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math-review

@athola/claude-night-market
8
0

Intensive mathematical analysis for numerical stability, algorithm correctness, and alignment with authoritative standards. Use for math-heavy code changes.

Install Skill

1Download skill
2Enable skills in Claude

Open claude.ai/settings/capabilities and find the "Skills" section

3Upload to Claude

Click "Upload skill" and select the downloaded ZIP file

Note: Please verify skill by going through its instructions before using it.

SKILL.md

name math-review
description Intensive mathematical analysis for numerical stability, algorithm correctness, and alignment with authoritative standards. Use for math-heavy code changes.
category specialized
tags math, algorithms, numerical, stability, verification, scientific
tools derivation-checker, stability-analyzer, reference-finder
usage_patterns algorithm-review, numerical-analysis, derivation-verification, stability-assessment
complexity advanced
estimated_tokens 200
progressive_loading true
dependencies pensive:shared, imbue:evidence-logging

Mathematical Algorithm Review

Intensive analysis ensuring numerical stability and alignment with standards.

Quick Start

/math-review

When to Use

  • Changes to mathematical models or algorithms
  • Statistical routines or probabilistic logic
  • Numerical integration or optimization
  • Scientific computing code
  • ML/AI model implementations
  • Safety-critical calculations

Required TodoWrite Items

  1. math-review:context-synced
  2. math-review:requirements-mapped
  3. math-review:derivations-verified
  4. math-review:stability-assessed
  5. math-review:evidence-logged

Core Workflow

1. Context Sync

pwd && git status -sb && git diff --stat origin/main..HEAD

Enumerate math-heavy files (source, tests, docs, notebooks). Classify risk: safety-critical, financial, ML fairness.

2. Requirements Mapping

Translate requirements → mathematical invariants. Document pre/post conditions, conservation laws, bounds. Load: modules/requirements-mapping.md

3. Derivation Verification

Re-derive formulas using CAS. Challenge approximations. Cite authoritative standards (NASA-STD-7009, ASME VVUQ). Load: modules/derivation-verification.md

4. Stability Assessment

Evaluate conditioning, precision, scaling, randomness. Compare complexity. Quantify uncertainty. Load: modules/numerical-stability.md

5. Evidence Logging

pytest tests/math/ --benchmark
jupyter nbconvert --execute derivation.ipynb

Log deviations, recommend: Approve / Approve with actions / Block. Load: modules/testing-strategies.md

Progressive Loading

Default (200 tokens): Core workflow, checklists +Requirements (+300 tokens): Invariants, pre/post conditions, coverage analysis +Derivation (+350 tokens): CAS verification, standards, citations +Stability (+400 tokens): Numerical properties, precision, complexity +Testing (+350 tokens): Edge cases, benchmarks, reproducibility

Total with all modules: ~1600 tokens

Essential Checklist

Correctness: Formulas match spec | Edge cases handled | Units consistent | Domain enforced Stability: Condition number OK | Precision sufficient | No cancellation | Overflow prevented Verification: Derivations documented | References cited | Tests cover invariants | Benchmarks reproducible Documentation: Assumptions stated | Limitations documented | Error bounds specified | References linked

Output Format

## Summary
[Brief findings]

## Context
Files | Risk classification | Standards

## Requirements Analysis
| Invariant | Verified | Evidence |

## Derivation Review
[Status and conflicts]

## Stability Analysis
Condition number | Precision | Risks

## Issues
[M1] [Title]: Location | Issue | Fix

## Recommendation
Approve / Approve with actions / Block

Exit Criteria

  • Context synced, requirements mapped, derivations verified, stability assessed, evidence logged with citations