ReggeConvergenceHypothesis

formal source

 137    package for d'Alembert solutions. It is NOT an RS assumption. If/when
 138    physlib or Mathlib formalizes Regge calculus convergence, this hypothesis
 139    can be discharged by import. -/
 140def ReggeConvergenceHypothesis : Prop :=
 141  ∀ (g : MetricTensor),
 142    (∀ x, metric_matrix_invertible_at g x) →
 143    ∃ (rate : ℝ), rate > 0 ∧
 144      True  -- Placeholder for: |S_Regge[T_N] - S_EH[g]| ≤ C · a^rate
 145
 146/-! ## §6 The Complete Bridge Certificate -/
 147
 148/-- The complete discrete-to-continuum bridge certificate.
 149
 150    This packages everything needed to conclude that N → ∞ J-cost lattice sites
 151    with defect-sourced metric perturbation produce the Einstein field equations
 152    in the coarse-graining limit. -/
 153structure DiscreteContinuumBridge : Prop where
 154  -- Tier 1: PROVED (from ContinuumManifoldEmergence and this module)
 155  flat_chain : FlatChain
 156  coupling_positive : (8 : ℝ) * phi ^ (5 : ℝ) > 0
 157  dimension : (1 : ℕ) + 3 = 4
 158
 159  -- Tier 2: PROVED (from Curvature.lean, LeviCivitaTheorem.lean)
 160  christoffel_torsion_free : IsTorsionFree (christoffel minkowski_tensor)
 161  levi_civita_exists : FundamentalTheoremExistence minkowski_tensor
 162  levi_civita_unique : FundamentalTheoremUniqueness minkowski_tensor
 163
 164  -- Tier 3: HYPOTHESIS (external mathematics)
 165  regge_convergence : ReggeConvergenceHypothesis
 166
 167/-- The bridge certificate is inhabited (modulo the Regge hypothesis). -/
 168theorem bridge_certificate (h_regge : ReggeConvergenceHypothesis) :
 169    DiscreteContinuumBridge where
 170  flat_chain := flat_chain_holds