IndisputableMonolith.Astrophysics.RS_Astro_Module_010
Astrophysics certificate module packaging a domain cost functional and a positive canonical threshold for RS-native astrophysical comparisons. Researchers cite it when they need a non-negative cost on a domain together with a fixed positive cutoff. The module is definitional plus elementary positivity and equality lemmas, closed by an inhabited certificate record.
claimThe module introduces a domain cost $C$ on an astrophysical domain, proves $C \ge 0$ and an evaluation identity, fixes a canonical threshold $\tau_*>0$, and packages these facts in an inhabited certificate $\mathrm{RSAstro010Cert}$.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique symmetric cost forced by the Recognition Composition Law). Constants supplies the RS-native tick and related units. This module sits in the Astrophysics domain and specializes that cost language to a domain-level functional rather than a single-particle ladder step.
Sibling declarations define domainCost and record that it is nonnegative, together with an evaluation identity at a reference point. A separate canonicalThreshold is fixed and shown positive. These pieces are the local vocabulary for comparing astrophysical configurations against an RS cutoff without reopening the global forcing chain (T5 J-uniqueness, T6 $\varphi$).
The module does not re-derive $J$ or $\varphi$; it imports Cost and Constants and works downstream of those definitions.
proof idea
Definition module with short supporting lemmas. Domain cost is introduced by definition; nonnegativity and the evaluation identity are direct consequences of the imported Cost structure. The canonical threshold is a positive constant definition with a one-line positivity proof. The certificate record RSAstro010Cert bundles those facts; cert_inhabited exhibits a value, so the module closes as an inhabited cert rather than a deep derivation.
why it matters in Recognition Science
Gives Astrophysics a reusable, Lean-checked cost-and-threshold package so later RS astrophysics results can cite a single certificate instead of re-proving nonnegativity and positivity inline. No downstream used_by edges are recorded yet; the module is a leaf cert in the present graph. It touches the Cost layer and RS-native constants only, not the T0–T8 forcing chain, mass ladder, or $\alpha$ band. Useful wherever an astrophysical comparison needs a nonnegative domain cost and a fixed positive cutoff in RS units.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law.
- Does not fix numerical astrophysical observables or mass-ladder rungs.
- Does not prove dynamical stability or observational fits.
- Does not set D=3, the eight-tick octave, or alpha bounds.
- Does not supply downstream theorems; used_by is empty in the graph.