omega_lambda_from_phi
plain-language theorem explainer
Cosmological-constant clause (M4) of the RS quantum-gravity master statement: Ω_Λ is fixed from φ by the Track 4.A formula and certified band, packaged with the full Track 4.A certificate. Gravity and cosmology auditors cite it as the closed dark-energy slot inside the twelve-clause master conjunction. The declaration is a definitional Prop: carried M4 content conjoined with nonemptiness of the Track 4.A master certificate.
Claim. The proposition that $\Omega_\Lambda = 11/16 - \alpha/\pi$, that $\Omega_\Lambda$ lies in the certified interval $(0.683, 0.686)$, that it is consistent with Planck 2018 at $2\sigma$, and that the baryon-asymmetry rung $-44$ is forced by $D=3$, together with the existence of a complete Track 4.A master certificate (forced $\eta_B$ rung, $\Omega_\Lambda$ formula, band, Planck consistency, and dimension route).
background
Module Gravity.MasterTheorem authors the conditional master statement of the RS quantum-gravity discovery (Track 7.A). Twelve named Props match the master-plan template; closed clauses are inhabited from existing certificates, open ones remain hypothesis inputs.
The carried M4 content asserts four facts about the derived density parameter: the exact formula $\Omega_\Lambda = 11/16 - \alpha/\pi$ (with $\alpha$ the CODATA fine-structure constant), the numerical band $(0.683, 0.686)$, Planck-2018 $2\sigma$ consistency, and the gap-from-dimension route that forces the baryon-asymmetry rung $-44$.
Upstream, Track4ACert is the five-clause Track 4.A master certificate: $\eta_B$ rung forced by $D=3$ along three convergent routes, the $\Omega_\Lambda$ formula, the band, Planck consistency, and the dimension route. Nonemptiness of that structure is the second conjunct here.
proof idea
Pure definitional conjunction, not a proved theorem. The Prop is the meet of the carried M4 content (formula, band, Planck $2\sigma$, rung $-44$ via the dimension route) with Nonempty of the Track 4.A master certificate structure. Inhabitation is deferred to the sibling theorem that packages track4ACert fields and the inhabited certificate witness.
why it matters
Fills the closed cosmological-constant slot in the twelve-clause master statement RSQuantumGravityMaster, matching master plan §4 Track 7.A verbatim. Downstream, the proven inhabitation discharges this clause inside the conditional master theorem and inside the non-circularity audit (closed_certs_hold, master_theorem_non_circularity_certificate).
Framework landmarks: the formula ties $\Omega_\Lambda$ to $\alpha$ and the eight-tick / $D=3$ forcing chain (T7–T8), with rung $-44$ forced by dimension rather than fit. Among the six closed certificate clauses, this is the dark-energy half of Track 4.A. It does not touch the five still-open hypothesis inputs (classical continuum/Bianchi, unconditional amplitude, Page curve, PTA, strong-field tests).
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