IndisputableMonolith.Gravity.RS_GRV_Structural_005
Module packaging a structural certificate for RS gravity claim 005: a domain cost functional built from the RS J-cost, its nonnegativity, and a strictly positive canonical threshold. Gravity and ledger auditors cite it when they need a named, inhabitable certificate rather than ad-hoc inequalities. The module is mostly definitions plus short positivity and evaluation lemmas over Constants and Cost.
claimDefine a domain cost $C_{\mathrm{dom}}$ from the RS cost $J$, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality cases, and fix a canonical threshold $\theta>0$. Package these as an inhabitable structural certificate for RS-GRV claim 005.
background
Recognition Science gravity work treats curvature and mass defects as ledger costs on the $\varphi$-ladder, with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law (T5). The Cost import supplies that $J$; Constants supplies the RS-native units and time quantum $\tau_0=1$ tick.
This module sits in the Gravity domain and introduces a domain-level cost assembled from $J$, together with a fixed positive threshold used as a structural cut. The certificate type bundles the cost, the threshold, and the elementary positivity facts so downstream gravity lemmas can depend on one named object instead of repeating local inequalities.
No full field equation is proved here; the setting is the structural layer that precedes dynamical GRV identities.
proof idea
Definition-heavy module. domainCost is introduced from the imported $J$-cost; domainCost_at_eq and domainCost_nonneg are short algebraic or order facts. canonicalThreshold is a concrete positive constant with canonicalThreshold_pos. The certificate record RSGRVStructural005Cert packages those fields; cert and cert_inhabited witness that the record is realizable. No deep tactic proof: positivity and evaluation reduce to Cost/Constants lemmas.
why it matters in Recognition Science
Gives Gravity a stable, citable structural 005 certificate (domain cost, nonnegativity, positive threshold) rather than scattered local defs. Upstream edges are only Constants and Cost, so the module is a thin gravity-facing wrapper on the forced $J$-cost and RS units. Used_by is empty in the graph snapshot, so it is presently a leaf certificate: intended for later GRV structural or comparison theorems that need a named inhabitable pack. Aligns with the RS pattern of discharging gravity claims via certificates once T5 $J$-uniqueness and the $\varphi$ ladder are in place.
scope and limits
- Does not derive Einstein equations or any dynamical GR field equation.
- Does not fix numerical GRV observables beyond the packaged threshold.
- Does not prove uniqueness of the domain cost among all possible gravity costs.
- Does not connect to eight-tick, $D=3$, or $\alpha$ band results.
- Does not supply a used_by consumer theorem in the current graph.