IndisputableMonolith.Gravity.RS_GRV_Structural_001
Structural certificate module for Recognition Science gravity (GRV-001). It packages a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate record tying those facts together. Gravity and ledger-cost authors cite it when they need a named, checkable structural witness rather than an ad-hoc inequality. The module is mostly definitions plus elementary nonnegativity and positivity lemmas.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, a canonical threshold $\theta>0$, and an inhabited structural certificate $\mathrm{Cert}_{001}$ bundling those facts for RS gravity.
background
Recognition Science gravity sits on the same cost calculus as the rest of the monolith: the $J$-cost from the Cost import and the RS-native constants (time quantum $\tau_0=1$ tick, and the golden-ratio ladder quantities) from Constants. Domain cost is the local ledger penalty attached to a gravitational or geometric domain; the canonical threshold is the positive cutoff against which that cost is compared when a structural inequality is asserted.
This file does not derive Einstein equations or the full RS mass ladder. It only freezes the structural side conditions that later GRV lemmas are allowed to assume: nonnegativity of the domain cost, a concrete positive threshold, and a single certificate type that packages both so downstream proofs can demand one inhabited witness instead of re-proving the same inequalities.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short positivity/nonnegativity facts (likely unfolding the Cost primitives and Constants). domainCost_at_eq is an evaluation or simplification identity. RSGRVStructural001Cert is a structure (or Prop bundle) whose fields are those facts; cert and cert_inhabited supply a concrete inhabitant so the certificate is not vacuous. No deep tactic proof: the argument is packaging plus elementary Cost/Constants lemmas.
why it matters in Recognition Science
Gives Gravity a named structural certificate (GRV-001) so later RS gravity results can depend on one inhabited record rather than scattered inequalities. Upstream edges are only Constants and Cost, so the module is intentionally thin: it freezes nonnegativity of domain cost and positivity of the canonical threshold in RS-native units. No downstream used_by edges are recorded yet; the certificate is meant as a stable interface for subsequent GRV structural and dynamical lemmas. It does not itself close T5--T8 forcing, RCL identities, or the $\alpha$ band; it only supplies the gravity-side structural witness those developments can import.
scope and limits
- Does not derive Einstein field equations or Newtonian limits.
- Does not prove uniqueness of the domain cost or threshold.
- Does not connect to the eight-tick octave or $D=3$ forcing chain.
- Does not establish numerical GR fits or observational bounds.
- Does not discharge dynamical stability or singularity claims.