module module high

`IndisputableMonolith.Physics.PMNSCorrections`

The PMNSCorrections module defines vertex counts for D-cubes and the atmospheric and solar correction coefficients that arise from cubic voxel topology. Neutrino physicists deriving PMNS parameters from first principles would cite these for the geometric constraints on mixing. The module consists entirely of direct definitions that rest on the cubic ledger imported from MixingGeometry.

claimLet $V(D) = 2^D$ be the number of vertices in a $D$-cube. The atmospheric coefficient (eq. 6) and solar coefficient (eq. 10) are defined from the cube edge and face counts together with the RS time quantum, supplying the PMNS correction terms.

background

This module sits inside the Recognition Science treatment of mixing matrices. It imports the cubic voxel topology from MixingGeometry, which formalizes the constraints that force CKM and PMNS parameters, and the fundamental time quantum from Constants. The central objects are the vertex count $V = 2^D$ together with the derived edge and face counts for both 2-cubes and 3-cubes; these quantities parameterize the atmospheric and solar correction coefficients.

proof idea

This is a definition module, no proofs. It introduces the cube geometry primitives (cube_vertices, cube_edges_count, cube_faces, cube3_*) and then directly states the atmospheric_coefficient and solar_coefficient expressions that follow from them.

why it matters in Recognition Science

The definitions supplied here are imported by MixingDerivation, which carries out the geometric derivation of the full CKM and PMNS mixing matrices from the cubic ledger structure in Phase 7.2. They supply the concrete correction terms needed to replace numerical fits with topological proofs.

scope and limits

Does not derive the numerical values of the mixing angles.
Does not prove the forcing of the mixing matrix from the ledger.
Does not address CKM-sector corrections.
Does not include higher-dimensional or radiative corrections.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Physics.MixingDerivation module_import

depends on (3)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Constants.Alpha module_import
IndisputableMonolith.Physics.MixingGeometry module_import

declarations in this module (24)

def cube_vertices L63
def cube_edges_count L66
def cube_faces L69
theorem cube3_vertices L77
theorem cube3_edges L78
theorem cube3_faces L79
def atmospheric_coefficient L89
theorem atmospheric_coefficient_eq_6 L91
def atmospheric_correction L94
theorem atmospheric_correction_eq L96
def solar_coefficient L107
theorem solar_coefficient_eq_10 L109
def solar_correction L112
theorem solar_correction_eq L114
def cabibbo_coefficient L126
theorem cabibbo_coefficient_eq_3_2 L128
theorem cabibbo_coefficient_from_geometry L130
def cabibbo_correction L136
theorem cabibbo_correction_eq L138
theorem atmospheric_matches L145
theorem solar_matches L151
theorem cabibbo_matches L157
structure CorrectionDerivationCert L169
theorem correction_derivation_verified L177