track1_mixed_axis_row100_coeff_cert_endpoint_holds
plain-language theorem explainer
The exact rational residual-coefficient row at multi-index (1,0,0) vanishes as a boolean certificate. Track 7 and the translation-invariance bridge cite this as the Session 208 split-row probe for Track 1.B. The proof is a one-line term wrapper of the native-decided Freudenthal-axis stencil certificate.
Claim. The boolean residual-coefficient certificate for the non-origin multi-index $(1,0,0)$ evaluates to true: that row of the exact $\mathbb{Q}$ residual table vanishes.
background
Track 7 is the Gravity fork-handoff integration lane. It records parallel endpoints from Track 1.B stationarity reduction, physical residual/Bianchi interfaces, many-body amplitude lifts, Page-capacity transfer, dark-energy $w(z)$ bands, and falsifier packaging, without upgrading the discovery claim.
The residual object is the exact rational coefficient table of the Freudenthal-axis stencil residual. The predicate rowResidualCoeffsZero asserts that every entry of a chosen multi-index row is zero (exposed as a boolean). The origin row is the translation-invariance baseline; the $(1,0,0)$ row is the first non-origin split-row probe.
Upstream, rowResidualCoeffsZero_100_eq_true already decides that the $(1,0,0)$ row vanishes by native_decide. The endpoint Prop simply packages that fact for the handoff certificate.
proof idea
One-line term proof: the endpoint is definitionally rowResidualCoeffsZero (1,0,0) = true, and the proof is exactly the upstream theorem rowResidualCoeffsZero_100_eq_true, itself discharged by native_decide on the finite rational residual table.
why it matters
This is the Session 208 split-row coefficient endpoint consumed by Track 7. It feeds forkHandoffIntegrationCert, the integration-lane certificate that bundles Track 1/2/3/4/6 handoffs.
Mathematically it validates the row-split certificate route for Track 1.B: not only the origin residual row but also a mixed-axis non-origin row vanishes. That is the first concrete check that residual vanishing is not an origin artifact, and it is the theorem-shaped statement the translation-invariance bridge is meant to consume.
It also surfaces the next gap named in the endpoint doc: all 125 rows should either be generated sparsely or replaced by a translation-invariance argument, rather than certified one multi-index at a time. In the RS gravity stack this sits under the discrete stencil/Regge residual analysis that supports the master-theorem handoff, not under the T0–T8 forcing chain itself.
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