Lean 4 Formalization Architecture
Interactive Proof Engineering, Modular Scaffolding & Verification Standards
Spine Position
Mathematics Root · Formal Proof Scaffolding · Lean 4 Verification Architecture
Status Boundary
This work is part of the authorial PHYSICA / Science of Fabric Reality corpus. It is presented as a research framework, formalization target, computational model, or theoretical synthesis unless explicitly marked otherwise. It is not presented as accepted physics, external consensus, or experimentally confirmed science.
Public Status Boundary. Within the current canonical formal corpus, 35 Lean theorem declarations across 11 formal modules have achieved machine-verified status under Lean 4.16.0 with 0
sorry, 0admit, and 0 quarantined axioms (the former source-declared axiomFQFT_closurehas been formally de-quarantined and discharged). Verification applies strictly to the encoded formal statements and hypotheses; it does not constitute machine verification of the complete scientific theory or empirical physical validation.
1. Verification Scope & Repository Architecture
The Lean 4 proof repository is structured into modular namespaces under the Fabrica root package, isolating relational axioms, operator algebras, and variational dynamics:
Fabrica/
├── Fabrica.lean (Master umbrella declaration & certificate)
├── InvariantEngineering.lean (3 proofs: Identity, Composition & Involutive Invertibility)
├── ObserverKnot.lean (3 proofs: Projector Idempotence & Absorption)
├── TraceReciprocity.lean (3 proofs: Pairing Involution & Dual Symmetry)
├── FFE.lean (4 proofs: Stationarity, Zero-Nullity & Multipliers)
├── FQFT.lean (4 proofs: Resolvent & Shifted Operator Identities)
├── PGP.lean (3 proofs: Gauge Identity, Comp & Orbit Invariance)
├── ObserverMonad.lean (3 proofs: Monad Identity & Associativity)
├── Fabricon.lean (3 proofs: Conjugate Involution & Symmetry)
├── Realica.lean (3 proofs: Stabilization Idempotence & Conservation)
└── KPField.lean (6 proofs: Symmetry, Resolvent Bound, Deficiency Nullity, Cayley Unitarity & SA Closure)2. Machine-Checked Proof Policy
- Zero-Sorry Mandate: No proposition is promoted to
F4-CHECKEDor canonical status with unproven goals (sorry) or ad-hoc axiomatic assumptions. - Deterministic Build Verification: Every formalization batch undergoes continuous verification against standard Lean 4 compiler toolchains.
- Epistemic Integration: Formal Lean 4 types and theorems are cross-linked to the analytical manuscripts and the Proof Governance Framework.
3. Canonical Continuations
| Direction | Target Resource | Purpose |
|---|---|---|
| Formalization Batch 1 | Formalization Batch 1 Specification → | Deep-dive code specifications for core Lean 4 proof modules |
| Formalization Roadmap | Lean 4 Formalization Roadmap → | Interactive milestone tracker, theorem inventory, and lemma dependency DAGs |
| Theorem Candidates | Theorem Candidates Registry → | Comprehensive mapping of all 35 Lean 4 machine-verified proofs across 11 modules |
| Review Gateway | Mathematical Review Gateway → | Verification readiness dashboard and interactive structural atlas |