bridge_certificate

formal source

 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
 184    PROVED (zero sorry in this chain):
 185      RCL → J unique → φ forced → D=3 → 8-tick →
 186      η = diag(-1,+1,+1,+1) → Γ from metric → Riemann → Ricci →
 187      Einstein → flat vanishing → coupling κ = 8φ⁵
 188
 189    HYPOTHESIZED (explicit, not axiom):
 190      1. Regge convergence (external math, Cheeger-Muller-Schrader 1984)
 191      2. Metric smoothness for mixed partial symmetry (Schwarz theorem)
 192      3. Jacobi determinant formula (standard matrix calculus)
 193      4. Palatini divergence vanishing (boundary terms)
 194      5. MP stationarity (RRF → Euler-Lagrange)
 195
 196    The five hypotheses are all standard external mathematics or physics,
 197    not RS-specific assumptions. -/
 198structure EndToEndChain : Prop where