IndisputableMonolith.Astrophysics.RS_AST_Structural_007
Certificate module for Recognition Science astrophysics structural claim 007. It packages a nonnegative domain cost functional, a strictly positive canonical threshold, and an inhabited certificate record tying the two. Astrophysicists checking RS structural bounds would cite the cert. The module is mostly definitions plus elementary positivity and evaluation lemmas, not a deep derivation.
claimDefine a domain cost $C$ on the relevant astrophysical domain, prove $C \ge 0$ and an evaluation identity at equality cases, fix a canonical threshold $\theta > 0$, and package an inhabited certificate asserting the structural 007 relation between $C$ and $\theta$ in RS-native units.
background
Recognition Science measures mismatch with a cost functional descending from the unique $J$-cost forced by the Recognition Composition Law, $J(x) = (x + x^{-1})/2 - 1$. The Cost import supplies that infrastructure; Constants supplies the RS time quantum $\tau_0 = 1$ tick and related native units.
This module sits in the Astrophysics domain and isolates structural claim 007: a domain-level cost compared against a fixed positive threshold. Sibling names indicate a domain cost map, its nonnegativity, an on-equality evaluation lemma, a canonical threshold with positivity, and a certificate type with an inhabited instance.
No forcing-chain step (T0–T8) is re-proved here; the module assumes the global RS cost and constant layer and only assembles the local structural certificate.
proof idea
Definition-and-certificate module rather than a long proof script. Domain cost is introduced as a def; nonnegativity and the evaluation-at-equality fact are short lemmas. The canonical threshold is a positive constant def. The certificate record bundles those pieces; inhabitation is a one-line constructor application. No deep tactic proof is required beyond positivity and rewriting.
why it matters in Recognition Science
Gives a named, checkable certificate object for RS astrophysics structural claim 007 so downstream astrophysics developments can depend on a single inhabited cert instead of re-assembling cost and threshold facts. Used_by is currently empty in the mirror graph, so this is a leaf packaging module rather than an intermediate lemma in a longer chain. It keeps structural numerics (cost versus threshold) aligned with the RS cost layer and native constants without reopening J-uniqueness or the eight-tick octave.
scope and limits
- Does not derive the domain cost from the Recognition Composition Law or J-uniqueness.
- Does not prove observational astrophysics; only packages a structural cost-threshold certificate.
- Does not fix numerical mass, alpha, or cosmological parameters beyond the imported constants layer.
- Does not assert used-by consumers; the mirror currently lists none.
- Does not discharge unrelated RS_AST structural claim numbers.