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

/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

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

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

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:

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

## 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