Formalization Targets & Verification Pipelines
Proof Assistant Translation, Lemma DAGs & Machine-Checked Claim Governance
Spine Position
Research Root · Formalization Pipelines, Proof Obligations & Machine Verification
Public Status Boundary. This document governs the systematic translation of theoretical propositions in the Science of Fabric Reality into formal proof assistant specifications (primarily Lean 4). No proposition is promoted to verified theorem status without machine-checked verification receipts.
1. Formalization Verification Hierarchy
Propositions ascend through a strict seven-stage verification ladder:
text
Concept Definition → Symbol & Axiom Typing → Lemma Formulation → Analytical Proof Sketch → Lean 4 Machine Formalization → CI Verification (0 sorry, 0 admit, 0 quarantined axioms) → Canonical PromotionAxiomatic boundary: The formal corpus maintains 0 sorry, 0 admit, and 0 quarantined axioms (the former provisional axiom FQFT_closure has been discharged by constructive inductive scale closure).
2. Machine-Verified Theorems & Active Modules (Lean 4 Suite)
The formal repository comprises 11 compiled Lean 4 modules (leanprover/lean4:v4.16.0), containing 35 machine-verified theorems (across 10 operational theorem modules and umbrella certificate):
| Domain / Module | Machine-Verified Lean 4 Theorems | Count | Formal Status |
|---|---|---|---|
KP-Field Operator Dynamics (Fabrica.KPField) | thm_kp_kernel_symmetry, thm_kp_generator_symmetry, thm_kp_resolvent_bound, thm_kp_deficiency_indices_nullity, thm_kp_cayley_transform_unitary, thm_kp_selfadjoint_domain_closure | 6 | MACHINE_VERIFIED |
Invariant Engineering (Fabrica.InvariantEngineering) | thm_invariant_identity, thm_invariant_composition, thm_invariant_invertible | 3 | MACHINE_VERIFIED |
Fabric Field Equations (Fabrica.FFE) | thm_ffe_variational_stationarity, thm_finite_ffe_kkt_zero_nullity, thm_ffe_homogeneous_triviality, thm_ffe_multiplier_superposition | 4 | MACHINE_VERIFIED |
Fractal Field Theory (Fabrica.FQFT) | thm_resolvent_two_sided_inverse, thm_first_resolvent_identity_algebraic, thm_shifted_operator_difference, thm_first_resolvent_identity_exact | 4 | MACHINE_VERIFIED |
Observer Knots (Fabrica.ObserverKnot) | thm_obs_idempotent_composition, thm_obs_identity_projector, thm_obs_product_absorption | 3 | MACHINE_VERIFIED |
Observer Monads (Fabrica.ObserverMonad) | thm_monad_left_identity, thm_monad_right_identity, thm_monad_associativity | 3 | MACHINE_VERIFIED |
Pasev Gauge Principle (Fabrica.PGP) | thm_pgp_gauge_identity, thm_pgp_gauge_composition, thm_pgp_gauge_orbit_invariance | 3 | MACHINE_VERIFIED |
Fabricon Relationality (Fabrica.Fabricon) | thm_fabricon_reflexive_coupling, thm_fabricon_conjugate_involution, thm_fabricon_coupling_symmetry | 3 | MACHINE_VERIFIED |
Realica Stabilization (Fabrica.Realica) | thm_stabilization_fixed_point_idempotence, thm_stabilization_state_convergence, thm_realica_partition_conservation | 3 | MACHINE_VERIFIED |
Trace Reciprocity (Fabrica.TraceReciprocity) | thm_trace_involution, thm_trace_dual_symmetry, thm_trace_dual_reflexive | 3 | MACHINE_VERIFIED |
Prelude & Foundations (Fabrica.Prelude) | Relational lattice primitives, metric types, and core foundations | — | CORE_DEPENDENCY |
| Total Corpus | 35 Machine-Verified Theorems (0 sorry, 0 admit, 0 quarantined axioms) | 35 | CONFIRMED |
3. Strict Promotion Invariant & Epistemic Boundaries
- Deterministic Verification Gate: No proposition in the Science of Fabric Reality is promoted from
FORMALIZATION_TARGETtoVERIFIED_THEOREMwithout deterministic machine-checked execution receipts emitted bylake env lean. - Axiomatic Discharge Boundary: The former provisional axiom
FQFT_closureinFabrica.FQFThas been discharged and de-quarantined by constructive inductive scale closure, establishing zero unverified axioms in the formal core. - Continuous vs. Discrete Boundary: Machine verification in Lean 4 currently proves discrete, algebraic, and relational properties. Continuous field equations and empirical calibrations remain subject to
ACTIVE_P4_SEALS = 0.
4. Canonical Continuations
| Direction | Target Resource | Purpose |
|---|---|---|
| Results Ledger | Scientific Results Ledger → | 35 machine-verified Lean 4 theorems across 11 modules and negative null benchmark ( |
| Reproducibility | Computational Reproducibility → | RFC 8785 JCS verification receipts and reproducible Lean 4 proof environment |
| Proof Tracker | Lean 4 Formalization Roadmap → | 35 machine-verified theorem records and lemma dependency DAGs |
| Formalization Batch 1 | Formalization Batch 1 Specifications → | Direct Lean 4 code specifications across all 11 verified modules |
| Axioms Register | Constitutional Axioms & Object Register → | Source-backed primitives and quarantined formal proposals |
| Proof Governance | Proof Governance & Verification Scale → | Orthogonal status coordinates |
| Simulation Lab | Simulation Atlas & Numerical Testbeds → | Discretized numerical solvers, null tests ( |