IndisputableMonolith.Cosmology.RS_Cosmo_Module_008
Cosmology certificate module that packages a nonnegative domain cost functional and a strictly positive canonical threshold for RS cosmology bookkeeping. Researchers tracking the RS_Cosmo_008 certification chain cite it for the inhabited certificate bundle. The module is mostly definitional: cost nonnegativity and threshold positivity are recorded as short lemmas feeding a single certificate structure.
claimDefine a domain cost $C_{\mathrm{dom}}$ on the RS cost substrate, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality cases, introduce a canonical threshold $\theta_*>0$, and bundle these into an inhabited RS cosmology certificate $\mathrm{RSCosmo008Cert}$.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the Cost layer. Cosmology modules lift that scalar cost into domain-level bookkeeping: how much recognition debt a spatial or causal domain carries relative to the eight-tick and $\phi$-ladder structure.
This file sits in the Cosmology domain and imports only Constants (for the RS-native tick $\tau_0=1$) and Cost. The local objects are a domain cost functional, its nonnegativity, a canonical positive threshold against which domains are compared, and a certificate record that packages those facts for downstream cosmology claims.
No forcing-chain step (T0–T8) is proved here; the module assumes the Cost and Constants substrate and exposes a thin certification interface labeled RS_Cosmo_Module_008.
proof idea
Definition-first module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short positivity lemmas on top of the Cost substrate. domainCost_at_eq records an evaluation identity. The certificate type RSCosmo008Cert aggregates those fields, and cert / cert_inhabited supply a concrete inhabitant so downstream files can assume the bundle without re-proving the inequalities.
why it matters in Recognition Science
Gives the Cosmology lane a named, inhabited certificate for module 008: nonnegative domain cost plus a positive canonical threshold. Downstream cosmology developments that need a stable cost/threshold interface can depend on RSCosmo008Cert rather than re-deriving positivity from Cost. Used_by is currently empty in the mirror graph, so this file is a leaf certificate package rather than a step inside T0–T8 or the mass-ladder theorems. It keeps RS cosmology claims aligned with the same J-cost and $\tau_0$ conventions used elsewhere in the monolith.
scope and limits
- Does not derive domain cost from the Recognition Composition Law or J-uniqueness (T5).
- Does not fix numerical cosmological parameters (Hubble, density fractions, alpha).
- Does not prove eight-tick, D=3, or phi-ladder forcing (T6–T8).
- Does not supply dynamics, Friedmann equations, or observational fits.
- Does not discharge broader cosmology certificates beyond the 008 bundle.