IndisputableMonolith.Astrophysics.RS_Astro_Module_011
Astrophysics module that packages a domain cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold into a single inhabited certificate. Observers of RS galactic or stellar scaling arguments would cite the certificate as a typed bundle of cost bounds. The module is mostly definitional: cost is specialized from the global J-cost, then wrapped with positivity lemmas into RSAstro011Cert.
claimDefine a domain cost $C_{\mathrm{dom}}$ on the relevant astrophysical scale, prove $C_{\mathrm{dom}}\ge 0$ and the pointwise evaluation identity, fix a canonical threshold $\theta>0$, and package these into an inhabited certificate object for RS astrophysics module 011.
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 Cost import supplies that functional and its elementary inequalities; Constants supplies the RS-native tick $\tau_0=1$ used to anchor dimensionless ratios.
This module sits in the astrophysics layer. It specializes the global cost to a domain cost $C_{\mathrm{dom}}$ appropriate to the 011 scaling problem (stellar or galactic recognition thresholds), records that the cost is nonnegative, and introduces a strictly positive canonical threshold against which domain cost is compared. The certificate type simply bundles those facts so downstream astrophysics lemmas can assume one inhabited package rather than a scatter of hypotheses.
proof idea
Definition-first module. domainCost is introduced as a specialization of the imported Cost functional; domainCost_at_eq and domainCost_nonneg are short algebraic or rewriting lemmas off that definition. canonicalThreshold is a positive constant (canonicalThreshold_pos). RSAstro011Cert is a structure packing those pieces; cert and cert_inhabited discharge inhabitation by assembling the already-proved fields. No deep tactic proof; the work is naming and packaging.
why it matters in Recognition Science
Gives the astrophysics stack a single typed certificate for module 011 cost-and-threshold facts, so later galactic or stellar recognition bounds can import one object instead of re-proving nonnegativity and positivity. Used_by is presently empty in the mirror graph, so this is a leaf packaging layer rather than a parent of named theorems. It sits downstream of Cost and Constants and upstream of any future RS astrophysics claims that need a canonical cost threshold on the phi-ladder or eight-tick timing skeleton. Does not itself force D=3, phi, or the alpha band; it only localizes cost data for astrophysical use.
scope and limits
- Does not derive domainCost from first principles beyond the imported Cost functional.
- Does not prove numerical mass, luminosity, or rotation-curve formulae.
- Does not force phi, eight-tick structure, or D=3 inside this module.
- Does not supply observational fits or error bars; only formal cost and threshold packaging.
- Does not list downstream consumers; used_by is empty in the current graph.