IndisputableMonolith.Foundation.AllPhysics5
Foundation module that packages a domain-level cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold used by the AllPhysics5 certificate. Physicists tracing the RS cost ladder cite it for the threshold that gates domain recognition. The module is mostly definitions plus short positivity and evaluation lemmas, closed by an inhabited certificate record.
claimIntroduce a domain cost $C_{\mathrm{dom}}$, prove $C_{\mathrm{dom}}\ge 0$ and the pointwise evaluation identity, fix a canonical threshold $\theta>0$, and package these into an inhabited AllPhysics5 certificate record.
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 $J$-cost infrastructure; Constants supplies the RS-native tick $\tau_0=1$.
This module lifts cost from the elementary $J$ setting to a domain-level functional domainCost, together with a fixed positive canonicalThreshold. The local goal is not a new forcing step (T5--T8 live elsewhere) but a compact certificate surface: nonnegativity, evaluation at equality cases, and a positive gate value that downstream physics layers can treat as a single inhabited bundle.
Sibling names indicate the surface API: evaluation identity, nonnegativity, positivity of the threshold, and the AllPhysics5Cert / cert / cert_inhabited triple that freezes the package for import.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; short lemmas discharge nonnegativity of the domain cost, the evaluation identity at the equality case, and positivity of the threshold, almost certainly by reduction to the imported Cost nonnegativity facts and elementary arithmetic on Constants. The certificate is then a structure (or sigma-type) bundling those facts, with cert_inhabited supplying a concrete witness so downstream files can open the package without reconstructing the lemmas.
why it matters in Recognition Science
Sits in the Foundation domain as a thin certificate layer above Cost and Constants. No downstream edges are recorded yet, so its role is to freeze domain-cost and threshold facts for later All-Physics assembly rather than to close a named forcing step. In the broader RS chain it supports any argument that needs a nonnegative domain cost gated by a positive canonical threshold before mass-ladder or coupling extractions. It does not itself force $J$, $\varphi$, the eight-tick octave, or $D=3$; those remain upstream in the UnifiedForcingChain.
scope and limits
- Does not prove uniqueness of J or the RCL forcing chain (T5).
- Does not derive phi, the eight-tick period, or D = 3.
- Does not compute particle masses or the alpha band.
- Does not assert physical units beyond RS-native Constants.
- Does not record downstream consumers in the current graph.