The unity of equations,
verified by real math.
A cross-domain coupling engine with four layered checks, a four-phase AI review board modelled on academic peer review, and a formal scope-frozen discharge protocol. Every reference value comes from a real symbolic math engine — sympy, mpmath, and python-flint — not from an LLM. The board is asked for formulas and citations; the architect runs the arithmetic.
Where the engine is now
Phase 12 established the foundation: six flagship equations — Newton II, Hooke, Fourier, Fick, Ohm, Work-Energy — each with a real canonical problem that passes the four-check verification pipeline (symbolic canonicalization, stratified property-based sampling, high-precision mpmath, python-flint interval arithmetic). Phase 13 layers composites on top: two parent equations plus a transducer producing a new physical system whose prediction is verified against a textbook reference.
Canonical problem library
Each equation in the corpus gets a problems.yaml with at least one closed-form problem and a board-sourced citation chain. The reference numeric value is computed locally by a real CAS, never by the board. Six equations covered; more coming.
Four-check verification
Symbolic equivalence via canonicalization (rational normalization → trig/power simp → polynomial remainder → branch-cut-aware discriminating random eval). Hypothesis-based stratified property testing. mpmath high-precision fragility check. python-flint interval arithmetic as the genuinely independent numeric engine.
Composites from parents
Two verified parent equations plus a transducer compose into a new physical system. Newton II + Hooke → simple harmonic oscillator. Newton II + Work-Energy → work done by constant force. Each composite gets its own reference value, its own four-check verification, its own ledger entry.
Port-Hamiltonian transducers
Every cross-domain coupling carries a named transducer with explicit ports (effort/flow), Dirac structure, and a symbolic power-conservation equation verified at composition time — conservation by construction, not by post-hoc numeric check.
AI review board
Four-phase academic-mirror protocol: independent drafts, consolidated briefing + informed vote, editor synthesis, bounded rebuttal. Three core reviewers — Claude Opus 4.6 · OpenAI GPT-5 · Gemini 2.5 Pro — with Grok-4 as optional fourth seat on high-stakes governance rounds (architecture review, adversarial testing). Cost-neutrality disclaimer, specialist personas, rubric scoring, COI self-declaration, all-must-respond enforcement.
No corner cuts
On any verification failure, the Failure Investigation Protocol fires: state audit, assumption audit, literature RAG, board failure review. Equation modifications require explicit user approval. Tolerance loosening is categorically forbidden.
Canonical problems in the ledger
6 equations each with a verified closed-form problem. Board provided the formula and primary-source citations; local sympy + mpmath computed the authoritative numerical value; four-check verification passed.
Composites verified
Phase 13 composites: two parent equations plus a coupling produce a new physical prediction, verified against a textbook reference with the same four-check pipeline as a single-equation canonical.
Layer 5 coupling sieve (Phase 11)
The earlier structural-matching sieve, reviewed by the board in Phase 11 before the current v5 protocol. 2 tier-I equivalences and 12 tier-II structural analogies were emitted; 15 were promoted to PROVED under the old protocol. These records remain in the ledger as Phase 11 audit and are being re-evaluated under the stricter Phase 12+ rules.
Ledger at a glance
Every record — proof, conjecture, rejection, failure investigation, or board discharge — is browsable on the full ledger. The full protocol is documented on the methodology page.