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plain-language theorem explainer
Conditional master theorem for Recognition Science quantum gravity: if five open-track hypotheses hold, the twelve-clause discovery statement follows. Eight clauses are already discharged from existing Lean results (forcing chain, J-cost uniqueness, (1,3) emergence, Hawking/SI anchors, φ-cosmology, discriminators, zero free parameters). Track 7.A authors cite this as the gated statement. The proof body is still a sorry stub.
Claim. Assume: (i) Regge action converges to Einstein–Hilbert with contracted discrete Bianchi; (ii) amplitude-linear channel forcing holds unconditionally; (iii) the dynamical Page curve is derived; (iv) the RS PTA stochastic-GW spectrum is distinct from inflationary $n_t$; (v) RS strong-field predictions (S-stars, EHT shadow, Shapiro delay) are distinct from pure GR. Then the twelve-clause RS quantum-gravity master statement holds.
background
Track 7.A authors the master quantum-gravity statement as a twelve-clause conjunction matching the master-plan template. Eight clauses are already closed from prior sessions; five remain open and are packaged as typed hypothesis structures, not axioms.
Closed substrate pieces include the T0–T8 forcing spine (φ fixed, eight-tick octave, $D=3$), J-cost uniqueness from the recognition composition law, and Lorentzian $(1,3)$ spacetime emergence. Gravity/SI anchors already in hand: Hawking temperature in SI units, leading-log black-hole entropy coefficient as an RS discriminator, QNM spectrum distinct from LQG/string, $\Omega_\Lambda$ from $\phi$ (Track 4.A), BMV two-qubit entropy positivity, and zero free dimensionless parameters in the gravity sector.
The five inputs name the open tracks: Regge→EH continuum plus discrete Bianchi (1.B/1.C); unconditional amplitude-linear forcing (2.C/2.D); dynamical Page-curve derivation (3.C); PTA stochastic GW vs inflation (6.B); strong-field tests vs pure GR (6.C).
proof idea
Scaffolding only: the proof body is an empty sorry stub. The intended shape, per the module plan, is constructive assembly of the twelve-clause conjunction: inhabit each of the eight closed clause Props by citing the existing certificates (UnifiedForcingChain, J-cost uniqueness, SpacetimeEmergenceCert, pure-two-qubit entropy positivity, HawkingTemperatureSI, BlackHoleEntropySI, Track4ACert, DiscriminatorCert, ZeroFreeParameters), and discharge the four open classical/quantum/observational slots by projecting the corresponding fields out of the five hypothesis structures. No algebraic reduction is present yet.
why it matters
This is the Track 7.A master-statement authoring step: it freezes the discovery claim as a Lean Prop while keeping open tracks explicit (anti-retreat). Framework landmarks already wired in include T0–T8, J-uniqueness via the recognition composition law, $D=3$, eight-tick structure, φ-derived $\Omega_\Lambda$, and the SI black-hole/Hawking discriminators.
No downstream theorems depend on it yet (used_by empty). The unconditional master (zero hypothesis inputs) is gated on closing Tracks 1.B/1.C, 2.C/2.D, 3.C, 6.B, and 6.C, plus the master-plan done-criteria (paper, falsifier register, §8 checklist). Until those close, this conditional form is the strongest honest theorem the repo can state.
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