Pith. sign in
module module moderate

IndisputableMonolith.Gravity.Analysis.ReggeExactMidpointM2TTIdentity4DM2NumChunk14

show as:
view Lean formalization →

Chunk 14 of the generated midpoint m² TT-identity certificates for 4D Regge calculus. It holds a contiguous block of kernel-decidable integer equalities (scale-32 foldl tables) used when assembling m2Num = 8·explicitZ over all 4096 index tuples. Gravity auditors of the exact discrete curvature identity cite it only inside that assembly chain. Content is pure certificate data: no analytic argument beyond kernel decide.

claimA finite block of certified integer equalities for the midpoint $m^2$ transverse-traceless identity in 4D Regge calculus, evaluated on scale-32 kernel tables and closed by kernel decision on a contiguous subset of the $4096$ index tuples.

background

In the RS gravity analysis stack, the Regge exact midpoint $m^2$ TT identity is a discrete curvature identity on 4D triangulations. The imported kernel-certificate module supplies script-generated Int List.foldl tables at scale 32, proved with kernel decide only (no native_decide), from scripts/qg/regge_4d_m2_kernel_certs_20260721.py.

This file is one numbered chunk in the m2Num certificate stream. Sibling entries such as the $e_{320000}$–$e_{320023}$ block are individual certified equalities for successive index tuples. The full cover is $4096$ tuples; downstream assembly multiplies the explicit $Z$ contribution by 8 to obtain m2Num.

proof idea

Generated certificate module, not a hand proof. Each local entry is a one-shot kernel decide on a foldl evaluation against the imported scale-32 kernel tables. Structure is a flat list of kernel-closed integer identities for one contiguous index block; no lemmas beyond the kernel cert import and no tactic creativity.

why it matters in Recognition Science

Imported by the m2Num assemble module, whose doc-comment states the goal: assemble m2Num = 8·explicitZ over all 4096 index tuples. Every chunk must close or the global m2Num identity fails. The module is scaffolding in the discrete-gravity verification path that underwrites exact midpoint TT identities used later in RS gravity analysis; it does not itself state a physical law, only a certified arithmetic slice of one.

scope and limits

used by (1)

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

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (256)

… and 176 more