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:
Concept Definition → Symbol & Axiom Typing → Lemma Formulation → Analytical Proof Sketch → Lean 4 Machine Formalization → CI Verification (0 Sorry / 0 Unproven Axioms) → Canonical Promotion2. Active Formalization Packages (Lean 4 Suite)
The repository maintains 28 machine-verified theorem records across nine formal mathematical domains:
| Domain / Package | Key Verified Theorems | Lean 4 Module | Machine Status |
|---|---|---|---|
| Invariant Engineering | THM-INV-COMP-01, THM-INV-INV-01, THM-FABRICA-CYCLE-01, THM-FABRICA-CYCLE-02 | Fabrica.InvariantEngineering | 100% VERIFIED |
| Observer Knots | THM-OBS-IDEMPOTENT-01, THM-OBS-PROJ-ID-01, THM-TRACE-SELF-ADJOINT-01 | Fabrica.ObserverKnot | 100% VERIFIED |
| Trace Reciprocity | THM-TRACE-RECIPROCITY-01, THM-TRACE-DUAL-EVAL-01, THM-TRACE-REFL-01 | Fabrica.TraceReciprocity | 100% VERIFIED |
| Fabric Field Equations | THM-FFE-STATIONARITY-01, THM-FFE-HOMOGENEOUS-01, THM-FFE-SUPERPOSITION-01, THM-FFE-KKT-UNIQUE-01 | Fabrica.FFE | 100% VERIFIED |
| Fractal Quantum Field Theory | THM-FQFT-RESOLVENT-02, THM-FQFT-RESOLVENT-ID-01, THM-FQFT-DIRICHLET-EL-01, THM-FQFT-COVARIANCE-01 | Fabrica.FQFT | 100% VERIFIED |
| Pasev Gauge Principle | THM-PGP-IDENTITY-01, THM-PGP-COMPOSITION-01, THM-PGP-ORBIT-01 | Fabrica.PGP | 100% VERIFIED |
| Observer Monads | THM-MONAD-LEFT-ID-01, THM-MONAD-RIGHT-ID-01, THM-MONAD-ASSOC-01 | Fabrica.ObserverMonad | 100% VERIFIED |
| Fabricon Relationality | THM-FABRICON-REFLEXIVE-01, THM-FABRICON-INVOLUTION-01, THM-FABRICON-SYMMETRY-01 | Fabrica.Fabricon | 100% VERIFIED |
| Realica Infinite Stabilization | THM-STABILIZATION-IDEMP-01, THM-STABILIZATION-CONV-01, THM-REALICA-CONSERVE-01 | Fabrica.Realica | 100% VERIFIED |
3. Strict Promotion Invariant
No proposition in the Science of Fabric Reality is promoted from FORMALIZATION_TARGET to VERIFIED_THEOREM without deterministic machine-checked execution receipts. Continuous field theories and empirical models remain subject to ACTIVE_P4_SEALS = 0.
4. Canonical Continuations
| Direction | Target Resource | Purpose |
|---|---|---|
| Proof Tracker | Lean 4 Formalization Roadmap → | 28 machine-verified theorem records and lemma dependency DAGs |
| Axioms Register | Constitutional Axioms & Object Register → | Source-backed primitives and quarantined formal proposals |
| Proof Governance | Proof Governance & Verification Scale → | Six-stage M0–M5 verification and publication lifecycle |
| Simulation Lab | Simulation Atlas & Numerical Testbeds → | Discretized numerical solvers, null tests ( |