MasterTheoremStructuralCert
plain-language theorem explainer
Certificate packing the fully structural RS quantum-gravity master theorem with all five hypothesis slots filled by named structural witnesses, plus a closure-status audit and a Nonempty conjunction for those five hypothesis types. Gravity-track auditors cite it as the Session-102 zero-input structural master receipt. Pure structure definition; concrete inhabitants are assembled in sibling defs.
Claim. A certificate record with three fields: (1) the RS quantum-gravity master theorem holds when applied to the five structural witnesses (Regge$\to$EH continuum with discrete Bianchi, unconditional amplitude-linear channel forcing, derived Page curve, PTA stochastic GW spectrum distinct from inflationary $n_t$, and strong-field tests distinct from GR); (2) a closure-status tally (closed / structural / open counts with sum identity); (3) the conjunction that each of those five hypothesis structures is inhabited.
background
Module Gravity Track 7.A packages the master theorem in fully structural form: zero free hypothesis inputs at the call site, all five slots pre-filled by structural witnesses. Session trajectory: Session 97 authored the master with five open hypothesis inputs; Sessions 100–101 retired PTA, strong-field, and Page-curve slots structurally; Session 102 retires the remaining Track 1.B/1.C and Track 2.C/2.D slots the same way, leaving zero inputs.
Upstream hypothesis shells are thin Prop-carriers: RegEHContinuumAndBianchi (Regge action converges to Einstein–Hilbert with error bound, plus contracted discrete Bianchi), AmplitudeLinearForcedUnconditional (channel response forced linear without factor-product substrate axiom), PageCurveDerived, PTAStochasticGWDistinctFromInflation, and strong-field distinctness from GR. Each has a structural witness inhabitant (e.g. ptaDistinctFromInflationWitness). MasterTheoremClosureStatus records closed/structural/open counts with a total identity for audit.
The module is explicit that this is structural-grade, not dynamical: the fully unconditional master still needs geometric residual estimates and physical Schläfli identities.
proof idea
No proof body: this is a structure declaration. The three fields are typed obligations only. Downstream, masterTheoremStructuralCert fills them by pointing structural_master_holds at rs_quantum_gravity_master_structural, closure_status at closureStatus_as_of_session_102, and all_hypotheses_inhabited at honest_scope_statement. Inhabitation of the certificate itself is then the one-line ⟨masterTheoremStructuralCert⟩.
why it matters
This is the Session-102 structural master receipt for RS quantum gravity: the single object that says the master statement runs with zero hypothesis inputs at the call site, every clause theorem-grade or structural-witness-grade. Downstream, ForkHandoffIntegrationCert and the fork A–F / A–C–F one-statements consume Nonempty MasterTheoremStructuralCert so Track 7 can integrate many-body channel lifts, Schläfli-to-stationarity reductions, Page-layer and falsifier packages without re-opening the five slots.
It does not finish the dynamical program. Module doc keeps Track 1.B (Regge residual bound) and Track 1.C (physical Schläfli) as multi-session open geometric work; amplitude-linear and Page-curve dynamical lifts remain future. In the broader RS chain this sits on the gravity side of classical recovery and quantum-channel forcing, not on T5–T8 forcing of $J$, $\varphi$, eight-tick, or $D=3$.
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