math-review

## Table of Contents - [Quick Start](#quick-start) - [When to Use](#when-to-use) - [Required TodoWrite Items](#required-todowrite-items) - [Core Workflow](#core-workflow) - [1. Context Sync](#1-context-sync) - [2. Requirements Mapping](#2-requirements-mapping) - [3. Derivation Verification](#3-derivation-verification) - [4. Stability Assessment](#4-stability-assessment) - [5. Proof of Work](#5-proof-of-work) - [Progressive Loading](#progressive-loading) - [Essential Checklist](#essential-checklist) - [Output Format](#output-format) - [Summary](#summary) - [Context](#context) - [Requirements Analysis](#requirements-analysis) - [Derivation Review](#derivation-review) - [Stability Analysis](#stability-analysis) - [Issues](#issues) - [Recommendation](#recommendation) - [Exit Criteria](#exit-criteria) # Mathematical Algorithm Review Intensive analysis ensuring numerical stability and alignment with standards. ## Quick Start ```bash /math-review ``` **Verification:** Run the command with `--help` flag to verify availability. ## 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 ## When NOT To Use - General algorithm review - use architecture-review - Performance optimization - use parseltongue:python-performance - General algorithm review - use architecture-review - Performance optimization - use parseltongue:python-performance ## 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` 6. `math-review:findings-verified` ## Core Workflow ### 1. Context Sync ```bash pwd && git status -sb && git diff --stat origin/main..HEAD ``` **Verification:** Run `git status` to confirm working tree state. 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. Proof of Work ```bash pytest tests/math/ --benchmark jupyter nbconvert --execute derivation.ipynb ``` **Verification:** Run `pytest -v tests/math/` to verify. Log deviations, recommend: Approve / Approve with actions / Block. **Load**: `modules/testing-strategies.md` ### 6. Verify Findings Are Grounded (`math-review:findings-verified`) Every issue must cite a real location and a verbatim anchor. Write findings to `.review/findings.json` and confirm each citation resolves: ```bash python plugins/imbue/scripts/citation_verifier.py \ --findings .review/findings.json --repo-root . ``` Drop or label `UNVERIFIED` any finding the verifier fails (exit `1`); only verified findings enter the report. See `Skill(imbue:review-core)` Step 5 for the protocol and `Skill(imbue:structured-output)` for the finding schema. ## 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 ```markdown ## 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: file.py:123 - Anchor: `verbatim source text at line 123` - Issue: [what is wrong] | Fix: [remediation] | Evidence: [E1] ## Recommendation Approve / Approve with actions / Block ``` Every issue's `Anchor` is the exact source text at `Location`; it is what `citation_verifier.py` re-reads to prove the finding is real. **Verification:** Run the command with `--help` flag to verify availability. ## Exit Criteria - Context synced, requirements mapped, derivations verified, stability assessed, evidence logged with citations - Every reported issue carries a `Location` + verbatim `Anchor`, and `citation_verifier.py` confirmed all citations (exit `0`) or unverified issues were dropped or labeled `UNVERIFIED`