IndisputableMonolith.Astrophysics.RS_Astro_Module_001
First certificate module for Recognition Science astrophysics. It packages a domain cost functional (built from the RS J-cost), its nonnegativity, a positive canonical threshold, and an inhabited certificate record. Astrophysicists working in the RS stack cite it as the typed entry point for Module 001 bounds. The file is mostly definitions plus short positivity and equality lemmas, not a deep derivation.
claimDefine a domain cost $C_{\mathrm{dom}}$ on the RS cost layer, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fix a canonical threshold $\theta_*>0$, and package these facts into an inhabited certificate $\mathsf{RSAstro001Cert}$.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. The imported Cost layer exposes that functional; Constants supplies the RS-native tick $\tau_0=1$.
This module sits in the Astrophysics domain and introduces a domain-level cost built on that infrastructure, together with a positive numerical threshold intended as a comparison scale for later astro bounds. Sibling names indicate an equality lemma for evaluation at a point, nonnegativity of the domain cost, positivity of the threshold, and a certificate record that bundles the claims.
No external paper proposition is attached in the supplied docs; the local setting is a thin, certificate-first interface rather than a full galactic or cosmological derivation.
proof idea
Definition-and-certificate module. The domain cost and canonical threshold are introduced as defs; short lemmas record evaluation equality, nonnegativity of the cost, and positivity of the threshold (likely by unfolding to known J-cost or constant facts from the Cost and Constants imports). The certificate type collects those properties, and an inhabitation proof assembles the pieces into a single record. No multi-step analytic argument appears at module scope.
why it matters in Recognition Science
Gives the Astrophysics slice a typed Module-001 certificate so downstream RS astro developments can depend on a single inhabited bundle rather than ad-hoc cost and threshold hypotheses. It does not yet feed named parent theorems in the graph (used_by is empty); its role is infrastructural: lock the cost/threshold interface early, aligned with the J-cost and RS-native units from the foundation. Later mass-ladder, eight-tick, or galactic-scale results can import this cert once concrete bounds are proved against $\theta_*$.
scope and limits
- Does not derive galactic rotation curves, dark-matter replacements, or mass-ladder spectra.
- Does not prove uniqueness of the domain cost beyond the packaged lemmas.
- Does not connect the threshold to T7 eight-tick or T8 D=3 forcing steps.
- Does not supply numerical astrophysical fits or observational comparisons.
- Does not discharge any sorry outside the listed sibling lemmas.