IndisputableMonolith.Gravity.Analysis.ReggeTTGateBBridgeCore
Literal rational coefficient table for the Regge TT continuum spike, identifying each tet-block contribution with explicit raw stencil weights. Gravity analysts working Gate B (convention bridge from raw stencil to committed spike LHS) cite it. The module is mostly algebraic identities equating core triple sums to the six-block spike decomposition.
claimA fixed table of rational raw coefficients for the Regge TT continuum certificate: core weights, slot dispersions, mid-slot doubles, polynomial edge coefficients, and triple terms, together with equalities identifying each of the six tet-blocks and the full triple sum with the committed spike sum $\sum_{k=0}^{5}\mathrm{tetBlock}_k$.
background
In the Recognition Science gravity stack, Regge TT analysis treats discrete tetrahedral (tet) blocks whose continuum limit must match a locked spike certificate. Gate C-A2f identifies the kernel with the raw Jacobian coefficient; the present module supplies the concrete rational table that makes that identification numerical rather than schematic.
Upstream sits the continuum certificate spike module, which defines the spike LHS as the sum of six tet-blocks. Downstream Gate B asks that the interface moment fold, built from the actual raw stencil (support, phase quadratic, amplitude), equal that spike sum under the seven TT hypotheses.
Definitions introduced here are the core weight, slot dispersion, mid-slot double, polynomial edge coefficient, and the triple term assembled from them. Six block-equalities and one global sum-equality pin the table to the spike decomposition.
proof idea
Definition-heavy core with algebraic equalities, not a single theorem. Each coreBlockk_eq is a direct rational arithmetic identity matching one tet-block to its stencil contribution. The capstone coreTripleSum_eq_spikeSum assembles the six blocks and rewrites the triple sum as the committed spike LHS. No analytic estimates; pure coefficient bookkeeping over finite index sets (Fin big-operators).
why it matters in Recognition Science
Feeds ReggeTTGateBBridge, which closes panel-locked Gate B (GateBConventionTarget of the Bloch convention audit) in the QG full-theory campaign, Paper C / Pillar 1, Lane C. That parent module needs the moment fold on the raw stencil to equal tetBlock0 + ... + tetBlock5 under the seven TT hypotheses; without this rational table the bridge has no concrete coefficients to equate. The doc-comment ties the table to Gate C-A2f kernel identification with the raw Jacobian coefficient, so the core is the numerical spine of the convention bridge rather than a free parameter choice.
scope and limits
- Does not prove the Gate B moment-fold equality; only supplies the coefficient table and block identities.
- Does not derive the raw Jacobian kernel; defers that identification to Gate C-A2f.
- Does not address continuum error bounds or continuum-limit rates.
- Does not discharge the seven TT hypotheses; they remain ambient assumptions for the parent bridge.
- Does not claim uniqueness of the rational table outside the locked spike convention.