/math-review

name: math-review
description: Verifies math-heavy code for algorithmic correctness and numerical stability. Use when reviewing scientific algorithms, ML models, or numerical code.
alwaysApply: false
category: specialized
tags:
- math
- algorithms
- numerical
- stability
- verification
- scientific
tools: []
usage_patterns:
- algorithm-review
- numerical-analysis
- derivation-verification
- stability-assessment
complexity: advanced
model_hint: deep
estimated_tokens: 200
progressive_loading: true
dependencies:
- imbue:proof-of-work
- imbue:review-core
- imbue:structured-output

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`