IndisputableMonolith.Gravity.RS_GRV_Structural_008
Gravity-side structural certificate module that packages a domain cost, its nonnegativity and evaluation identity, and a strictly positive canonical threshold into an inhabited RS-GRV-008 certificate. Gravity authors cite it when a later GRV lemma needs a named, reusable cost-threshold pair rather than ad-hoc constants. The module is mostly definitions plus short positivity and equality lemmas; the certificate is discharged by inhabitation.
claimThe module introduces a domain cost $C$ (built from the RS $J$-cost), proves $C \ge 0$ and an evaluation identity for $C$ at a reference point, defines a canonical threshold $\theta > 0$, and packages these into an inhabited structural certificate $\mathrm{RSGRVStructural008Cert}$.
background
Recognition Science gravity work sits on the same cost calculus as the rest of the monolith. The Cost import supplies the unique $J$-cost $J(x) = (x + x^{-1})/2 - 1$ forced by the Recognition Composition Law; Constants supplies the RS-native tick and related units. In this gravity slice the cost is specialized to a domain cost: a nonnegative functional used to measure structural mismatch or residual in the GRV (gravity) setting.
The module also fixes a canonical threshold, a strictly positive scalar against which the domain cost is compared. That pair (cost, threshold) is the minimal data a later structural lemma needs in order to state a gap, a bound, or a regime split without reopening the definition of $J$.
Local theoretical setting: a thin Gravity certificate layer, not a full field equation. It does not derive Einstein equations or fix $G$; it only freezes the cost-threshold interface labeled Structural 008.
proof idea
Definition-heavy module. domainCost is introduced and tied to the imported cost; domainCost_at_eq is an evaluation identity; domainCost_nonneg is nonnegativity inherited from $J$. canonicalThreshold is a named positive constant with canonicalThreshold_pos. The bundle RSGRVStructural008Cert collects those facts; cert and cert_inhabited show the certificate type is inhabited. No deep tactic proof: short algebraic or library lemmas plus structure inhabitation.
why it matters in Recognition Science
Gives the Gravity stack a stable Structural-008 handle: a named domain cost, its nonnegativity, and a positive canonical threshold, so downstream GRV arguments can cite one certificate instead of re-proving cost facts. Imports only Constants and Cost, so it sits early in the gravity dependency cone and does not itself depend on curvature or metric lemmas. No used_by edges are recorded in the mirror graph yet; the intended consumers are later RS gravity structural or phenomenological modules that need a frozen cost-threshold pair. Framework landmarks touched only indirectly: the $J$-cost uniqueness (T5) and the Cost layer that every mass and coupling ladder also uses.
scope and limits
- Does not derive Einstein field equations or any metric dynamics.
- Does not fix numerical $G$, $c$, or $\hbar$ beyond what Constants already provides.
- Does not prove uniqueness of the canonical threshold among all positive scalars.
- Does not establish observational gravity bounds or solar-system tests.
- Does not close later GRV structural numbers beyond the 008 certificate interface.