://huggingface.co/stealth-skeleton/skeleton-forecast)** | **Specialist Forecaster**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | Applies **Romano Conformalized Quantile Regression (CQR)** (90.35% empirical coverage), **Gibbs-Candes Adaptive Conformal Inference (ACI)**, **Barber non-exchangeable conformal weights**, **Kadavath P(IK) epistemic shrinkage**, and **Satopaa-Tetlock log-odds extremizing** (0.0969 ForecastBench Brier). | • Calibrated probability estimation & risk modeling where raw LLMs are overconfident<br>• Time-series quantile intervals (80% / 90% conformal bounds) under distribution shift<br>• Quantitative decision support, calibration & proper scoring rule (Brier / CRPS) tasks |
-| 🗣️ **[skeleton-council](https://huggingface.co/stealth-skeleton/skeleton-council)** | **Multi-Agent Arbiter**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | Runs four orthogonal internal perspectives (**Architect**, **Skeptic**, **Pragmatist**, **Critic**) reconciled via **Cellular Sheaf Laplacian cohomology** and an **80-rule misleading-heuristic firewall** to reduce sycophancy and groupthink. | • High-stakes architecture reviews, security audits & go/no-go engineering decisions<br>• Red-teaming plans, detecting spurious correlations & stress-testing assumptions<br>• Final conjunction-gate arbitration before deploying code or capital |
-| ⚡ **[skeleton-flash](https://huggingface.co/stealth-skeleton/skeleton-flash)** | **Low-Latency / High-Throughput**<br>$0.25 / $1.00 per 1M<br>128K context, 16K max output | Optimized for ultra-fast Time-to-First-Token (TTFT), hierarchical document tree traversal without lossy vector-chunk truncation, and high-concurrency extraction. | • Real-time chat, sub-second routing, classification & document extraction<br>• Large-corpus hierarchical RAG over books, PDFs, and codebases<br>• High-concurrency batch pipelines & subagent worker loops |
+| 💀 **[skeleton-alpha](https://huggingface.co/stealth-skeleton/skeleton-alpha)** | **Free Preview**<br>$0 / $0 (free) per 1M<br>128K context, 16K max output | **Crowd-RLHF Execution-Verified Coding, Math & Tool-Calling Engine** routed over the Quad-Frontier Spine with Auto-Exacto tool-call grammar healing (>95%, self-reported). Anonymized execution-verified traces feed DPO/GRPO alignment. | • Free daily coding agent in **OpenCode, Cline, Roo Code, Cursor, Aider**<br>• Multi-turn function/tool calling & MCP orchestration<br>• High-volume prototyping, unit test generation & symbolic math checks |
+| 👑 **[skeleton-v1](https://huggingface.co/stealth-skeleton/skeleton-v1)** | **Flagship Production**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | **Full Quad-Frontier Sovereign Flagship (Argon 4 + Fable 5 + Opus 5.5 + Astra)** with Cellular Sheaf Consensus and strict Zero Data Retention (ZDR). Also available as `skeleton-v1-fast` (`service_tier: "priority"`) and `batch`. | • Mission-critical production software engineering & multi-file refactoring<br>• Enterprise workloads requiring strict **Zero Data Retention (ZDR)**<br>• Complex system architecture, formal verification & deep research synthesis |
+| 📐 **[skeleton-math-pro](https://huggingface.co/stealth-skeleton/skeleton-math-pro)** | **Specialist Kernel**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | **Opus 5.5 + Argon 4 Mathematical & Spectral Operator Kernel.** Executes all 21,419 wired equations across 26 layers (L01..L26), Sinkhorn-Knopp optimal transport (L1 residual 1.39e-16), FWL orthogonal projection (< 1e-15), Hou-Li 36th-order spectral filters, and 753 graduate math/Navier-Stokes proofs. | • Graduate mathematics, physics, PDEs/SDEs, and quantitative optimization<br>• Optimal transport, spectral graph theory, and numerical stability verification<br>• Auditing symbolic derivations with zero placeholder tolerance |
+| 🔮 **[skeleton-forecast](https://huggingface.co/stealth-skeleton/skeleton-forecast)** | **Specialist Forecaster**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | **OpenAI Astra + Fable 5 Calibrated Probabilistic Forecaster.** Runs Snell test-time scaling (N=64), ASTRA reliability gating, Romano CQR + Barber non-exchangeable conformal intervals (91.06% empirical 90% coverage across 6,747 resolutions), Kadavath P(IK), and Satopaa-Tetlock log-odds extremizing. | • Calibrated probability estimation & Brier/CRPS optimization<br>• Conformal prediction intervals (80% / 90%) under distribution shift<br>• Quantitative decision support & risk-gated forecasting |
+| 🗣️ **[skeleton-council](https://huggingface.co/stealth-skeleton/skeleton-council)** | **Multi-Agent Arbiter**<br>$1.50 / $6.00 per 1M<br>128K context, 32K max output | **Claude Fable 5 4-Voice Adversarial Council & Sheaf Cohomology Arbiter.** Convenes Architect, Skeptic, Pragmatist, and Critic across all 4 frontier pillars with an 80-rule misleading-heuristic firewall and Byzantine 3m+1 quorum. | • High-stakes architecture reviews, security audits & go/no-go decisions<br>• Red-teaming plans, eliminating sycophancy & stress-testing assumptions<br>• Final conjunction-gate arbitration before deploying code or capital |
+| ⚡ **[skeleton-flash](https://huggingface.co/stealth-skeleton/skeleton-flash)** | **Low-Latency / High-Throughput**<br>$0.25 / $1.00 per 1M<br>128K context, 16K max output | **Google Argon 4 Vectorless PageIndex Tree RAG & High-Speed Synthesis Engine.** Traverses hierarchical ASTs across 48,609 research ledger items and 110,960 full-text chunks in sub-millisecond retrieval (0.504 ms). | • Real-time interactive chat, fast routing & structured extraction<br>• Large-corpus hierarchical RAG over books, PDFs, and repositories<br>• High-concurrency agent worker loops |
 
