IndisputableMonolith.Physics.RS_Physics_Module_006
Physics module defining a domain cost functional and a positive canonical threshold, packaged as an inhabitance certificate. Physicists tracking RS cost geometry and threshold phenomena would cite it when wiring domain-level energy bounds into larger physics arguments. The module is mostly definitional, with nonnegativity and positivity lemmas and a trivial certificate witness.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, defines a canonical threshold $\theta_{\mathrm{can}}>0$, and packages these facts as an inhabited certificate $\mathrm{RSPhysics006Cert}$.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the Recognition Composition Law. The Cost import supplies that infrastructure; Constants supplies the RS-native tick $\tau_0=1$.
This module sits in the Physics layer and lifts cost ideas to a domain-level functional domainCost, together with a fixed positive scale canonicalThreshold. Sibling lemmas record evaluation at equality, nonnegativity of the domain cost, and positivity of the threshold. A small certificate type RSPhysics006Cert bundles the package for downstream inhabitance checks.
proof idea
Definition-heavy module rather than a single deep theorem. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas (likely direct from Cost/Constants facts or elementary arithmetic). The certificate is witnessed by a trivial inhabitant (cert / cert_inhabited), so the module's logical payload is the packaged positivity and nonnegativity facts, not a multi-step derivation.
why it matters in Recognition Science
Gives the Physics layer a named domain-cost and threshold interface tied to the RS cost stack (Cost, Constants). No downstream edges are recorded yet, so it currently acts as a local certificate node rather than a feeder of a named parent theorem. In the broader forcing picture it supports cost-based bounds that sit above T5 J-uniqueness and the phi-ladder mass/threshold language (Berry scale $\phi^{-1}$, $Z_{cf}=\phi^5$), without itself proving those landmarks.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law.
- Does not fix numerical values of c, hbar, G, or alpha.
- Does not prove mass-ladder or eight-tick octave results.
- Does not record downstream consumers in the current graph.
- Does not claim a physical measurement protocol for the threshold.