IndisputableMonolith.Cosmology.RS_COS_Structural_005
Structural cosmology module packaging a domain-level J-cost, a positive canonical threshold, and an inhabited certificate that the structural claim RS-COS-005 holds. Cosmologists working in the RS ledger would cite the certificate and the nonnegativity/positivity lemmas. The module is mostly definitional: cost and threshold are closed-form, then wrapped in a cert record with an inhabitation proof.
claimDefine a domain cost $C(\cdot)$ built from the RS $J$-cost, a canonical threshold $\theta>0$, and a certificate record asserting the RS-COS structural claim 005 (domain cost controlled by $\theta$). The module proves $C\ge 0$, $\theta>0$, and that the certificate type is inhabited.
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law and the T5 uniqueness step. Cosmology modules lift that cost from single ratios to domain-scale aggregates that track structural imbalance on the ledger.
This file sits in the Cosmology domain and imports only Constants (RS-native units, including the tick $\tau_0$) and Cost (the $J$-cost API). Sibling declarations introduce domainCost (the domain aggregate), equality at evaluation points, nonnegativity, a canonicalThreshold with a positivity lemma, and a certificate bundle RSCOSStructural005Cert with an inhabitation witness.
The local setting is structural rather than dynamical: no FLRW evolution or observational likelihood is claimed here, only the cost/threshold scaffolding needed to state claim 005 cleanly.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as closed defs; domainCost_at_eq is an evaluation identity; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity arguments from the Cost layer. The certificate type RSCOSStructural005Cert packages those facts, and cert / cert_inhabited supply a concrete inhabitant so downstream code can treat claim 005 as discharged at the structural level.
why it matters in Recognition Science
Gives Cosmology a named structural certificate (RS-COS-005) rather than an ad-hoc inequality. Downstream pages can import the inhabited cert instead of re-proving domain-cost nonnegativity or threshold positivity. In the broader RS chain this is bookkeeping under the forced $J$-cost (T5) and RS-native constants, not a new forcing step like T6--T8. No used_by edges are recorded yet, so the module is a leaf certificate ready for later cosmology assembly theorems.
scope and limits
- Does not derive observational cosmology constraints or fit data.
- Does not prove dynamical evolution equations (Friedmann, Boltzmann, etc.).
- Does not fix numerical values of cosmological parameters beyond the threshold positivity claim.
- Does not discharge other RS-COS structural numbers; only claim 005 is packaged here.
- Does not extend the T0--T8 forcing chain; it consumes Cost/Constants only.