IndisputableMonolith.Gravity.Analysis.ReggeExactMidpointM2TTIdentity4DM2NumChunk09
Chunk 09 of machine-generated kernel certificates for the 4D midpoint m² transverse-traceless identity in Regge analysis. It holds a block of explicit edge lemmas (e_210000-style) that discharge discrete kernel checks by `decide` on scale-32 tables. Downstream assembly folds these chunks into m2Num = 8·explicitZ over all 4096 index tuples. Citation target for anyone auditing the numeric half of the Regge midpoint identity.
claimA finite block of certified equalities for the discrete 4D midpoint $m^2$ TT kernel: each lemma asserts a concrete integer/table identity on a labeled multi-index (the $e_{21\ldots}$ family in this chunk), obtained from scale-32 fold tables, with no floating-point residual.
background
Recognition Science gravity analysis here works in a discrete Regge setting: curvature and mass-squared data live on a 4D simplicial complex, and the midpoint $m^2$ transverse-traceless (TT) identity is an exact algebraic relation among those data. The parent kernel-certificate module is generated by scripts/qg/regge_4d_m2_kernel_certs_20260721.py and uses only List.foldl plus scale-32 tables, with kernel goals closed by decide (never native_decide).
This file is one numbered chunk in that certificate stream. Sibling declarations are pure edge lemmas named by multi-index (e.g. the $e_{210000}$–$e_{210023}$ block). They do not introduce new physics constants; they pin finite combinatorial identities needed before global assembly.
Upstream import is solely the kernel-cert hub. Downstream, the assemble module sums $m_2^{\mathrm{Num}} = 8\cdot\mathrm{explicitZ}$ over the full $4096$ index tuples.
proof idea
Definition-and-certificate module, not a single narrative proof. Each edge lemma is a closed decide on a precomputed integer table entry from the scale-32 fold. No analytic expansion or calculus; the argument is exhaustive finite check of the kernel predicate on that multi-index. Chunk boundaries are bookkeeping only: same proof pattern as sibling chunks, different index range.
why it matters in Recognition Science
Feeds ReggeExactMidpointM2TTIdentity4DM2NumAssemble, whose doc-comment states the goal: assemble $m_2^{\mathrm{Num}} = 8\cdot\mathrm{explicitZ}$ over all 4096 index tuples. Without every chunk discharging its slice, the global numeric identity cannot be imported as a proved fact. In the gravity domain this is infrastructure for the exact midpoint $m^2$ TT relation on the 4D Regge complex, a discrete stand-in for continuum TT gauge constraints. It does not itself touch the forcing chain (T0–T8) or the J-cost law; it is a verified arithmetic substrate those continuum claims may later cite when matching discrete spectra.
scope and limits
- Does not prove the full 4096-tuple assembly; only one index chunk.
- Does not introduce continuum limits, curvature scalars, or Einstein equations.
- Does not use native_decide or runtime evaluation; kernel decide only.
- Does not claim physical units or RS constants (c, G, phi ladder) inside the lemmas.
- Does not address odd-parity or non-midpoint stencils outside the generated tables.
used by (1)
depends on (1)
declarations in this module (256)
-
theorem
e_210000 -
theorem
e_210001 -
theorem
e_210002 -
theorem
e_210003 -
theorem
e_210010 -
theorem
e_210011 -
theorem
e_210012 -
theorem
e_210013 -
theorem
e_210020 -
theorem
e_210021 -
theorem
e_210022 -
theorem
e_210023 -
theorem
e_210030 -
theorem
e_210031 -
theorem
e_210032 -
theorem
e_210033 -
theorem
e_210100 -
theorem
e_210101 -
theorem
e_210102 -
theorem
e_210103 -
theorem
e_210110 -
theorem
e_210111 -
theorem
e_210112 -
theorem
e_210113 -
theorem
e_210120 -
theorem
e_210121 -
theorem
e_210122 -
theorem
e_210123 -
theorem
e_210130 -
theorem
e_210131 -
theorem
e_210132 -
theorem
e_210133 -
theorem
e_210200 -
theorem
e_210201 -
theorem
e_210202 -
theorem
e_210203 -
theorem
e_210210 -
theorem
e_210211 -
theorem
e_210212 -
theorem
e_210213 -
theorem
e_210220 -
theorem
e_210221 -
theorem
e_210222 -
theorem
e_210223 -
theorem
e_210230 -
theorem
e_210231 -
theorem
e_210232 -
theorem
e_210233 -
theorem
e_210300 -
theorem
e_210301 -
theorem
e_210302 -
theorem
e_210303 -
theorem
e_210310 -
theorem
e_210311 -
theorem
e_210312 -
theorem
e_210313 -
theorem
e_210320 -
theorem
e_210321 -
theorem
e_210322 -
theorem
e_210323 -
theorem
e_210330 -
theorem
e_210331 -
theorem
e_210332 -
theorem
e_210333 -
theorem
e_211000 -
theorem
e_211001 -
theorem
e_211002 -
theorem
e_211003 -
theorem
e_211010 -
theorem
e_211011 -
theorem
e_211012 -
theorem
e_211013 -
theorem
e_211020 -
theorem
e_211021 -
theorem
e_211022 -
theorem
e_211023 -
theorem
e_211030 -
theorem
e_211031 -
theorem
e_211032 -
theorem
e_211033