czChunk4
plain-language theorem explainer
Fourth static data block of rational coupling coefficients for the 4D Regge midpoint m² transverse-traceless kernel certificate. Gravity analysts cite it when assembling the full coupling table or checking the bridge that matches generated chunk data to the certified list. The body is a literal list of CZ records (numerator, denominator, defect multi-indices), not a derived proof.
Claim. Define the fourth chunk of the coupling table as an explicit finite list of records, each a rational coefficient $n/d$ together with integer multi-indices for the edge defects $\mathrm{de}_i$, primed defects $\mathrm{dep}_j$, and second-order defect slots used by the midpoint $m^2$ TT kernel identity in 4D Regge calculus.
background
This module holds machine-generated kernel certificates for the midpoint $m^2$ transverse-traceless identity in 4D Regge gravity. Certificates are built from integer fold tables at scale 32 and are discharged only by decide (no native evaluation).
Each entry is a CZ record: a signed numerator, a natural denominator, and integer coordinates for the defect channels that appear in the linearized Regge Hessian analysis (edge length defects and their first and second variations). Sibling chunks czChunk0–czChunk5 (and further) partition the same table so that individual lists stay small enough for the kernel checker.
The upstream structure is only the CZ packing type; there is no analytic lemma behind this particular list. Values come from the generator script named in the module header.
proof idea
There is no proof. The declaration is a closed definition whose right-hand side is a concrete list literal of CZ constructors. Each row hard-codes one rational weight and its defect multi-index. Downstream, czChunk4_bridge re-checks equality against the corresponding generated chunk by a single decide.
why it matters
The full coupling table couplingZList is the concatenation of all chunks, including this one. That table is the certified coefficient data for the midpoint $m^2$ TT kernel identity in the 4D Regge exact-flat Hessian analysis. Without the chunks, the bridge theorems and the assembled list cannot typecheck or decide.
In the broader Recognition gravity stack this sits inside discrete curvature / Regge scaffolding that feeds continuum limits and massless spin-2 mode checks. It does not itself invoke the forcing chain (T5–T8), the Recognition Composition Law, or the $\varphi$-ladder mass formula; it is pure certified linear-algebra data for the 4D kernel.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.