Table of Contents
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
math-review:context-syncedmath-review:requirements-mappedmath-review:derivations-verifiedmath-review:stability-assessedmath-review:evidence-loggedmath-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
