IndisputableMonolith.Astrophysics.RS_AST_Structural_005
Structural certificate module for RS astrophysics claim 005. It packages a domain cost functional, a canonical positive threshold, elementary nonnegativity and evaluation lemmas, and an inhabited certificate record. Astrophysicists working the RS structural ladder would cite the cert bundle when wiring claim 005 into larger mass or morphology arguments. The module is mostly definitional scaffolding with short positivity proofs.
claimThe module introduces a 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 structural certificate $\mathsf{Cert}_{005}$ for RS astrophysics claim 005.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the Cost layer, forced uniquely by the Recognition Composition Law and the T5 step of the unified forcing chain. Astrophysical structural claims lift that cost to domain-level functionals that score how far a configuration sits from an RS-native morphology or mass ladder.
This module sits in the Astrophysics domain and imports only Constants (RS-native units, including the tick $\tau_0=1$) and Cost. Sibling declarations name a domain cost, its pointwise evaluation and nonnegativity, a canonical threshold with positivity, and a certificate record RSASTStructural005Cert together with an inhabited instance. No external physics hypotheses are imported beyond those two foundations.
proof idea
Definition-first module. The domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short algebraic or Cost-layer lemmas; evaluation-at-a-point is an equality lemma. The certificate is a structure bundling those facts, discharged by an inhabited instance. There is no deep tactic proof: the argument is packaging plus elementary Cost inequalities.
why it matters in Recognition Science
Gives claim 005 a machine-checkable structural handle inside the RS astrophysics stack: a nonnegative domain cost, a positive threshold, and a cert record that downstream morphology or ladder arguments can require as a hypothesis. Used_by is currently empty, so this is a leaf certificate rather than an intermediate lemma. It aligns with the broader RS pattern of turning each structural assertion into an inhabited cert whose numeric content ultimately traces to J-cost, $\varphi$, and the eight-tick octave, without yet closing any open mass-formula or $\alpha$-band obligation.
scope and limits
- Does not derive domain cost from the J-uniqueness theorem T5.
- Does not prove any observational astrophysics fit or mass-ladder identity.
- Does not fix numerical values of c, hbar, G, or alpha.
- Does not discharge other RS_AST structural claims beyond 005.
- Does not assert uniqueness of the canonical threshold.