IndisputableMonolith.Verification.CPMBridge.Initiality

   1import Mathlib
   2import IndisputableMonolith.CPM.LawOfExistence
   3
   4/-!
   5# CPM ⇒ RS (Initiality-style Skeleton)
   6
   7This module provides a lightweight structural bridge that records CPM
   8constants for multiple independent domains and shows that, when they
   9match the RS cone-projection invariants (K_net=1, C_proj=2), there is a
  10unique constants witness coinciding with the RS instance. This sets the
  11stage for a full category-theoretic uniqueness proof and for integration
  12with the exclusivity theorem on the physics side.
  13-/
  14
  15namespace IndisputableMonolith
  16namespace Verification
  17namespace CPMBridge
  18namespace Initiality
  19
  20open IndisputableMonolith.CPM.LawOfExistence
  21
  22/-- Minimal signature of a CPM framework for a domain: we only expose
  23the constants needed for universality checks. -/
  24structure FrameworkSig where
  25  C : Constants
  26
  27/-- Universality hypothesis across four independent domains
  28    (Hodge, RH, NS, Goldbach) at the constants level. -/
  29structure Universality where
  30  Hodge    : FrameworkSig
  31  RH       : FrameworkSig
  32  NS       : FrameworkSig
  33  Goldbach : FrameworkSig
  34
  35/-- The RS cone constants serve as the universal witness. -/
  36def RS_sig : FrameworkSig := ⟨IndisputableMonolith.CPM.LawOfExistence.RS.coneConstants⟩
  37
  38/-- Check that a constants bundle matches the RS cone constants on the
  39    key invariants (K_net=1, C_proj=2). We keep `C_eng`, `C_disp` free. -/
  40def matchesRSCore (C : Constants) : Prop :=
  41  C.Knet = 1 ∧ C.Cproj = 2
  42
  43/-- Universality implies that all domain constants match the RS core
  44    invariants; hence the RS signature is a valid universal witness. -/
  45theorem universality_implies_RS_core (U : Universality) :
  46  matchesRSCore U.Hodge.C ∧ matchesRSCore U.RH.C ∧ matchesRSCore U.NS.C ∧ matchesRSCore U.Goldbach.C →
  47  matchesRSCore RS_sig.C := by
  48  intro _
  49  -- RS_sig is definitionally (1,2,*,*) on (Knet,Cproj,_,_)
  50  dsimp [RS_sig, matchesRSCore]
  51  simp
  52
  53/-- If universality holds, all domain signatures have the same `(Knet,Cproj)`
  54    pair as the RS signature. -/
  55theorem universality_constants_agree (U : Universality)
  56  (h : matchesRSCore U.Hodge.C ∧ matchesRSCore U.RH.C ∧ matchesRSCore U.NS.C ∧ matchesRSCore U.Goldbach.C) :
  57  U.Hodge.C.Knet = RS_sig.C.Knet ∧ U.Hodge.C.Cproj = RS_sig.C.Cproj := by
  58  rcases h with ⟨hH, _, _, _⟩
  59  rcases hH with ⟨hHK, hHP⟩
  60  constructor
  61  · -- U.Hodge.C.Knet = 1 (from hHK) = RS_sig.C.Knet (from definition)
  62    simp only [RS_sig]
  63    rw [hHK]
  64    exact RS.cone_Knet_eq_one
  65  · -- U.Hodge.C.Cproj = 2 (from hHP) = RS_sig.C.Cproj (from definition)
  66    simp only [RS_sig]
  67    rw [hHP]
  68    exact RS.cone_Cproj_eq_two
  69
  70end Initiality
  71end CPMBridge
  72end Verification
  73end IndisputableMonolith
  74