czChunk5
plain-language theorem explainer
Fifth data chunk of rational coupling coefficients for the 4D Regge midpoint m² transverse-traceless kernel certificate. Gravity analysts cite it when assembling the full coupling table via concatenation. The body is a literal list of CZ records (numerator, denominator, defect multi-indices), produced by the kernel-cert generator script.
Claim. A fixed finite list of coupling records, each a rational $n/d$ together with integer multi-indices for the edge-length defects $\Delta e$ and $\Delta e'$ (and related second-variation slots) that appear in the midpoint $m^2$ TT identity kernel on a 4D Regge complex.
background
The module supplies machine-generated kernel certificates for the midpoint $m^2$ transverse-traceless identity in 4D Regge calculus. Certificates are built from integer fold and scale-32 tables so that kernel membership can be discharged by decide alone (no native_decide).
Each record is a CZ structure: a rational coefficient num/den paired with integer coordinates that mark which defect channels (edge variations and their primed counterparts) the term couples. Sibling chunks czChunk0–czChunk4 and later chunks play the same role; together they form the complete coupling table.
Upstream, the only dependency is the CZ record type itself. Downstream assembly concatenates every chunk into one master list used by the identity certificate.
proof idea
There is no proof: the declaration is a pure data definition. The right-hand side is an explicit list literal of CZ constructors, each field fully annotated (Int/Nat). Values come from the generator script scripts/qg/regge_4d_m2_kernel_certs_20260721.py and are frozen into Lean so later decide steps can read them as closed terms.
why it matters
The chunk is one of sixteen slices that couplingZList concatenates into the full coupling table for the midpoint $m^2$ TT kernel certificate. The bridge theorem czChunk5_bridge asserts that the corresponding generated chunk, mapped through toCZ, equals this list, tying the script output to the in-kernel data.
In the broader Recognition gravity stack this supports exact (non-numeric) verification of the Regge Hessian / Bloch-data identities that underwrite the continuum limit of the discrete action. It does not itself invoke the forcing chain (T5–T8) or the Recognition Composition Law; it is infrastructure for the 4D curvature-squared / mass-gap side of the discrete gravity analysis.
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