IndisputableMonolith.Gravity.Analysis.SRSTTFirstVariation4DAudit
Audit layer for the Euclidean weak-field TT directional first variation of the closed 4D midpoint Bloch symbol. Gravity analysts cite it to check that the cross-term variation and its continuum transport sit on the banked Einstein–Hilbert face without hidden gaps. Structure is import-and-review of the parent first-variation development rather than a new derivation.
claimModule-level audit of the TT directional first variation of the closed 4D midpoint Bloch symbol $B_{\mathrm{mid}}$ in the Euclidean weak-field transverse-traceless sector, and of the torus-normalized continuum face obtained by transporting that variation through the banked limit $S_{\mathrm{RS}}\to S_{\mathrm{EH}}$ on the polarized combinations $H\pm K$.
background
Recognition Science gravity work reduces continuum Einstein–Hilbert structure from discrete recognition action on a closed 4D lattice. The parent module derives the genuine cross-term (directional) first variation of the exact midpoint Bloch symbol in the Euclidean weak-field TT sector, then moves that variation to a continuum face via the banked convergence $S_{\mathrm{RS}}\to S_{\mathrm{EH},4d}^{\mathrm{closed}}$ on $H+K$ and $H-K$ together with polarization.
An audit module in this stack does not re-prove the variation identities. It packages the honesty constraints, naming conventions, and review surface so that the first-variation claims can be checked against the closed 4D EH face without reopening the full lattice calculus. TT means transverse-traceless metric perturbations; the midpoint Bloch symbol is the discrete quadratic form whose continuum limit is the EH kinetic structure.
proof idea
This is an audit module, not a derivation module. It imports SRSTTFirstVariation4D and exposes the parent argument for review: TT directional first variation of the midpoint Bloch symbol, then continuum transport by the banked closed 4D RS-to-EH Tendsto on the polarized pairs $H\pm K$. No independent proof body is the point; the structure is import, surface the honesty binding, and freeze the claim boundary for downstream gravity analysis.
why it matters in Recognition Science
Sits in the Gravity domain as the review face for the 4D TT first-variation bridge from discrete recognition action to continuum Einstein–Hilbert structure. Downstream consumers (none linked yet in the graph) would cite the audited variation when assembling weak-field continuum limits or polarization identities. In the broader RS chain this supports the gravity side of the discrete-to-continuum program once the eight-tick and $D=3$ landmarks fix the lattice geometry; the audit keeps the honesty binding of the parent module visible so the EH face is not treated as free-standing scaffolding.
scope and limits
- Does not re-derive the TT first variation of the midpoint Bloch symbol.
- Does not prove $S_{\mathrm{RS}}\to S_{\mathrm{EH}}$; that limit is banked upstream.
- Does not treat Lorentzian signature or strong-field regimes.
- Does not supply new continuum curvature identities beyond the audited face.
- Does not claim downstream use sites; the graph lists none.