IndisputableMonolith.Physics.RS_Physics_Module_011
Physics module packaging a domain-level cost functional, its non-negativity, and a positive canonical threshold, together with an inhabited certificate bundle. A physicist citing RS domain energetics or threshold comparisons would land here. The file is mostly definitions plus short positivity and equality lemmas over the imported J-cost and constants.
claimIntroduce a domain cost $C_{\mathrm{dom}}$, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fix a canonical threshold $\theta>0$, and package these facts as an inhabited RS Physics 011 certificate.
background
Recognition Science measures mismatch with the J-cost from the Cost module, $J(x)=(x+x^{-1})/2-1$, forced unique by the T5 step of the unified forcing chain. Constants supplies the RS-native tick $\tau_0=1$ and related units ($c=1$, $\hbar=\varphi^{-5}$).
This module lifts that scalar cost to a domain-level functional domainCost, records that the cost is nonnegative, and names a positive canonicalThreshold against which domain costs are compared. The local setting is pure physics bookkeeping: no dynamics, only the static cost/threshold interface used by later RS physics certificates.
Upstream imports are thin: Mathlib for real analysis, Constants for RS units, Cost for $J$ and related inequalities.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; domainCost_at_eq is an evaluation identity; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity lemmas over the imported cost. RSPhysics011Cert bundles those facts, with cert and cert_inhabited witnessing that the certificate type is inhabited. No deep tactic scripts; structure is define, prove sign, package.
why it matters in Recognition Science
Gives the Physics domain a named cost-and-threshold certificate (RS Physics 011) so downstream energetics and selection arguments can cite one inhabited bundle rather than ad-hoc inequalities. Sits under the Cost/$J$ layer and the Constants unit system; feeds any parent that needs a nonnegative domain cost compared to a fixed positive threshold. No used_by edges are recorded yet, so the module is presently a leaf certificate surface rather than a proved forcing-chain step (T5–T8 live elsewhere).
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; those live upstream in Cost/forcing.
- Does not fix numerical values of masses, alpha, or G; only domain cost and a canonical threshold.
- Does not prove dynamics, evolution, or eight-tick timing; static cost interface only.
- Does not record downstream consumers; used_by is empty in the graph snapshot.