Track1DTTHessianLichnerowiczEncodedCoeffOriginColumnReductionEndpoint
plain-language theorem explainer
Coefficient-only origin-column data for the TT Hessian/Lichnerowicz residual at N=5 implies a raw typed-column residual certificate and the raw origin-column reduction endpoint. Track 1.D and Track 7 handoff consumers cite this Prop as the packaging of that step. It is a pure implication definition chaining the smallest generator-facing coeff surface into the raw residual route without storing an origin table.
Claim. If coefficient-only origin-column formula data for the transverse-traceless Hessian/Lichnerowicz residual at $N=5$ is supplied (two edge-operator kernels and seven residual-generator coefficient rows), then there exists a raw typed-column residual certificate and the raw origin-column reduction endpoint holds.
background
Module Gravity.MasterTheoremHandoffIntegration is the Track 7 integration-lane receipt for parallel fork handoffs (A–F). It records what new endpoints prove without upgrading the discovery claim, and leaves Track 1 displacement-class leaves open.
The coefficient-only origin-column structure is the smallest generator-facing surface for the TT Hessian/Lichnerowicz residual: it stores the Regge Hessian and lattice Lichnerowicz kernels plus seven residual-generator coefficient rows, and proves origin-row scalar formulas and the translated residual formula against the generator map. The raw typed-column residual certificate removes the explicit residual matrix from generator input, supplying only an origin-column residual table and a translation law for the encoded Regge−Lichnerowicz residual.
Upstream, the raw origin-column reduction endpoint says that such a raw certificate feeds the typed-column origin-table residual route (origin column/row tables, residual kernel, periodic residual entries) without an explicit residual matrix input.
proof idea
Definitional Prop, not a proved theorem. The body is the implication: from coefficient-only origin-column formula data, conclude Nonempty of the raw typed-column residual certificate together with the already-defined raw origin-column reduction endpoint. No tactics; the holds theorem later discharges it by constructing the raw certificate via ofCoeffOriginColumnData and invoking the raw endpoint holds lemma.
why it matters
Packages the Track 1.D coefficient-only origin-column residual endpoint consumed by Track 7. Downstream, the holds theorem asserts this Prop; the translated coefficient-only reduction endpoint chains through it (translated coeff data → coeff origin-column data ∧ this endpoint); and ForkHandoffIntegrationCert aggregates Track 1 reduction/interface packages among forks A–F without closing open Schläfli leaves. In the gravity master-theorem lane this is a handoff surface: it shrinks generator-facing input to kernels plus seven coefficient rows, then routes into the residual origin-table machinery. It does not touch T0–T8 forcing, RCL, or the alpha band; it is local to the discrete TT shear residual stack at N=5.
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