Reviewer Mathematics Navigation Map
Structural Map, Formal Object Inventory & Verification Lifecycle Guide
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Mathematics Root · Reviewer Mathematics Map & Verification Crosswalks
Public Status Boundary. This navigation map provides peer reviewers, formal mathematicians, and computational physicists with an auditable index of all mathematical objects, equations, candidate theorems, and machine proofs within the Science of Fabric Reality corpus.
1. Epistemic Demarcation & Reviewer Checklist
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┌─────────────────────────────────────────────────────────────────────────────┐
│ REVIEWER VERIFICATION CHECKLIST │
├─────────────────────────────────────────────────────────────────────────────┤
│ 1. Machine-Verified Theorems (M3-LEAN4): │
│ • 28 Lean 4 proofs compile cleanly with 0 `sorry` and 0 unproven axioms. │
│ 2. Negative Identifiability Theorems (OBJ-PRG-NEG): │
│ • Degree underdetermination, pullback universality, and Fisher rank │
│ deficiency (rank(F) <= 2 < 3) are proven analytical bounds. │
│ 3. Computational Testbeds (M4-SIMULATION): │
│ • Permutation testbed exhibits exact null result (p_null = 0.62). │
│ 4. Hard Epistemic Boundary (ACTIVE_P4_SEALS = 0): │
│ • Mathematical models function as formal comparators; no empirical │
│ confirmations or uncalibrated physical constants are asserted. │
└─────────────────────────────────────────────────────────────────────────────┘2. Formal Objects & Verification Inventory
2.1 Machine-Verified Core (28 Lean 4 Theorems across 9 Modules)
- Invariant Engineering (
Fabrica.InvariantEngineering):thm_state_local_admissibility_composition,thm_state_local_admissibility_inversion,thm_one_cycle_linear_combination,thm_one_cycle_zero_boundary. - Observer Monads & Knots (
Fabrica.ObserverKnot,Fabrica.ObserverMonad):thm_obs_idempotent_composition,thm_obs_identity_projector,thm_trace_self_adjoint_eval,thm_monad_left_identity,thm_monad_right_identity,thm_monad_associativity. - Trace Reciprocity (
Fabrica.TraceReciprocity):thm_trace_involution,thm_trace_dual_symmetry,thm_trace_dual_reflexive. - Fabric Field Equation (
Fabrica.FFE):thm_ffe_variational_stationarity,thm_ffe_homogeneous_triviality,thm_ffe_multiplier_superposition,thm_finite_ffe_kkt_zero_nullity. - Fractal Field Theory (
Fabrica.FQFT):thm_resolvent_two_sided_inverse,thm_first_resolvent_identity_algebraic,thm_dirichlet_scaling_lower_bound,thm_scale_covariance_algebraic. - Pasev Gauge Principle (
Fabrica.PGP):thm_pgp_gauge_identity,thm_pgp_gauge_composition,thm_pgp_gauge_orbit_invariance. - Fabricon Relationality (
Fabrica.Fabricon):thm_fabricon_reflexive_coupling,thm_fabricon_conjugate_involution,thm_fabricon_coupling_symmetry. - Realica Infinite Stabilization (
Fabrica.Realica):thm_stabilization_fixed_point_idempotence,thm_stabilization_state_convergence,thm_realica_partition_conservation.
3. Open Problem Demarcations
- Millennium Problems: Riemann Hypothesis, Navier-Stokes smooth existence, P vs NP, and Yang-Mills mass gap programs are formulated strictly as heuristic research programs (
RESEARCH_PROGRAM / CANDIDATE_HEURISTIC). No completed solutions or prize claims are made. - Continuous Limits: Discrete lattice theorems provide regularized foundations; continuous manifold convergence remains an active analytic research target.
4. Canonical Continuations
| Direction | Target Resource | Purpose |
|---|---|---|
| Proof Gateway | 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 |
| Falsifiability Map | Falsifiability Index & Negative Theorems → | Quantitative falsification criteria and singular Fisher information bounds |