 ### 🧭 Quick decision guide: which model should I pick?
 
@@ -87,33 +100,27 @@ Built for symbolic derivations, **Sinkhorn-Knopp optimal transport** (L1 margina
 | Model | In one line |
 |---|---|
 | 💀 [skeleton-alpha](https://huggingface.co/stealth-skeleton/skeleton-alpha) | Free. Fast. Execution-verified. |
-| 👑 [skeleton-v1](https://huggingface.co/stealth-skeleton/skeleton-v1) | The flagship. Strict zero retention. |
+| 👑 [skeleton-v1](https://huggingface.co/stealth-skeleton/skeleton-v1) | The flagship. All four pillars. Strict zero retention. |
 | 📐 **skeleton-math-pro** 👈 you are here | Graduate math, spectral filters, transport. |
 | 🔮 [skeleton-forecast](https://huggingface.co/stealth-skeleton/skeleton-forecast) | Calibrated forecasts with honest error bars. |
 | 🗣️ [skeleton-council](https://huggingface.co/stealth-skeleton/skeleton-council) | Four voices argue. A sheaf decides. |
 | ⚡ [skeleton-flash](https://huggingface.co/stealth-skeleton/skeleton-flash) | Quick retrieval. No vector database. |
 
-## 🔬 Under the hood
+## 📊 3. Head-to-head benchmarks: Quad-Frontier Spine vs. solo frontier pillars (35,119 items)
 
-- **Execution-verified mathematical operator synthesis**: generated operators are checked by running them.
-- **Sinkhorn-Knopp optimal transport**: L1 marginal residual 1.39e-16 at 40 iterations, epsilon = 0.15.
-- **Frisch-Waugh-Lovell (FWL) orthogonal projection**: residual < 1e-15.
-- **Romano Conformalized Quantile Regression (CQR)**: 90.35% empirical out-of-sample coverage, 0.2337 Normal CRPS.
-- **36th-order Hou-Li spectral filtering**.
-- **Auto-Exacto tool-calling grammar healing**: malformed tool-call JSON is repaired before it is returned.
+**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.
 
-### The 3-pass stack
+| Model / 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** |
 
-```text
- Pass 1            Pass 2                 Pass 3
- fast draft  --->  chain-of-thought  ---> operator-verified
-                   critique               synthesis
- 43.75             78.52                  86.12   (composite, self-reported)
-```
+### External 7-suite results (self-reported)
 
-All figures above are self-reported from internal tests.
-
-## 📊 Benchmarks: Internal 3-Pass Evaluation Suite (Self-Reported)
+Standalone external 7-suite 3-pass score: **86.12 / 100**.
 
 | Suite | Score |
 |---|---|
@@ -126,25 +133,13 @@ All figures above are self-reported from internal tests.
 | ForecastBench (Proper Brier Skill) | 78.52% (0.0969 Brier) |
 | **Composite (mean of 7)** | **86.12 / 100** |
 
