IndisputableMonolith.Cosmology.HubbleTensionBound
This module supplies the RS-predicted lower bound on the late-to-early Hubble ratio H_0. Cosmologists comparing RS predictions to the Hubble tension would cite the bound when checking consistency with observed expansion rates. The module organizes the argument as a chain of definitions and supporting lemmas that establish the bound's positivity and placement inside the empirical band.
claimThe RS lower bound on the late-to-early Hubble ratio satisfies $hubbleRatioLower > 1$, with the ratio lying inside the interval delimited by $hubbleRatioLower$ and $hubbleRatioUpper$ and centered near the empirical value $empiricalCentral$.
background
Recognition Science derives cosmological quantities from the time quantum τ₀ = 1 tick supplied by the imported Constants module. The present module works in the cosmology domain and introduces the late-to-early Hubble ratio together with its RS-derived lower bound. Sibling declarations such as lower_pos and band_nontrivial then verify that this bound is positive and lies inside the observed interval.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the lower bound required by downstream consistency statements such as IsConsistentWithRS and HubbleTensionCert. It therefore closes the cosmological application of the RS forcing chain by furnishing the concrete numerical interval against which the Hubble tension can be tested.
scope and limits
- Does not derive the numerical value of H_0 itself.
- Does not incorporate supernova or CMB data sets.
- Does not address spatial curvature or dark-energy models beyond the ratio bound.