IndisputableMonolith.Cosmology.RS_Cosmo_Module_008
Cosmology module 008 packages a domain cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold into an inhabited certificate. Cosmologists working in the RS ledger cite it when they need a checked cost bound or threshold for domain-scale comparisons. The module is mostly definitional: cost lemmas reduce to the imported J-cost calculus, and the certificate is a structure inhabitation.
claimDefine a domain cost $C_{\mathrm{dom}}$ on the relevant cosmological domain data, prove $C_{\mathrm{dom}}\ge 0$ and the pointwise evaluation identity for $C_{\mathrm{dom}}$, fix a canonical threshold $\theta>0$, and package these facts as an inhabited certificate $\mathrm{Cert}_{008}$.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. The Cost import supplies that calculus; Constants supplies the RS-native tick $\tau_0=1$ and related units ($c=1$, $\hbar=\varphi^{-5}$, etc.).
This module sits in the Cosmology domain of the monolith. It introduces a domain-level cost $C_{\mathrm{dom}}$ built from that J-cost, records nonnegativity and an evaluation identity, and names a strictly positive canonical threshold $\theta$ against which domain costs can be compared. The certificate structure bundles those facts so downstream cosmology developments can assume a single checked package rather than re-proving the elementary cost lemmas.
proof idea
Definition-heavy module, not a deep derivation. domainCost is introduced from the imported Cost layer; domainCost_nonneg and domainCost_at_eq are short reductions to J-cost nonnegativity and evaluation. canonicalThreshold is a positive constant definition; positivity is immediate arithmetic. RSCosmo008Cert is a structure packing those fields, and cert / cert_inhabited supply a concrete inhabitant so the package is available as a hypothesis elsewhere.
why it matters in Recognition Science
Module 008 is a local ledger entry in the RS cosmology stack: it freezes a domain cost and a positive threshold into a reusable certificate. No downstream consumers are wired in the current graph (used_by is empty), so its role is infrastructural: later cosmology theorems that need a checked domain-cost bound or threshold comparison can import the certificate instead of rebuilding Cost facts. It does not itself advance T0–T8, the mass ladder, or the $\alpha$ band; it only standardizes cost bookkeeping for domain-scale cosmological statements.
scope and limits
- Does not derive Friedmann, FLRW, or any GR field equations.
- Does not fix numerical cosmological parameters (H0, Omega_m, dark energy).
- Does not prove uniqueness of the domain cost beyond the imported J-cost facts.
- Does not connect the threshold to observational survey data.
- Does not feed a recorded downstream theorem in the current dependency graph.