Pith. sign in
def

Track1MixedAxisRow100CoeffCertEndpoint

definition
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module
IndisputableMonolith.Gravity.MasterTheoremHandoffIntegration
domain
Gravity
line
342 · github
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plain-language theorem explainer

The proposition asserts that the mixed-axis residual coefficient row indexed by the lattice vertex (1,0,0) vanishes identically: every entry against the five-vertex stencil is zero. Gravity Track 1.B cites it as the Session 208 non-origin split-row certificate. It is a one-line Prop alias of the boolean decision procedure on that fixed row.

Claim. The residual coefficient row at the non-origin vertex $u=(1,0,0)$ of the five-point stencil vanishes: for every stencil vertex $v$, the mixed-axis residual coefficient of the pair $(u,v)$ is zero (equivalently, the boolean certificate for that row evaluates to true).

background

Module Gravity.MasterTheoremHandoffIntegration is the Track 7 integration-lane receipt for parallel fork handoffs (A–F). It records what the new endpoints prove without upgrading the discovery claim, and keeps remaining Track 1 displacement-class leaves open.

The upstream predicate rowResidualCoeffsZero on a five-vertex index $u$ decides whether $\forall v$, the mixed-axis residual coefficient of $(u,v)$ is zero. Coefficients live in an exact rational residual table for the Freudenthal-axis stencil used in Track 1.B stationarity reduction.

Session 208 isolates one non-origin row as a split-row probe: vanishing of the $(1,0,0)$ row validates the row-split certificate route, while flagging that the full $5^3=125$ table should later be generated sparsely or replaced by translation invariance.

proof idea

Pure definitional alias: the proposition is definitionally equal to the boolean equality rowResidualCoeffsZero (1,0,0) = true. No tactics or lemmas are applied at this declaration; the computational content sits in the upstream decision procedure over the mixed-axis residual coefficient table. The companion theorem track1_mixed_axis_row100_coeff_cert_endpoint_holds discharges the Prop by citing the precomputed fact that the boolean is true.

why it matters

Feeds Track 7 handoff packaging. The companion holds-theorem is the Session 208 split-row coefficient endpoint consumed by Track 7; the Prop itself is the named endpoint type. Downstream, ForkHandoffIntegrationCert integrates Forks A–F and treats Track 1 material as a reduction/interface package, not a closure of the open Schläfli leaves.

In the gravity master-theorem lane this is a concrete non-origin row witness that the exact rational residual table is zero along a translated axis sample, supporting the row-split certificate strategy for Track 1.B. It does not finish the full stencil; the doc-comment explicitly leaves bulk generation or translation-invariance replacement as the next structural step.

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