rs_quantum_gravity_master_one_statement
plain-language theorem explainer
Under five named open-track hypotheses (Regge–EH continuum plus discrete Bianchi, unconditional amplitude-linear forcing, dynamical Page curve, PTA stochastic-GW spectrum distinct from inflation, and strong-field tests distinct from pure GR), the full Recognition Science quantum-gravity master conjunction holds. Anyone citing the Track 7.A one-statement form of the discovery uses this packaging. The proof is a one-line term application of the conditional master theorem.
Claim. For any witnesses of (i) Regge action converging to Einstein–Hilbert with contracted discrete Bianchi, (ii) unconditional amplitude-linear channel forcing, (iii) dynamical Page-curve derivation, (iv) RS PTA stochastic gravitational-wave background distinct from inflationary $n_t$, and (v) RS strong-field predictions distinct from pure GR, the master quantum-gravity statement holds: the T0–T8 substrate with unique cost and Lorentzian $1{+}3$ signature, classical continuum recovery, amplitude-linear and BMV positivity, Hawking temperature and black-hole entropy in SI, echo and discriminator certificates, zero free parameters, and the observational distinctness clauses supplied by those witnesses.
background
Gravity Track 7.A authors the master theorem of the RS quantum-gravity discovery as a twelve-clause conjunction matching the master-plan template. Eight clauses are CLOSED and discharged from Lean anchors in Sessions 89–96 (Hawking temperature SI, black-hole entropy SI, echo SI, $\Omega_\Lambda$, BMV entropy, discriminators, zero free parameters). Five tracks remain OPEN and appear as named hypothesis structures.
Those structures package: discrete-to-continuum Regge $\to$ Einstein–Hilbert convergence plus contracted discrete Bianchi (D2 classical recovery); amplitude-linear forcing lifted off any factor-product joint-substrate axiom; dynamical Page-curve entropy evolution (Page time $M^3$ scaling already closed); PTA stochastic-GW spectrum distinct from inflationary $n_t$; and strong-field tests (S-stars, EHT shadow, Cassini Shapiro) distinct from pure GR.
The master proposition is the conjunction of substrate facts (T0–T8, cost uniqueness, Lorentzian $1{+}3$), the classical-limit pair, amplitude-linear plus BMV positivity, SI Hawking/entropy/echo observables, and the observational distinctness clauses. The conditional theorem already proves that conjunction once the five hypothesis packs are supplied.
proof idea
One-line term proof: the declaration is definitionally the $\forall$-quantified form of the conditional master theorem. Applying rs_quantum_gravity_master_conditional to the five hypothesis arguments yields RSQuantumGravityMaster directly. No extra algebraic work; the eight closed clauses were already discharged inside the conditional proof from the Sessions 89–96 anchors.
why it matters
This is the Track 7.A authored one-statement packaging of the quantum-gravity master theorem: the citation form that presents the discovery as a single quantified claim rather than a curried implication. It sits at the end of the MasterTheorem module and currently has no downstream Lean dependents; its role is archival and paper-facing.
Framework landmarks it bundles include the forcing chain T0–T8 (unique $J$, $\phi$, eight-tick octave, $D=3$), cost uniqueness, Lorentzian $1{+}3$ emergence, classical Regge–EH recovery, amplitude-linear quantum channel response, and SI black-hole thermodynamics. The doc-comment is explicit: the discovery is complete only when the five open hypotheses become theorem-grade and the falsifier register is fully populated. Until then this remains the conditional master packaging, not an unconditional claim that quantum gravity has been derived.
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