DiscreteContinuumBridge

formal source

 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
 171  coupling_positive := coupling_from_phi
 172  dimension := by norm_num
 173  christoffel_torsion_free := levi_civita_torsion_free minkowski_tensor
 174  levi_civita_exists := fundamental_theorem_existence minkowski_tensor
 175  levi_civita_unique := fundamental_theorem_uniqueness minkowski_tensor
 176  regge_convergence := h_regge
 177
 178/-! ## §7 Summary: The Full Chain -/
 179
 180/-- The end-to-end chain from the Recognition Composition Law to the
 181    Einstein field equations, with explicit accounting of what is proved
 182    versus what is hypothesized.
 183