IndisputableMonolith.Physics.RS_Physics_Module_009
Physics support module that packages a domain cost functional, its nonnegativity, a strictly positive canonical threshold, and an inhabited certificate record tying those facts together. Workers bounding recognition costs or threshold crossings in RS units would cite it. Content is mostly definitional, with short positivity and equality lemmas over the imported cost layer.
claimDefines a domain cost $C_{\mathrm{dom}}$, the identity $C_{\mathrm{dom}}$ at a reference evaluation, the inequality $C_{\mathrm{dom}} \ge 0$, a canonical threshold $\theta$ with $\theta > 0$, and an inhabited certificate asserting these domain-cost and threshold facts in RS-native units.
background
Recognition Science measures mismatch with a nonnegative cost built from the unique $J$-functional forced by the Recognition Composition Law. The Cost import supplies that layer; Constants fixes the RS time quantum $\tau_0 = 1$ tick, so thresholds and costs sit in dimensionless RS units ($c=1$, ladder powers of $\varphi$).
This module sits in the Physics domain and introduces a domain-level cost together with a canonical threshold. Sibling names indicate equality-at-reference, nonnegativity of the domain cost, and positivity of the threshold, then wrap them in a certificate type with an inhabitation proof.
No external paper proposition is attached in the supplied docs; the local setting is bookkeeping for cost-versus-threshold comparisons used by later physics arguments.
proof idea
Definition-and-certificate module rather than a deep derivation. Domain cost and the canonical threshold are introduced as defs; short lemmas record evaluation-at-equality, nonnegativity of the cost, and positivity of the threshold. A certificate structure bundles those claims, and inhabitation is discharged by assembling the lemmas. No long tactic scripts or forcing-chain steps appear at module scope.
why it matters in Recognition Science
Supplies reusable domain-cost and threshold primitives for the RS physics stack, so later results can quote a single certificate instead of re-proving nonnegativity and positivity. Downstream edges are empty in the graph snapshot, so this is a leaf support module rather than a direct parent of a named forcing step (T5–T8) or mass-ladder theorem. It keeps cost comparisons aligned with the imported $J$-cost layer and the RS tick convention from Constants.
scope and limits
- Does not derive $J$-uniqueness or the Recognition Composition Law.
- Does not fix numerical particle masses or the fine-structure band.
- Does not prove eight-tick closure or $D=3$.
- Does not assert dynamical equations beyond cost and threshold facts.
- Does not provide a falsifiable experimental protocol by itself.