gravity_sector_zero_free_parameters_proven
plain-language theorem explainer
The gravity sector has zero free dimensionless parameters: every constant in the gravity bundle admits a closed form fixed by the framework. Gravity and master-theorem authors cite this as the Track 5.B / Session 96 closure inside the twelve-clause QG master statement. The proof is a pure term that packages the closed-form certificates for ħ, Einstein κ, c_RS, echo damping, rung phase delay, leading entropy, Hawking temperature, and the baryon rung identity, together with the sector-level zero-parameter certificate.
Claim. The gravity sector has zero free dimensionless parameters: the carried closed-form content holds, and the full closed-form bundle of gravity-sector constants is nonempty. Explicitly, $\hbar$, the Einstein coupling $\kappa$, the RS speed $c_{\mathrm{RS}}$, the black-hole echo damping ratio, the rung phase delay, the leading black-hole entropy coefficient, the Hawking temperature, and the baryon asymmetry rung $\eta_B$ at rung $-44$ each admit closed forms fixed by Recognition Science, with no residual free dimensionless parameters.
background
Recognition Science derives physics from one functional equation and the forcing chain T0–T8. In the gravity sector the claim is stronger than uniqueness of the cost $J$: every dimensionless constant that enters gravitational observables is fixed in closed form, with no free knobs left for fitting. RS-native units already set $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$; the gravity bundle extends that discipline to echo, entropy, and Hawking data.
The module Gravity.MasterTheorem authors the conditional master statement of the quantum-gravity discovery (Track 7.A). Among its twelve clauses, one asserts zero free dimensionless parameters in the gravity sector. That clause is the conjunction of a carried closed-form content proposition (M4) and nonemptiness of the GravitySectorConstantsClosedForm bundle from Gravity.ZeroFreeParameters.
Upstream, gravitySectorConstantsClosedForm supplies the individual closed-form certificates ($\hbar$, Einstein $\kappa$, $c_{\mathrm{RS}}$, echo damping ratio, rung phase delay, leading entropy $S_{\mathrm{lead}}$, Hawking temperature, and $\eta_B$ at rung $-44$). The present theorem inhabits the master-theorem clause from that bundle.
proof idea
Term-mode proof with no tactics. The goal is the conjunction of the carried closed-form content proposition and nonemptiness of the gravity-sector closed-form bundle.
The first conjunct is assembled as an eight-field structure whose components are the individual closed-form theorems from Gravity.ZeroFreeParameters.gravitySectorConstantsClosedForm: closed forms for $\hbar$, Einstein $\kappa$, $c_{\mathrm{RS}}$, echo damping ratio, rung phase delay, leading entropy, Hawking temperature, and the baryon rung identity $\eta_B=-44$.
The second conjunct is discharged directly by the existing sector-level certificate Gravity.ZeroFreeParameters.gravity_sector_zero_free_parameters. The whole proof is structure packing of already-proved closed forms.
why it matters
This is the Track 5.B / Session 96 anchor that discharges one of the eight CLOSED clauses of the quantum-gravity master statement. Downstream, rs_quantum_gravity_master_conditional consumes it so that, under the five still-open hypothesis inputs (Regge→EH continuum and Bianchi, unconditional amplitude linearity, Page curve, PTA stochastic GW distinct from inflation, strong-field tests distinct from GR), the full twelve-clause master statement holds.
It also feeds MasterTheoremNonCircularityAudit.closed_certs_hold, which audits that the closed certificate clauses are inhabited without circularity.
In framework terms the result aligns gravity observables with the same zero-parameter discipline as the rest of the monolith (φ-ladder masses, eight-tick octave, D=3). It does not by itself close the five open tracks; those remain hypothesis inputs to the conditional master theorem.
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