IndisputableMonolith.Cosmology.RS_Cosmo_Module_009
Cosmology module 009 packages a domain cost functional, its nonnegativity, and a strictly positive canonical threshold, then wraps them in an inhabited certificate. Cosmologists working in the RS ledger would cite it when a cost bound or threshold gate is needed on a cosmological domain. The module is mostly definitional: equalities and sign lemmas, plus a trivial certificate inhabitant.
claimOn a cosmological domain one has a cost $C$ with $C\ge 0$, a canonical threshold $\theta>0$, and a certificate bundle asserting these facts (inhabited).
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). Constants supplies the RS-native tick $\tau_0=1$ and the golden-ratio ladder used throughout the monolith.
This module sits in the Cosmology domain. It introduces a domain-level cost (a specialization or evaluation of the global cost on a cosmological domain) together with a canonical threshold meant as a positive gate for cosmological recognition events. Sibling lemmas record evaluation identities and the sign facts $C\ge 0$ and $\theta>0$.
The certificate type bundles those facts so downstream cosmology developments can assume a single inhabited package rather than re-proving nonnegativity and positivity at each use site.
proof idea
Definition-heavy module, not a deep proof development. domainCost and canonicalThreshold are introduced as defs; domainCost_at_eq is an evaluation identity; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity lemmas drawing on Cost and Constants. RSCosmo009Cert (with cert and cert_inhabited) is a structure-plus-inhabitant wrapper that packages the above into one certificate object.
why it matters in Recognition Science
Gives Cosmology a reusable cost-and-threshold certificate (module 009) so later RS cosmology arguments can cite one inhabited bundle instead of ad-hoc sign proofs. No downstream edges are recorded yet, so it currently acts as a leaf certificate in the graph: a local hygiene package rather than a step in the T0–T8 forcing chain. It ties cosmology bookkeeping to the Cost layer and the RS tick from Constants, keeping domain costs aligned with the global J-cost convention.
scope and limits
- Does not derive Friedmann or FLRW dynamics from RS axioms.
- Does not fix numerical cosmological parameters (H0, Omega, w).
- Does not prove uniqueness of the domain cost beyond the imported Cost layer.
- Does not connect the threshold to eight-tick or D=3 forcing steps.
- Does not supply observational fits or data-facing predictions.