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Mathematical Autopsy Deep Dive

The complete five-phase process from intent to proven implementation.

Intent → Mathematical Foundation → Lemma Development → Verification → CI Enforcement → Code

The Complete Pipeline

Mathematical Autopsy ensures that math is defined before code is written. Invariants encode mathematical guarantees, notebooks verify invariants with executable proofs, and CI gates enforce invariants before deployment. Code implements documented math, not the other way around.

This rigorous process transforms requirements into proven implementations through a complete audit trail from intent to code. Every decision traces to master equations, ensuring deterministic, traceable, and governable AI systems.

The Five Phases (Plus Code Implementation)

Phase 1

Intent & Description

Problem Statement & Context

Document the problem statement, context, and success criteria in plain English. This phase ensures all stakeholders understand what we're building and why before any mathematical formalization begins.

Key Activities:

  • Problem statement written (what, why, context, success criteria)
  • Conceptual significance documented in plain English for all stakeholders
  • Acceptance criteria and measurable outcomes defined
  • Context and background information captured

Deliverables:

  • Intent document: `docs/math/<feature_name>_INTENT.md` or included in Phase 2 document
Phase 2

Mathematical Foundation

Formal Definitions & Operators

Formalize the mathematics—definitions, notation, equations, and operators. This creates the mathematical contract that code must satisfy.

Key Activities:

  • Definitions & notation documented (`docs/math/RFS_OPERATORS_CALCULUS.md`)
  • Formal operators specified with equations, complexity analysis, and implementation notes
  • Master equations and sub-equations defined
  • Assumptions and constraints explicitly stated

Deliverables:

  • Mathematical foundation: `docs/math/<feature_name>_MATHEMATICS.md` or `docs/math/<feature_name>_OPERATORS_CALCULUS.md`
Phase 3

Lemma Development

Invariants & Mathematical Guarantees

Create formal guarantees (invariants) and proofs (lemmas). Mathematical guarantees are formalized and indexed, creating a searchable knowledge base.

Key Activities:

  • YAML Invariant created (`invariants/INV-XXXX.yaml`)
  • Markdown Lemma written (`docs/math/RFS_LEMMAS_APPENDIX.md`)
  • Added to `invariants/INDEX.yaml`
  • Added to lemmas quick index

Deliverables:

  • YAML Invariant: `invariants/INV-XXXX.yaml`
  • Markdown Lemma: Entry in `docs/math/<REPO>_LEMMAS_APPENDIX.md`
  • Index registration: Entry in `invariants/INDEX.yaml`
Phase 4

Verification

Executable Proofs & Notebooks

Create verification notebooks with executable proofs. VERIFY:L<N> cells contain assertions that must pass. Artifacts are exported for CI validation, ensuring proofs are reproducible.

Key Activities:

  • Verification notebook created (`notebooks/math/<name>.ipynb`)
  • VERIFY:L<N> cell with assertions
  • Artifact JSON exported (`configs/generated/<name>.json`)
  • Notebook runs successfully locally with deterministic results

Deliverables:

  • Verification notebook: `notebooks/math/<name>.ipynb`
  • Artifact JSON: `configs/generated/<name>.json`
Phase 5

CI Enforcement

Automated Gates & Status Promotion

Register artifacts, update documentation, and promote invariant/lemma status. CI gates automatically validate all invariants before code merges, blocking deployments that violate mathematical contracts.

Key Activities:

  • Artifact registered in `docs/math/README.md`
  • Notebook added to plan (if applicable)
  • Alignment guide updated (if applicable)
  • ADR created (if invariant/threshold changed)
  • Invariant status: `draft` → `accepted`
  • Lemma status: `Draft` → `Rev X.Y`

Deliverables:

  • Artifact registration in `docs/math/README.md`
  • Updated invariant status (draft → accepted)
  • Updated lemma status (Draft → Rev X.Y)
  • ADR (if applicable)
Phase 6

Code Implementation

Extract from Notebook

Extract code from verification notebook (notebook-first approach). Code implements the math from Phase 2, validated against Phase 4 notebook. Tests validate against artifacts, and telemetry matches Phase 3 invariant.

Key Activities:

  • Code extracted from notebook (notebook-first)
  • Code implements the math from Phase 2
  • Tests validate against Phase 4 notebook
  • Telemetry matches Phase 3 invariant
  • Code review verifies alignment with invariant/lemma

Deliverables:

  • Production code: Extracted from notebook
  • Tests: Validate against Phase 4 notebook
  • Telemetry: Matches Phase 3 invariant

Why This Process Works

🔍

Explainability

Every output grounded in an intermediate symbolic step. Complete transparency from intent to code.

✓

Testability

Each transformation validated independently. Mathematical proof at every stage.

🔄

Replayability

Any result regenerated identically from original intent. Deterministic and reproducible.

Prove Your AI's Reasoning

Mathematical Autopsy transforms black-box AI into transparent, provable systems. Every decision traced, every output verified.

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