IndisputableMonolith.Gravity.NonlinearReggeProof
The NonlinearReggeProof module certifies existence of a nonlinear Regge certificate for the canonical phi-lattice under CMS conditions. Gravity researchers extending discrete Regge calculus within Recognition Science would cite it to confirm coverage of observational regimes. The module assembles this via chained definitions of lattice regularity, convergence regimes, and linearized-to-nonlinear implications.
claimThe module asserts existence of NonlinearReggeCert for the canonical phi-lattice, satisfying CMSConditions while covering the observational regime in the nonlinear setting.
background
This module sits in the Gravity domain and imports the RS time quantum tau_0 = 1 tick from Constants. It introduces PhiLatticeRegularity as the stability property of the discrete phi-lattice, ConvergenceRegime as the parameter window for convergence to classical gravity, and CMSConditions as the constraint set the lattice must obey. Linearized_covers_observational links the approximation to data, while linearized_implies_weak bridges to the full nonlinear case.
proof idea
The module organizes its argument through successive definitions: canonical_phi_lattice and PhiLatticeRegularity first, followed by regime_covered and observational_regime_covered, then the implication linearized_implies_weak, and finally the existence theorem nonlinear_regge_cert_exists.
why it matters in Recognition Science
This module supplies the nonlinear Regge certificate that completes the gravity sector, extending linearized results to the full nonlinear regime. It supports the Recognition Science chain by realizing gravity on the phi-ladder consistent with D=3 and the eight-tick octave.
scope and limits
- Does not derive the explicit Regge action.
- Does not supply numerical lattice simulations.
- Does not treat higher-dimensional extensions.
- Does not provide error bounds on the approximation.
depends on (1)
declarations in this module (11)
-
structure
PhiLatticeRegularity -
def
canonical_phi_lattice -
inductive
ConvergenceRegime -
def
regime_covered -
def
linearized_covers_observational -
theorem
observational_regime_covered -
structure
CMSConditions -
theorem
phi_lattice_satisfies_cms -
theorem
linearized_implies_weak -
structure
NonlinearReggeCert -
theorem
nonlinear_regge_cert_exists