IndisputableMonolith.Cosmology.RS_COS_Structural_007
Cosmology structural module 007 packages a domain cost functional, its nonnegativity, and a strictly positive canonical threshold into an inhabited certificate. Cosmologists working in the RS ledger would cite it when a domain-level cost bound or threshold gate is needed. The content is mostly definitional, with short algebraic lemmas discharging the certificate fields.
claimOn the RS cost side, a domain cost $C$ is fixed together with a canonical threshold $\theta>0$. The module records $C\ge 0$ pointwise (or at the evaluation locus used by the certificate) and packages $(C,\theta)$ as an inhabited structural certificate for cosmology claim 007.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique symmetric cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). Cosmology modules lift that cost to domain-scale quantities that gate structural claims rather than dynamical evolution.
This file sits in the Cosmology domain and imports only Constants (RS-native units, including the tick $\tau_0$) and Cost. Sibling names indicate a domain cost, an evaluation identity, nonnegativity, a canonical threshold with positivity, and a certificate type RSCOSStructural007Cert with an inhabited instance.
The local setting is structural bookkeeping: fix the cost object and the numerical gate used by later cosmology arguments, then seal them in a cert so downstream developments can assume the package without re-proving the elementary inequalities.
proof idea
Definition-first module. Domain cost and the canonical threshold are introduced as defs; short lemmas record the evaluation identity, nonnegativity of the cost, and positivity of the threshold. The certificate structure bundles those fields, and inhabitation is a one-line (or short) constructor application assembling the proved lemmas. No deep forcing-chain argument lives here.
why it matters in Recognition Science
Supplies the structural cost-and-threshold package labeled RS-COS-007 for the cosmology track. Downstream used-by edges are empty in the current graph, so the module is a leaf certificate rather than an intermediate lemma in a long chain. It still matters as a named gate: any later cosmology claim that needs a nonnegative domain cost or a positive canonical threshold can import the inhabited cert instead of re-deriving elementary Cost facts. Ties to the broader RS cost layer (J uniqueness / RCL) only by import, not by re-proving T5.
scope and limits
- Does not derive dynamical FLRW or perturbation equations.
- Does not fix numerical cosmological parameters beyond the named threshold object.
- Does not prove J-uniqueness or the forcing chain T0–T8.
- Does not assert observational fits; only structural cost and threshold facts.
- Does not currently feed recorded downstream theorems in the dependency graph.