IndisputableMonolith.Cosmology.Cosmology
Module collecting Recognition Science cosmology primitives: a domain cost functional, its nonnegativity and evaluation identities, a positive canonical threshold, and an EOS Deep-4 certificate type with an inhabited witness. Cosmology and RS-constants readers cite it for the cost and threshold layer under equation-of-state claims. Content is mostly definitions and elementary lemmas over the Cost and Constants imports.
claimDefines a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and pointwise evaluation identities, introduces a canonical threshold $\theta_*>0$, and packages an EOS Deep-4 certificate type that is inhabited.
background
Recognition Science builds cosmology on the same cost calculus used elsewhere in the monolith. The Cost import supplies the J-cost infrastructure; Constants supplies RS-native units, including the fundamental time quantum $\tau_0=1$ tick.
This module sits in the Cosmology domain. Sibling declarations introduce a domain cost (with equality-at-a-point and nonnegativity lemmas), a strictly positive canonical threshold, and an EOS Deep-4 certificate bundle together with a witness that the certificate type is inhabited.
No forcing-chain step (T0–T8) is restated here; the module is a local interface layer that packages cost and threshold data for later cosmological claims.
proof idea
Definition-and-lemma module rather than a single theorem. Domain cost is introduced as a definition; nonnegativity and evaluation identities are short algebraic or rewriting lemmas over Cost. The canonical threshold is a positive constant (positivity lemma). EOSDeep4Cert is a structure or Prop bundle; cert and cert_inhabited supply a concrete inhabitant. No deep tactic scripts are indicated by the sibling list.
why it matters in Recognition Science
Gives Cosmology a named cost, threshold, and EOS Deep-4 certificate surface so later RS cosmology results can cite nonnegativity and a positive threshold without reopening Cost. Downstream use edges are empty in the graph snapshot, so this module is presently a leaf interface rather than a proved parent theorem. It does not itself close T5–T8 or the mass ladder; it only stages domain-cost and EOS certificate language for that program.
scope and limits
- Does not prove a full cosmological model or FLRW dynamics.
- Does not derive $c$, $\hbar$, $G$, or $\alpha$ from first principles.
- Does not establish the eight-tick octave or $D=3$ (T7–T8).
- Does not claim observational fits or parameter posteriors.
- Does not discharge global forcing-chain uniqueness beyond local cost lemmas.