IndisputableMonolith.Cosmology.HubbleConstantPrecise2FromJCost
Module packaging a precise Hubble-constant certificate from the RS J-cost. Cosmology consumers cite the certificate, domain-cost bounds, and canonical threshold. Structure is definitional: evaluate J on a domain argument, prove nonnegativity and threshold positivity, then inhabit a cert record.
claimIntroduces a domain cost built from the J-cost $J(x)=(x+x^{-1})/2-1$, a canonical positive threshold, and a certificate structure $\mathrm{HubblePrecise2Cert}$ witnessing a second-precision Hubble relation relative to that threshold, together with nonnegativity and positivity lemmas and an inhabited cert instance.
background
Recognition Science forces a unique nonnegative cost $J$ via the Recognition Composition Law and the T5 uniqueness step; cosmologically relevant scales are read off evaluations of $J$ in RS-native units (with time quantum $\tau_0=1$ tick from Constants).
This Cosmology module imports Cost and Constants and defines a domain-cost wrapper around $J$, equality and nonnegativity facts for that wrapper, and a canonical threshold used as the cutoff in a precise Hubble certificate. The local objects are bookkeeping for an $H_0$ claim stated relative to $J$, not a re-derivation of FLRW dynamics.
proof idea
Definition module with thin lemmas. domainCost applies $J$; domainCost_at_eq and domainCost_nonneg are direct consequences of the Cost API. canonicalThreshold fixes the cutoff; canonicalThreshold_pos records positivity. HubblePrecise2Cert is the certificate bundle; cert and cert_inhabited supply a concrete inhabited instance. No forcing-chain argument is proved here.
why it matters in Recognition Science
Exposes a J-cost-native precise Hubble certificate for the RS cosmology stack, so downstream work can cite a structured cert rather than an ad-hoc numerical claim. No used_by edges are recorded yet, so the module is presently a leaf surface: importers would reach for HubblePrecise2Cert or cert when closing observational-consistency obligations on $H_0$. Anchors to T5 J-uniqueness through the Cost import; does not itself touch T7/T8 or the alpha band.
scope and limits
- Does not derive a numerical H0 value from the forcing chain alone.
- Does not resolve or fit the observational Hubble tension.
- Does not prove FLRW field equations or dark-energy dynamics.
- Does not connect eight-tick cadence or D=3 forcing into the cert.
- Does not claim the certificate is the unique possible H0 packaging.