IndisputableMonolith.Cosmology.RS_Cosmo_Module_001
First cosmology module in the RS stack: it defines a domain cost on the cosmology sector, records nonnegativity, and fixes a strictly positive canonical threshold. These facts are bundled into an inhabited certificate object for downstream use. Cosmologists citing RS baseline cost structure would start here. The module is mostly definitional, with short positivity and equality lemmas and a cert pack.
claimDefine a cosmology domain cost $C_{\mathrm{dom}}$, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fix a canonical threshold $\theta>0$, and package the pair into an inhabited certificate for RS cosmology module 001.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique symmetric cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). Constants supplies the RS-native tick $\tau_0=1$. Cosmology modules sit on top of that cost/tick substrate rather than introducing a separate action principle.
This file is the entry point for the cosmology domain. Sibling names indicate a domain-level cost functional, its pointwise evaluation identity, nonnegativity, and a canonical positive threshold. The threshold is the gate against which cosmological cost increments are later compared (analogous to other RS sector thresholds such as the Berry creation scale $\phi^{-1}$).
The certificate bundle (RSCosmo001Cert, cert, cert_inhabited) is the module's export surface: a single inhabited record that downstream cosmology lemmas can assume instead of re-proving the baseline inequalities.
proof idea
Definition module with thin lemmas, not a deep derivation. domainCost is introduced as the sector cost; domainCost_at_eq is an evaluation/unfolding identity; domainCost_nonneg is the nonnegativity claim inherited from the Cost layer's J-properties. canonicalThreshold is a fixed positive real; canonicalThreshold_pos is the positivity proof. RSCosmo001Cert packages those facts, and cert / cert_inhabited witness that the certificate type is inhabited. No multi-step forcing argument lives here.
why it matters in Recognition Science
Marks the first named cosmology module in the monolith (RS_Cosmo_Module_001). It anchors domain cost and the canonical threshold so later cosmology results can cite one certificate rather than re-open Cost and Constants. No downstream edges are recorded yet (used_by is empty), so its role is infrastructural: close the baseline for the cosmology domain the way early forcing-chain modules close J-uniqueness and $\phi$ before physics applications. Framework landmarks it prepares for (without proving) are the eight-tick octave timing and RS-native constants used in cosmological scales. Open work sits above this file: actual cosmological identities, ladder mass links, and observational bridges are not claimed here.
scope and limits
- Does not derive Friedmann, FLRW, or any GR field equations.
- Does not fix numerical cosmological parameters (H0, Omega, dark energy).
- Does not prove uniqueness of the domain cost beyond the Cost import.
- Does not connect the threshold to observational data or surveys.
- Does not discharge later cosmology certificates or forcing-chain steps T0–T8.