Track1MixedAxisFullResidualCoeffCertEndpoint
plain-language theorem explainer
Names the Track 1.B Session-212 endpoint: every coefficient of the corrected N=5 mixed-axis stencil residual is zero. Gravity auditors and the Track 7 fork-handoff package cite it as the residual-coefficient receipt. The body is a one-line definitional alias of the full residual-coefficient certificate.
Claim. The proposition asserting that for every pair of vertices $u,v$ on the five-vertex stencil, the mixed-axis residual coefficient vanishes: $\mathrm{mixedAxisResidualCoeff}(u,v)=0$.
background
This module is the Track 7 integration-lane receipt for parallel fork handoffs in the gravity master theorem. It records what each fork endpoint proves without upgrading the discovery claim; remaining Track 1 displacement-class leaves stay open.
The aliased content is the full coefficient-vanishing statement for the corrected $N=5$ axis-stencil residual: a finite certificate required before converting the coefficient audit into the canonical periodic mixed-hinge deficit target at $N=5$. Upstream, that certificate is the universal quantification that every mixed-axis residual coefficient on Vertex5 pairs is zero.
The residual language sits next to the alpha-genesis residual (signed first-order genesis value against CODATA), but here the object is the stencil coefficient residual, not the fine-structure residual band.
proof idea
Definitional alias only: the endpoint proposition is definitionally equal to the full residual-coefficient certificate. No tactics, no lemmas applied at this site. The companion theorem track1_mixed_axis_full_residual_coeff_cert_endpoint_holds discharges the endpoint by supplying the existing fullResidualCoeffCert witness.
why it matters
Gives Track 7 a stable name for the Session-212 Track 1.B full rational residual certificate so the fork-handoff structure can consume it uniformly with the other endpoints (Schläfli reduction, displacement-class reductions, many-body lift, Page-capacity, $w(z)$ band, falsifier sensitivity).
Downstream, ForkHandoffIntegrationCert packages Forks A–F and treats the Track 1 material as a reduction/interface package, not a closure of the open Schläfli leaves. The holds theorem pins this endpoint as a concrete handoff fact. In the broader RS gravity lane this is bookkeeping for the discrete stencil side of the master theorem, not a new forcing-chain step (T0–T8) or a mass/alpha derivation.
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