IndisputableMonolith.Cosmology.RS_COS_Structural_010
Structural cosmology module that packages a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate RSCOSStructural010Cert. Cosmology workers cite it when a ledger-side cost bound must sit above a fixed recognition threshold. The module is mostly definitions plus elementary positivity and equality lemmas over the RS cost layer.
claimDefine a domain cost $C_{\mathrm{dom}}$ (nonnegative), a canonical threshold $\theta_*>0$, and a certificate asserting the structural COS-010 relation between $C_{\mathrm{dom}}$ and $\theta_*$ in RS-native units built from the J-cost.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the Cost layer, with constants (including the tick $\tau_0$) from Constants. Cosmology structural claims rephrase large-scale ledger constraints as inequalities between aggregated domain costs and fixed thresholds, rather than as metric FLRW postulates.
This module sits in that structural track. It introduces a domain-level cost functional, records that the cost is nonnegative and stable under the stated equality cases, and fixes a positive canonical threshold against which the cost is compared. The certificate type RSCOSStructural010Cert packages those facts so downstream cosmology lemmas can assume a single inhabited witness instead of re-proving the elementary cost properties.
proof idea
Definition-and-certificate module, not a deep derivation. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity arguments from the Cost import; domainCost_at_eq records an evaluation identity. RSCOSStructural010Cert bundles the pieces, and cert_inhabited supplies a concrete inhabitant so the certificate is available as a hypothesis elsewhere.
why it matters in Recognition Science
Gives cosmology a reusable structural certificate (COS-010) tying domain cost to a canonical threshold in the RS ledger language. No downstream used_by edges are recorded yet, so the module is a leaf packaging step: it closes the local cost/threshold interface that later expansion, horizon, or void-statistics arguments can import without touching raw Cost lemmas. It does not itself force D=3, the eight-tick octave, or the alpha band; those remain upstream forcing-chain landmarks.
scope and limits
- Does not derive FLRW metrics, scale factor dynamics, or observational Hubble fits.
- Does not prove uniqueness of the canonical threshold beyond the local positivity lemma.
- Does not connect domain cost to mass-ladder rungs or alpha bounds.
- Does not supply downstream cosmology theorems; used_by is currently empty.
- Does not replace the T0–T8 forcing chain; it only packages a cost/threshold certificate.