IndisputableMonolith.Physics.RS_Physics_Module_002
Physics module defining a domain cost functional and a canonical positive threshold used in Recognition Science bookkeeping. It packages nonnegativity of the cost, positivity of the threshold, and a small certificate type that witnesses the package is inhabited. Cite it when wiring cost comparisons or threshold gates into later RS physics lemmas. The content is definitional plus short positivity/nonnegativity arguments over the imported cost layer.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$ (nonnegative), a canonical threshold $\theta_{\mathrm{can}}>0$, pointwise evaluation identities for the cost, and a certificate bundle asserting these facts are available as a coherent RS physics package.
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 supplies the RS-native tick $\tau_0=1$ used as the time quantum.
This module sits in the Physics domain and specializes those primitives into a domain-level cost and a canonical threshold. Sibling declarations name the cost, its evaluation identity, nonnegativity, the threshold, its positivity, and a certificate type with an inhabitation witness.
No external physics model is assumed beyond the RS cost and constant stack already imported.
proof idea
Definition-heavy module. Cost and threshold are introduced as defs; nonnegativity and positivity are short lemmas over the Cost import; the certificate is a structure (or Prop bundle) with an inhabitation instance. No deep tactic development: the argument is packaging and elementary sign checks, not a multi-step derivation.
why it matters in Recognition Science
Gives Physics a reusable domain-cost and threshold gate so later RS physics results can compare costs against a fixed positive cutoff without re-proving sign facts. Downstream use is not yet wired in the graph (no used_by edges), so the module presently acts as a local certificate shelf for Module 002 rather than a forcing-chain step (T5–T8). It keeps cost bookkeeping aligned with the $J$-cost layer and the RS tick convention from Constants.
scope and limits
- Does not derive the $J$-cost uniqueness or RCL; those live upstream in Cost/Foundation.
- Does not fix numerical particle masses, $\alpha$, or rung assignments.
- Does not claim a forcing-chain step (T5–T8) or dimensional result.
- Does not yet feed named parent theorems in the dependency graph.
- Does not define dynamics, measurement postulates, or experimental protocols.