IndisputableMonolith.Gravity.RS_GRV_Structural_007
Module packaging a structural gravity certificate (RS-GRV-007): a nonnegative domain cost built from the RS J-cost, a positive canonical threshold, and an inhabited certificate record tying them together. Gravity and ledger auditors cite it as a named structural gate rather than a dynamical field equation. The content is definitional plus elementary positivity and evaluation lemmas, not a deep existence proof.
claimThe module introduces a domain cost $C$ (from the RS $J$-cost), a canonical threshold $\theta>0$, and a certificate record asserting the structural RS-GRV-007 package: nonnegativity of $C$, positivity of $\theta$, and the evaluation identity relating $C$ at the distinguished point to the threshold data.
background
Recognition Science gravity work sits on the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law, imported here via the Cost module, together with RS-native constants (time quantum $\tau_0=1$ tick) from Constants.
This file is a structural gate in the Gravity domain: it names a domain-level cost functional, records that the cost is nonnegative, and fixes a positive canonical threshold against which structural comparisons are made. Sibling declarations include evaluation-at-a-point identities and an inhabited certificate type RSGRVStructural007Cert, so downstream gravity lemmas can depend on a single named package rather than ad hoc inequalities.
The setting is ledger/structural, not continuum GR: no metric field equations are stated here; the objects are cost and threshold data in RS units.
proof idea
Definition module with thin lemmas. Domain cost is defined from the imported $J$-cost; nonnegativity and the pointwise evaluation identity are short algebraic or library facts. The canonical threshold is a positive constant definition; positivity is immediate. The certificate is a structure bundling those facts, with an inhabitation witness assembling the pieces. No multi-step analytic argument.
why it matters in Recognition Science
Gives Gravity a citable structural 007 package: cost, threshold, and cert in one place. Used_by is empty in the current graph, so this is a leaf packaging node rather than a proved parent theorem. It aligns with the RS program of replacing ad hoc gravity cutoffs by $J$-cost and $\phi$-native scales (cf. forcing chain cost uniqueness and RS constants). Downstream gravity or phenomenology modules can import the inhabited cert instead of re-proving nonnegativity and threshold positivity. Does not itself close dynamical GR recovery or mass-ladder claims.
scope and limits
- Does not derive Einstein equations or continuum GR dynamics.
- Does not fix numerical GRV observables beyond the named threshold package.
- Does not prove uniqueness of the domain cost among all possible gravity costs.
- Does not connect to eight-tick, $D=3$, or alpha-band forcing steps.
- Does not supply observational falsification tests for gravity data.