IndisputableMonolith.Cosmology.RS_COS_Structural_002
Module packaging RS cosmology structural claim 002: a domain cost functional, its nonnegativity and evaluation identity, a positive canonical threshold, and an inhabited certificate bundle. Cosmology auditors cite it when checking domain-cost bounds against the RS cost layer. The module is mostly definitions plus elementary positivity and equality lemmas, closed by a cert record.
claimDefine a domain cost $C_{\mathrm{dom}}$ (from the RS $J$-cost layer), prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at a reference point, fix a canonical threshold $\theta>0$, and package these into an inhabited structural certificate for RS-COS-002.
background
Recognition Science cosmology modules sit on the shared cost and constants layers. The cost import supplies the RS $J$-cost (the unique symmetric cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). Constants supply RS-native units, including the fundamental tick $\tau_0$.
This file is the structural-002 slice of that stack. It introduces a domain-level cost built from that $J$-layer, a canonical numerical threshold against which domain costs are compared, and a small certificate type that bundles the structural facts the claim needs. No forcing-chain step (T5--T8) is re-proved here; the module assumes the cost and constant infrastructure already in place.
proof idea
Definition-heavy module, not a single deep theorem. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are elementary nonnegativity/positivity facts; domainCost_at_eq is an evaluation identity. The certificate record RSCOSStructural002Cert (with cert and cert_inhabited) packages those facts so downstream cosmology developments can assume the structural bundle in one hypothesis rather than re-importing each lemma.
why it matters in Recognition Science
Gives cosmology a named structural certificate (RS-COS-002) tying domain cost to a positive canonical threshold inside the RS cost framework. Downstream used-by edges are empty in the current graph, so this is a leaf packaging module: it standardizes the claim interface rather than feeding a named parent theorem yet. It sits under the Cosmology domain and depends only on Constants and Cost, keeping the structural statement portable for later expansion, curvature, or horizon arguments that need a certified domain-cost bound.
scope and limits
- Does not derive domain cost from the T0--T8 forcing chain inside this file.
- Does not prove observational cosmology constraints or fit data.
- Does not fix numerical values of $c$, $\hbar$, $G$, or $\alpha$ beyond Cost/Constants imports.
- Does not assert uniqueness of the canonical threshold among all possible cutoffs.
- Does not supply downstream consumers; used_by is currently empty.