Compitum

Geometrically-aware AI routing with instantaneous, mechanistic feedback.

Compitum routes prompts across models using SPD metric geometry, constraint-aware selection, and Lyapunov-inspired trust-region updates. Feedback is immediate and mechanistic (process signals), not judge-based.

Contents

• G e t t i n g S t a r t e d
• # I n s t a l l
• # Q u i c k D e m o
• CLI
  • Route
  • Annotated Trace Examples
• Examples
  • Quickstart
  • Learning / Geometry
  • Pedagogy / Control of Error
  • Bridge Demo
  • Certificate Card (Markdown)
  • Batch Routing
  • Explain a Saved Certificate
• API Quickstart
• Accessibility
• LLM Usage
  • Quick: Use the Snapshot
  • Snapshot with Paleae
  • Useful Entry Points for LLMs
  • Traces for Verification
  • Build a Size-Budgeted Context Pack
• Philosophy
• Invariants
  • Coverage (selected)
• Mathematics: A Plain-Language Brief
  • Claims and Evidence (Code-Linked)
  • Thanks
• Control of Error
• Control Perspective
  • Closed-Loop Decomposition
  • Trust-Region Controller (SRMF)
  • Metric Update (Bounded, PD by Construction)
  • Stability Indicators (Operational)
  • Delay and Noise (Why Instantaneous Feedback Helps)
  • Control KPIs (What to Inspect)
  • Stability Evidence (0.1.1)
  • Decision Rule (for completeness)
  • References (Pointers)
• Trust From Regret
  • Definition (Operational)
  • Instantaneous Feedback → Faster Correction
  • Evidence (What to Report)
  • Helper Commands
  • Notes
• Learning Perspective (cs.LG)
  • Problem Setup
  • Decision Rule
  • Learning Components
  • Relation to ML Literature
  • Evaluation Protocol
  • Robustness and Limits
  • Reproducibility
  • Instantaneous Feedback vs. Delayed Reward (Significance)
  • Geometry & Coherence Evidence (0.1.1)
• Language Perspective (cs.CL)
  • Problem in NLP Terms
  • What We Emit (Certificate)
  • Relation to cs.CL Literature
  • Constraints and Safety
  • Coherence and Ambiguity
  • Evaluation for cs.CL
  • Reproducibility
  • Determinism & Explainability (0.1.1)
  • Limits (cs.CL)
• Instantaneous Feedback (Deep Dive)
  • Setup
  • Intuition: Variance and Latency
  • What to Measure
  • Engineering Consequences
  • Limits and Scope
• Mathematical Bridge (PS → ML)
• SRMF as a Lyapunov Functional
  • Setting and Assumptions
  • Lemma A (Learning Descent)
  • Lemma B (Zero‑Error Lyapunov Decay)
  • Lemma C (Two‑Timescale Isolation)
  • Composite Potential and SRMF Link
  • Practical Takeaway
• Statistical Methodology
  • Utility, Regret, and Pairing
  • Uncertainty, Calibration, and Intervals
  • KDE Prior and Bandwidth
  • Metric Learning and Regularization
  • Constraints and Shadow Prices
  • Multiple Comparisons and Pre‑registration
  • Sensitivity and Robustness
  • Reproducibility
• Certificate Schema
• Glossary
• A P I R e f e r e n c e
• compitum API
• Peer Review Package
  • Reviewer Quickstart
  • Claims and Contributions (Auditable)
  • Constraints Summary
  • Fair Evaluation Notes
  • Evaluation Protocol (Preregistered)
  • Datasets, Tasks, and Baselines
  • One-Shot Reproduction
  • Environment, Seeds, and Determinism
  • Mutation Testing (Cosmic Ray)
  • Results (Fill-In Table)
  • Results (Panel Averages - Auto-Included)
• Fixed-WTP Analysis (95% CI)
  • Routing Certificate: Anatomy and Example
  • Reviewer Checklist
  • Ablations and Frontiers (Suggested)
  • Known Limitations and Threats to Validity
  • Failure Modes and Guardrails
  • Limitations and Threats to Validity
  • Ethical and Responsible Use
  • How to Cite
  • Per-Baseline Win Rate
• Per-Baseline Win Rate (Standalone)
  • Frontier Gap
• Frontier Gap (Standalone)
  • Decision Rule and Control of Error
  • Mathematical Guarantees and Approximations
  • Sensitivity and Robustness
  • Calibration and Statistical Notes
  • Reproducibility Snapshot
  • Reviewer FAQ
  • Data Lock (Optional, Security-Oriented)
  • Control-of-Error Index (CEI)
  • cs.LG Fixed‑λ Summary (Paired Bootstrap)
  • cs.CL Summary (Per-Task and Routing Mix)
  • Trust From Regret
• Reproducibility
• Results Summary
  • Reproduce
• Fixed-WTP Analysis (95% CI)
• Per-Baseline Win Rate (Standalone)
• Frontier Gap (Standalone)
• Panel Summary
• Results by Task
• Compitum RouterBench Evaluation Summary
  • Metrics
  • Where Compitum Wins
  • Determinism
• RouterBench Fairness Notes
• Matbench (Offline Adapter)
• Matbench Regret (Offline)
  • Attestation and Groups
  • Baselines and Layers
• How We Evaluate Matbench (Offline)
• Baselines and Plots
• Emergent Layers
• Exporting a Task CSV
• Data Policy & Security
• Media: tess.mp4
  • Text Description (Alt)
• Public API Stability
• Artifact README (Reproducibility)
• Compliance Overview
• Operations Runbook
• Performance Notes
• Pedagogy and Control of Error
  • Evidence of “Control of Error” (0.1.1)
• Pedagogy Lab (Control of Error)
  • 1) Run the Demo
  • 2) Tweak beta_s (coherence weight)
  • 3) Explain a Flip
  • 4) Classroom Pack
• Teach Compitum (Educator Guide)
• Future Directions
  • Dual Shadow Pricing (Online Primal–Dual)
  • Robust Boundary Sensitivity
  • PyLantern Integration (Teaser)
  • Expanded Certificates
  • Evaluation Tracks
• Executive Overview
  • Contributions (At a Glance)

Useful links: README.md, CONTRIBUTING.md, ACCESSIBILITY.md, SECURITY.md, SUPPORT.md.

LLM Snapshots

Small, ready-to-share repository snapshot for LLM context:

• repo_snapshot.jsonl - lean pack (~39k tokens) with core docs and invariants.

Notes:

• JSONL files live alongside this page and are excluded from future snapshots.

• Prefer sharing the lean pack with Claude; it stays well under typical limits.

Ask Your LLM

• Attach the JSONL in chat and say: “Use the attached repo snapshot (JSONL lines with path+content). Cite path:line in answers.”

• Or with browsing enabled, ask it to fetch: https://compitum.space/docs/repo_snapshot.jsonl.