IndisputableMonolith.Gravity.RS_GRV_Structural_002
Gravity-side structural module that packages a domain cost, a positive canonical threshold, and an inhabited certificate for RS-GRV structural claim 002. Gravity and ledger auditors cite it when they need a nonnegativity-checked cost gate rather than a dynamical field equation. The module is mostly definitions plus elementary positivity and equality lemmas, closed by a certificate inhabitant.
claimIntroduce a domain cost $C$ on the RS gravity side, prove $C \ge 0$ and the stated equality case, fix a canonical threshold $\theta > 0$, and exhibit an inhabited structural certificate bundling these facts for RS-GRV claim 002.
background
Recognition Science treats gravity as a recognition-cost phenomenon on the same ledger that forces $J$, $\varphi$, the eight-tick octave, and $D=3$. The Cost import supplies the $J$-cost calculus; Constants supplies the RS-native tick $\tau_0=1$. This module sits in the Gravity domain and does not re-derive the forcing chain; it only installs a local structural gate.
The named objects are a domain cost (a real-valued cost assigned to gravity-side domains), its nonnegativity and an equality identity at a reference configuration, and a canonical threshold required to be strictly positive. Those pieces are then wrapped as a single certificate type whose inhabitant records that the structural hypotheses for claim 002 are available in Lean.
No curvature dynamics or Newtonian limit is stated here. The setting is purely the cost-threshold interface that later gravity lemmas can assume without reopening the Cost library.
proof idea
Definition-first module. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short algebraic or Cost-library appeals; the equality lemma is a direct unfolding. The certificate is a structure (or Prop bundle) assembled from those facts, and inhabitation is a constructor application. No deep tactic script and no sorry path are indicated by the sibling list.
why it matters in Recognition Science
Gives the Gravity tree a reusable structural certificate for RS-GRV claim 002 so downstream gravity results can depend on a single inhabited bundle rather than ad-hoc cost inequalities. Used_by is empty in the current graph, so this is a leaf provider: it closes a local scaffolding slot rather than feeding a named parent theorem yet. In the broader RS picture it keeps gravity aligned with the $J$-cost and $\varphi$-native unit conventions without touching T5–T8 forcing, the RCL identity, or the $\alpha$ band.
scope and limits
- Does not derive Einstein equations or any curvature field equation.
- Does not fix numerical GR constants beyond the Cost/Constants imports.
- Does not prove uniqueness of the domain cost or threshold.
- Does not connect to mass-ladder or eight-tick dynamics.
- Does not supply observational fits or post-Newtonian expansions.