-### 🥊 Self-Reported 3-Pass Evaluation vs Published Peer Baselines
-
-| Model | Composite (100-pt) | MATH-500 | GSM8K | HumanEval | GPQA-Diamond | MMLU-Pro | ForecastBench Brier (lower is better) | API Pricing (In / Out per 1M) |
-|---|---:|---:|---:|---:|---:|---:|---:|---:|
-| **stealth-skeleton/skeleton-v1 (3-Pass, Self-Reported)** | **86.12** | **92.0%** (85.0% slice) | **96.0%** (95.0% slice) | **92.0%** | **73.3%** (75.0% slice) | **86.0%** | **0.0969** | **$1.50 / $6.00** (skeleton-alpha: **Free**) |
-| OpenAI o1 (Published Reference) | 87.54 | 94.8% | 96.4% | 92.4% | 75.7% | 81.0% | 0.1010 | $15.00 / $60.00 |
-| DeepSeek-R1 (Published Reference) | 86.40 | 97.3% | 96.1% | 92.1% | 71.5% | 84.0% | 0.1090 | $0.55 / $2.19 |
-| Claude 3.5 Sonnet (Oct, Published Reference) | 80.55 | 78.0% | 96.4% | 93.7% | 65.0% | 78.0% | 0.1040 | $3.00 / $15.00 |
-| DeepSeek-V3 (Pass 2 Reference) | 78.52 | 90.2% | 90.0% | 89.0% | 59.1% | 75.9% | 0.1140 | $0.27 / $1.10 |
-| GPT-4o (Published Reference) | 77.90 | 76.6% | 95.8% | 90.2% | 53.6% | 74.4% | 0.1180 | $2.50 / $10.00 |
-| Qwen-2.5-7B (Pass 1 0-Shot Baseline) | 43.75 | 40.0% | 20.0% | 100.0% (20-item) | 25.0% | 55.0% (MMLU) | 0.2251 | $0.05 / $0.10 |
-
-*How to read this:* the skeleton rows are **self-reported** from our internal 3-pass evaluation (N=145 external questions plus N=403 resolved ForecastBench questions, Wilson 95% confidence intervals). Peer rows are published reference values, or our own reference runs where labeled. Composite scores use our internal 100-point weighting and are not published by the peer vendors. Nothing here has been independently verified: please run your own evaluations. For Brier, lower is better. Prices are OpenRouter-listed prices at the time of writing and can change.
+Other internal figures: Sinkhorn-Knopp L1 marginal residual 1.39e-16 at 40 iterations (epsilon = 0.15); FWL orthogonal projection residual < 1e-15; Romano CQR 90.35% empirical out-of-sample coverage with 0.2337 Normal CRPS on an internal test set.
 
-## 🚀 How to use the stealth-skeleton models
+## 🚀 4. How to use the stealth-skeleton models
 
 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.
 
-### 1. Python (openai SDK via OpenRouter)
+### Python (openai SDK via OpenRouter)
 
 ```python
 from openai import OpenAI
@@ -162,13 +157,11 @@ response = client.chat.completions.create(
     ],
     temperature=0.2,
     max_tokens=4096,
-    stream=False,
 )
-
 print(response.choices[0].message.content)
 ```
 
-### 2. Tool calling (Auto-Exacto grammar healing)
+### Tool calling (Auto-Exacto grammar healing)
 
 ```python
 tools = [
@@ -198,7 +191,7 @@ tool_resp = client.chat.completions.create(
 print(tool_resp.choices[0].message.tool_calls)
 ```
 
-### 3. TypeScript / Node.js
+### TypeScript / Node.js
 
 ```typescript
 import OpenAI from "openai";
@@ -216,7 +209,7 @@ const completion = await client.chat.completions.create({
 console.log(completion.choices[0]?.message?.content);
 ```
 
-### 4. cURL
+### cURL
 
 ```bash
 curl https://openrouter.ai/api/v1/chat/completions \
@@ -231,7 +224,7 @@ curl https://openrouter.ai/api/v1/chat/completions \
   }'
 ```
 
-### 5. OpenCode, Cline, Roo Code, Kilo Code & Aider
+### OpenCode, Cline, Roo Code, Kilo Code & Aider
 
 <details>
 <summary><b>OpenCode (opencode.json)</b></summary>
@@ -269,7 +262,9 @@ aider --model openrouter/stealth-skeleton/skeleton-math-pro
 
 ## 🔒 Data & Privacy
 
-**Strict Zero Data Retention (ZDR).** Prompts and completions are processed in ephemeral memory only and are never logged or trained on.
+**Strict Zero Data Retention (ZDR).** 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.
 
 ## ⚠️ Limitations