IndisputableMonolith.Gravity.RS_GRV_Structural_010
Structural certificate module for RS gravity claim 010. It defines a domain cost, records nonnegativity and evaluation identities, fixes a positive canonical threshold, and packages them in an inhabited certificate type. Gravity and ledger-cost workers cite the cert when wiring structural hypotheses. Content is mostly definitions plus elementary positivity and equality lemmas over the imported cost layer.
claimThe module introduces a domain cost $C$, proves $C\ge 0$ and the pointwise evaluation identity for $C$, fixes a canonical threshold $\theta>0$, and supplies an inhabited structural certificate bundling these facts for RS gravity structural item 010.
background
Recognition Science gravity sits on the same cost calculus as the rest of the monolith. The Cost import supplies the J-cost family (the unique symmetric cost solving the Recognition Composition Law), while Constants supplies RS-native units such as the tick $\tau_0$. Domain-level costs are the natural objects when comparing geometric or ledger domains rather than single ratios.
This module lives in the Gravity domain and is labeled Structural_010: a thin structural layer that freezes the cost and threshold data a later dynamical gravity theorem will assume. Sibling names indicate a domain cost with an evaluation identity and a nonnegativity proof, a strictly positive canonical threshold, and a certificate record that is provably inhabited.
No forcing-chain step (T5–T8) is re-proved here; the module only arranges cost and threshold facts so downstream GRV arguments can cite one certificate instead of a scatter of lemmas.
proof idea
Definition-and-certificate module, not a deep proof development. Domain cost is introduced as a def; nonnegativity and the evaluation identity are short lemmas over the Cost import. The canonical threshold is a positive constant (positivity lemma). The certificate type bundles these fields; inhabitation is a constructor application assembling the proved components. No substantial tactic scripts beyond elementary real inequalities.
why it matters in Recognition Science
Gives Gravity a single named structural certificate (RSGRVStructural010Cert) so later RS gravity results can depend on one inhabited record rather than ad hoc cost hypotheses. Used_by is presently empty: this is a leaf structural package waiting on dynamical consumers (curvature matching, G-normalization against $G=\phi^5/\pi$, or domain-defect bounds). It does not itself advance T5–T8 or the mass ladder; it only freezes the cost/threshold interface those gravity arguments will need.
scope and limits
- Does not derive Einstein equations or any dynamical field equation.
- Does not prove uniqueness of the domain cost beyond what Cost already gives.
- Does not fix numerical G, c, or alpha; only structural cost/threshold data.
- Does not discharge forcing-chain steps T5–T8.
- Does not yet feed a recorded downstream theorem (used_by empty).