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IndisputableMonolith.Gravity.MasterTheorem

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Gravity master-certificate module that packages the T0–T8 forcing spine, cost uniqueness, Lorentzian 1+3 signature, and related SI/discriminator closures as concrete carried propositions. Downstream Track 7 master-theorem variants import it to avoid universe metavariables from the full CompleteForcingChain package. Auditors of RS quantum-gravity claims use it as the single entry surface for the gravity bundle. Structure is a thin carrier layer over already-proved structural theorems.

claimThe module assembles carried propositions asserting that the full T0--T8 forcing chain holds from the Recognition Composition Law; the cost $J$ is unique with $J(x)=(x+x^{-1})/2-1$; spacetime signature is Lorentzian $1+3$; and the bundled gravity discriminators, black-hole SI lifts, Hawking temperature, and Track 4.A cosmology certificate are exposed as theorem surfaces with zero free parameters.

background

Recognition Science derives physics from the Recognition Composition Law on the cost $J$, forcing the chain T0 through T8: uniqueness of $J(x)=\cosh(\log x)-1$, the golden ratio $\varphi$ as self-similar fixed point, the eight-tick octave (period $2^3$), and $D=3$ spatial dimensions. Those inevitabilities live in UnifiedForcingChain.

This Gravity.MasterTheorem module is the Track 7 hub of the quantum-gravity master plan. It imports structural closures already proved elsewhere: black-hole entropy and Hawking temperature in SI (Track 3.B), echo rung algebra SI lift (3.D), three theorem-grade discriminators against LQG/string and rivals (Track 6), the 4×3 discriminator matrix, amplitude-linear quantum-channel forcing, no classical mediator, zero free parameters, spacetime emergence, and the Track 4.A cosmology certificate ($\eta_B$ exact rung, $\Omega_\Lambda$ band, Planck consistency).

Per the module doc, the design goal is a concrete carried proposition for the T0--T8 spine that avoids universe metavariables from the larger CompleteForcingChain package while still letting the master atom transitively expose those theorem surfaces.

proof idea

Not a single deep proof: a packaging and carrier module. It defines carried proposition types (T0_T8_carried_prop, CostUniqueness_carried_prop, Lorentzian_1_3_carried_prop, bmv_positive_unconditional_carried_prop) and supplies proven witnesses (T0_T8_holds_proven, CostUniqueness_proven, Lorentzian_1_3_proven, and the unconditional BMV positivity witness) by re-exporting or wrapping the imported structural certificates.

The recurring pattern is: name a Prop carrier, assert that it holds, and mark the assertion as proven from upstream modules (UnifiedForcingChain, BlackHoleEntropySI, DiscriminatorCert, Track4ACert, and siblings). No new calculus is introduced here; the work is interface hygiene so MasterTheoremStructural and MasterTheoremUnconditional can take zero or few hypothesis inputs.

why it matters in Recognition Science

Feeds the entire Gravity Track 7.A family: MasterTheoremPartial (3 remaining hypotheses), MasterTheoremDeeperPartial (2 remaining), MasterTheoremStructural (fully structural, zero hypothesis inputs, all five inputs pre-filled by structural witnesses), and MasterTheoremUnconditional (theorem-built witnesses for the five inputs of the older conditional master theorem). Also imported by PageCurveStructural and PageCurveDynamical, and by PTA structural discriminators (Gravity.PTAStructural, Cosmology.PTAStochasticGWStructural).

Without this carrier layer, each downstream master theorem would re-import CompleteForcingChain and risk universe metavariable issues. It is the audit surface that makes the gravity master atom transitively carry T0--T8, cost uniqueness, Lorentzian 1+3, SI black-hole closures, and the discriminator matrix. Framework landmarks directly exposed: T0--T8 forcing from RCL, uniqueness of $J$, $D=3$, and the zero-free-parameter claim for RS gravity.

scope and limits

used by (12)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (12)

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declarations in this module (38)