IndisputableMonolith.Gravity.Analysis.ReggeEdgeTTAttachment4DAudit
Audit layer for the 4D Regge edge transverse-traceless attachment on the 4-torus. It checks that the Euclidean 4×4 TT/gauge/transverse-trace split, once loaded onto axis-edge plane-wave modes, obeys the same quadratic-form convention used in the 3D chain. Gravity and discrete-QG workers cite it when verifying Wave 4 lane W4-1. Structure is import-and-audit over the plane-wave attachment module, not a new construction.
claimAudit of the attachment of the Euclidean $4\times 4$ transverse-traceless / gauge / transverse-trace decomposition to plane-wave edge loadings $E$ on axis edges of the 4-torus, with quadratic form $\sum_{ij} E_{ij} D^i D^j$ matching the 3D convention.
background
Recognition Science gravity work treats linearized metric degrees of freedom on a discrete 4-torus via Regge-style edge variables. The algebraic predecessor splits a Euclidean $4\times 4$ symmetric tensor into transverse-traceless (TT), gauge, and transverse-trace pieces. The plane-wave attachment layer then loads those pieces onto axis-edge modes, using the quadratic-form convention $\mathrm{polEdgeCoeff}(E,d)=\sum_{ij} E_{ij} D^i D^j$ already fixed in the 3D preflight chain.
This module sits one step above that attachment: it is the audit surface for Wave 4 / lane W4-1 (edge_tt_decomposition) in the QG full-theory campaign. Upstream doc states the goal as the "next kernel-checked increment after the algebraic EdgeTTDecomposition4D layer," so the audit is meant to certify that the plane-wave edge loadings respect the same split and symbol conventions rather than to redefine them.
proof idea
Definition and audit module over a single import: the 4D Regge edge TT attachment (plane-wave layer). No standalone constructive proof obligation is declared at module scope. The argument structure is: import the attachment API, then expose kernel-level checks that the TT/gauge/transverse-trace projectors, once evaluated on axis-edge plane-wave loadings of the 4-torus, reproduce the expected quadratic form and orthogonality relations already fixed algebraically and in 3D. Treat failures as audit flags against the attachment layer, not as new lemmas about continuum GR.
why it matters in Recognition Science
Closes the audit gap on Wave 4 lane W4-1 after the algebraic 4D edge TT decomposition and its plane-wave attachment. Downstream consumers (none linked yet in the graph) would be higher gravity-analysis or continuum-limit statements that assume a clean discrete TT sector on edges. In the broader RS forcing picture this is infrastructure for discrete gravity, not a T0–T8 landmark: it keeps the spin-2 / gauge bookkeeping honest on the 4-torus so later massless-graviton or curvature identifications do not smuggle mixed gauge pieces. Parent content is the imported attachment module; this file exists so those claims can be kernel-checked rather than trusted by construction.
scope and limits
- Does not construct the 4×4 TT/gauge/transverse-trace projectors; those live upstream.
- Does not prove continuum GR recovery or a graviton propagator.
- Does not treat non-axis edges, curved backgrounds, or Lorentzian signature.
- Does not alter the 3D quadratic-form convention; it only audits 4D agreement.
- Does not feed any recorded downstream theorem yet (used_by is empty).