IndisputableMonolith.Gravity.Analysis.ReggeTTBucketAggregation
A phase-independent literal rational table for all 36 Regge TT stencil slot pairs, written as bare match values rather than fiber sums. Gravity analysts cite it when auditing the C11 Bloch interface without tautological wiring to the objects under test. Entries come from offline closed forms of the flat-angle Jacobian and Freudenthal squared edge lengths, then each is kernel-checked against the raw aggregate weight.
claimThere is an independent $6\times 6$ rational stencil weight table $W_{ij}\in\mathbb{Q}$ on the 36 slot pairs of the Regge TT cell, never defined via fiber sums or the raw Jacobian coefficient. For each pair, the aggregated raw weight equals $W_{ij}$, and the table is symmetric under slot swap.
background
Regge calculus discretizes spacetime curvature on a simplicial complex; the TT (transverse-traceless) sector isolates the physical graviton-like modes. In the Recognition Science gravity campaign this sits inside the panel-locked C11 Bloch interface audit: the upstream module keeps the first gate deliberately narrow, with a literal $6\times 6\times 6$-shape triple sum over tetrahedra as the raw cell stencil, so that audit objects are not definitionally wired to the quantities they check.
This module supplies the companion rational bucket table. Weights are derived offline from the closed forms of the flat-angle Jacobian and the Freudenthal tetrahedron squared edge lengths, then recorded as bare rational literals. The table is phase-independent: it does not depend on Bloch phase factors that appear elsewhere in the interface.
Sibling lemmas relate the raw Jacobian coefficient to a norm quotient, evaluate it, prove each aggregate raw weight equals the corresponding rational entry, and record swap symmetry plus smoke checks against row-0 and worst-radical cases.
proof idea
Definition-first module: the main object is a bare match table of 36 literal rationals. Equality lemmas then proceed entrywise. Offline closed forms fix the expected rationals; aggregate_raw_weight_eq_rational kernel-verifies each slot pair against the raw stencil aggregate. Auxiliary facts reduce the raw Jacobian coefficient to a norm quotient, evaluate concrete coefficients, and prove swap symmetry of the rational weights. Smoke lemmas check selected rows (row 0 and a worst-radical case) against the table. No single global algebraic identity replaces the per-entry checks.
why it matters in Recognition Science
The table is the non-tautological rational reference demanded by the C11 panel audit. Upstream, the Bloch interface audit rejected attempt 1 for wiring stencil and bucket table definitionally to the audited objects; this independent literal table closes that gap. Downstream it is imported by the hinge-aware zero-mode module (Gate C-A3), which closes the hinge-aware zero-mode gate in the QG full-theory campaign (Paper C / Pillar 1, Lane C). Without a phase-independent rational baseline, zero-mode and hinge analyses cannot separate geometric stencil structure from Bloch-phase artifacts. The module does not itself prove the zero mode; it feeds the certified weights those proofs consume.
scope and limits
- Does not prove existence or uniqueness of the Regge TT zero mode.
- Does not derive the rationals inside Lean; offline closed forms are assumed and only entrywise equality is checked.
- Does not encode Bloch phase dependence; the table is intentionally phase-independent.
- Does not redefine rawJacobianCoefficient or the fiber-sum stencil; it audits them from outside.
- Does not address continuum GR limits or physical units beyond the discrete stencil.