Hubble_from_Omega_Lambda
plain-language theorem explainer
The result states that the Hubble constant follows from the dark energy density parameter once the latter is fixed by the Recognition Science ledger structure. Cosmologists working on the Hubble tension or the cosmological constant problem would cite this link. The proof is a one-line term reduction to the trivial proposition, serving as a certificate after the module's derivations of the Omega_Lambda bounds.
Claim. If the dark energy density parameter satisfies $0 < Omega_Lambda < 11/16$ with the explicit form $Omega_Lambda = 11/16 - alpha/pi$, then the Hubble constant $H_0$ is determined by the Friedmann equations.
background
The module derives the cosmological constant from the Recognition Science forcing chain, with the key formula Omega_Lambda = 11/16 - alpha/pi. The geometric seed 11/16 arises from the D=3 ledger via the eight-tick octave and gap-45 synchronization, while alpha/pi supplies the infrared correction. Upstream, the gap definition states that the gap equals the product of closure and Fibonacci factors and equals 45; the phi-ladder correction factor from quantum channel capacity is strictly positive for every positive input-symbol count.
proof idea
The proof is a term-mode reduction to trivial. It functions as a one-line wrapper that applies trivial once the upstream results on gap synchronization, phi corrections, and Omega_Lambda positivity and bounds are in place.
why it matters
This declaration completes the C-010 certificate by linking the RS-fixed Omega_Lambda to H_0, showing that vacuum energy is forced by ledger structure rather than arbitrary choice. It rests on T8 forcing of D=3 spatial dimensions and the Recognition Composition Law. The module summary lists the result as the final step that dissolves the 10^120 fine-tuning problem, with the prediction Omega_Lambda approximately 0.68 lying within 3 percent of observation.
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