IndisputableMonolith.Cosmology.RS_Cosmo_Module_001
First cosmology certificate module in the RS stack: it defines a domain cost on the recognition cost functional, a positive canonical threshold, and an inhabited certificate bundle RSCosmo001Cert. Cosmology auditors cite it as the typed entry point for Module 001 claims. The file is mostly definitions plus short positivity and evaluation lemmas over Cost and Constants.
claimOn the RS cost $J$, the module introduces a cosmology domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at a reference point, fixes a canonical threshold $\theta>0$, and packages these into an inhabited certificate $\mathrm{RSCosmo001Cert}$.
background
Recognition Science measures mismatch with the unique cost $J$ forced by the Recognition Composition Law (T5): $J(x)=(x+x^{-1})/2-1$. The Cost import supplies that functional; Constants supplies the RS-native tick $\tau_0=1$ and related units ($c=1$, $\hbar=\varphi^{-5}$, etc.).
This module sits in the Cosmology domain and treats Module 001 as a certificate layer rather than a full FLRW derivation. Sibling names indicate a domain-restricted cost, its nonnegativity, a positive canonical threshold, and a bundled certificate type with an inhabitation proof.
The local setting is therefore: fix the RS cost and constants, specialize a domain cost for cosmology bookkeeping, and expose a threshold that later expansion or horizon arguments can compare against.
proof idea
Definition-first module. It binds domainCost to the imported cost structure, then records an evaluation identity and a nonnegativity lemma (inherited from $J\ge 0$ on the positive reals). canonicalThreshold is a concrete positive constant; positivity is a one-line arithmetic check. RSCosmo001Cert / cert package those facts; cert_inhabited supplies a witness so downstream code can assume the certificate type is nonempty. No deep tactic proof: short wrappers over Cost and Constants.
why it matters in Recognition Science
Gives Cosmology a typed Module 001 certificate instead of free-floating constants. Downstream cosmology developments (horizon bookkeeping, threshold comparisons, domain-cost inequalities) are meant to import this bundle rather than re-derive $J$-nonnegativity or the threshold sign. In the broader RS chain it does not itself force $D=3$, the eight-tick octave, or the mass ladder; it only anchors cost-and-threshold hygiene for cosmology claims that will later sit on T5–T8 and the $\varphi$ ladder. With no used_by edges yet, it is an entry stub: the parent theorems are expected cosmology certificates that consume RSCosmo001Cert.
scope and limits
- Does not derive Friedmann equations or any FLRW metric dynamics.
- Does not fix numerical cosmological parameters beyond a canonical threshold sign.
- Does not prove uniqueness of the domain cost among all possible specializations of $J$.
- Does not connect to eight-tick, $D=3$, or mass-ladder forcing (T7–T8).
- Does not supply observational likelihoods or data fits.