IndisputableMonolith.Gravity.RS_GRV_Structural_009
Structural certificate package for RS gravity claim 009: a nonnegative domain cost built from the RS J-cost, a positive canonical threshold, and an inhabited certificate record tying them together. Gravity and constants auditors cite it when wiring cost-threshold inequalities into GRV structural lemmas. The module is mostly definitions plus elementary positivity and evaluation equalities over the Cost and Constants imports.
claimThe module introduces a domain cost $C$ (built from the RS cost $J$), proves $C \ge 0$ and an evaluation identity at a designated point, defines a canonical threshold $\tau_*>0$, and packages these into an inhabited structural certificate for RS gravity claim 009.
background
Recognition Science gravity work reduces structural checks to comparisons between a recognition cost and a fixed threshold. The Cost import supplies the unique $J$-cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$, which is nonnegative on $\mathbb{R}_{>0}$ and vanishes only at $x=1$. Constants supplies the RS-native units and fixed points (including $\varphi$) used to pin numerical scales.
This module sits in the Gravity domain as a narrow structural layer: it does not derive field equations. It defines a domain-level cost functional from $J$, records that the cost is nonnegative, fixes a canonical positive threshold, and wraps the pair into a certificate type so downstream GRV lemmas can assume a single inhabited record rather than re-proving the elementary inequalities.
proof idea
Definition-first module. The domain cost is introduced as a thin wrapper around the imported $J$-cost; an evaluation lemma records equality at a chosen argument by unfolding. Nonnegativity is inherited from the corresponding Cost lemma. The canonical threshold is a positive constant (positivity by direct arithmetic or Constants facts). The certificate is a structure bundling these fields; inhabitance is a constructor application assembling the proved fields. No deep tactic proof or forcing-chain step lives here.
why it matters in Recognition Science
Gives Gravity a reusable structural 009 certificate: cost nonnegativity plus a positive threshold in one inhabited record. Downstream GRV arguments can depend on the certificate rather than re-opening Cost. Within the RS stack this is scaffolding for gravity inequalities that eventually sit beside the forcing landmarks (unique $J$, $\varphi$, eight-tick period, $D=3$), not a replacement for them. The page lists no used-by edges yet, so the module is a leaf certificate ready for import by later GRV structural or comparison theorems.
scope and limits
- Does not derive Einstein equations, Newtonian limits, or any dynamical GR field content.
- Does not prove uniqueness of the domain cost beyond the imported $J$-cost facts.
- Does not fix numerical GRV observables or mass-ladder rungs.
- Does not discharge broader gravity claims outside structural certificate 009.
- Does not connect to eight-tick, $D=3$, or $\alpha$ band results in this file.