endpointRoute_master_theorem_valid
plain-language theorem explainer
The endpoint-route packing of the five quantum-gravity master witnesses yields a valid instance of the RS quantum-gravity master statement. Gravity auditors cite it to confirm that the Track 1 handoff path (single-slice and varying-cardinality receipts) is live audit surface, not dead code beside the physical-content D2 route. The proof is a pure term application of the conditional master theorem to those five installed witnesses.
Claim. The RS quantum-gravity master proposition holds for the five-tuple consisting of the endpoint-route Regge/Einstein-Hilbert continuum-and-Bianchi witness, the forced amplitude-linearity witness, the derived page-curve witness, the PTA stochastic-GW distinctness witness, and the strong-field distinctness witness.
background
The module Gravity.MasterTheoremUnconditional installs theorem-built witnesses for the five arguments of the older conditional master theorem, leaving that conditional statement as the audit surface and supplying zero-argument routes through it. The master proposition itself is the Track 7.A template: the T0--T8 forcing chain plus cost uniqueness and Lorentzian $1{+}3$ structure; Regge-to-Einstein-Hilbert continuum limit together with the contracted discrete Bianchi identity; forced amplitude linearity with unconditional BMV positivity; and the observational distinctness package (Hawking temperature in SI units, PTA stochastic GW, strong-field tests).
Two D2 routes exist for the continuum-and-Bianchi slot. The primary route names physical content directly (normalized nonlinear Regge aggregate on the canonical periodic six-tet cubic torus converges to the continuum EH integral; every Schläfli-satisfying Regge datum obeys the contracted discrete Bianchi identity). The endpoint route retained here packages the older Track 1 handoff receipts from the integration layer. Upstream forcing landmarks (eight-tick period, $D=3$, finite-dimensional Hamiltonian emergence) sit under the master template rather than in this packing step.
proof idea
One-line term wrapper. Feed the five canonical witnesses (endpoint-route continuum-and-Bianchi, forced amplitude linearity, derived page curve, PTA distinctness, strong-field distinctness) into the conditional master theorem rs_quantum_gravity_master_conditional, which assembles them into the master proposition. No extra tactics or intermediate lemmas.
why it matters
Closes the endpoint-route zero-argument surface for the quantum-gravity master statement (master plan §4 Track 7.A). The doc-comment is explicit: both D2 routes produce valid master outputs, and the endpoint route documents the Track 1 integration path rather than being dead code. Downstream use count is presently zero; the declaration is an audit endpoint, not an intermediate lemma. It sits beside the physical-content D2 packing and the honest physical-scope status record that follows in the same module: theorem-built witnesses are installed, yet those witnesses do not by themselves close the remaining physical-scope frontier. Framework landmarks touched only by inclusion are the T0--T8 chain, cost uniqueness, and the observational distinctness clauses inside the master template.
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