endpointRouteRegEHContinuumProp_holds
plain-language theorem explainer
The three Track-1 endpoint receipts (single-slice product-filter data, varying-cardinality product-filter data, and the physical D2 master witness) all hold simultaneously. Gravity auditors cite this as the zero-argument closure of the endpoint-receipt Regge/EH continuum proposition. The proof is a pure term packing the three already-proved handoff theorems into one conjunction.
Claim. The conjunction of (i) the single-slice product-filter data endpoint, (ii) the varying-cardinality product-filter data endpoint, and (iii) the physical $D_2$ master-witness endpoint holds. Equivalently, every concrete six-tet quadrature slice supplies single-slice product-filter data, staged cross-cardinality data plus a global residual envelope supply varying-cardinality product-filter data, and for every dimension/vertex/bond triple a physical Regge–Einstein–Hilbert $D_2$ master witness is inhabited.
background
This module supplies theorem-built, zero-argument witnesses for the five inputs that the older conditional quantum-gravity master theorem took as hypotheses. The conditional statement remains the audit surface; the present file installs the canonical unconditional route through it.
The $D_2$ clause of that master theorem asserts continuum recovery of the Einstein–Hilbert integral from Regge calculus, together with a discrete Bianchi identity. One retained audit path packages $D_2$ via three endpoint-receipt propositions from the Track-1 handoff layer: single-slice product-filter data on the canonical periodic six-tet cubic torus, varying-cardinality product-filter data with a global residual envelope, and a physical $D_2$ master-witness certificate for arbitrary dimension, vertex, and bond data.
The proposition being proved is exactly the conjunction of those three endpoint types. Upstream, each conjunct is already discharged by a named Track-1 theorem (Agent B endpoints consumed by Track 7).
proof idea
Pure term-mode construction of a triple. The three components are, in order: the single-slice product-filter endpoint theorem, the varying-cardinality product-filter endpoint theorem, and the physical $D_2$ master-witness endpoint theorem, all imported from the handoff-integration layer. No further rewriting or case analysis is required; the conjunction is inhabited by pairing the three prior proofs.
why it matters
Feeds the endpoint-receipt field of the canonical Regge/EH-plus-Bianchi witness used as the audit $D_2$ route into the unconditional master-theorem surface. Downstream, that witness sets the continuum clause equal to this proposition and the continuum proof equal to this theorem, while the Bianchi clause is filled by a separate concrete physical identity. The module doc retains this route explicitly for audit even though a primary physical-content $D_2$ witness is preferred. In the broader Recognition gravity stack it closes one of the five argument slots that formerly made the quantum-gravity master theorem conditional, without touching the eight-tick, $\phi$-ladder, or $T0$–$T8$ forcing chain directly.
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