IndisputableMonolith.Physics.RS_PHY_Structural_010
Defines a domain-level cost functional and a canonical positive threshold used by structural physics certificate RS-PHY-010. Supplies nonnegativity of the cost, positivity of the threshold, and an inhabited certificate bundle. Anyone checking the structural layer of Recognition Physics cites this module for the cost/threshold interface. The argument is definitional plus short positivity lemmas from the Cost import.
claimIntroduce a domain cost $C$ (nonnegative), a canonical threshold $\theta > 0$, and an inhabited certificate packaging $C$, $\theta$, and the stated inequalities for structural claim RS-PHY-010.
background
Recognition Science measures mismatch with a nonnegative cost built from the unique J-cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law. The Cost module supplies that infrastructure; Constants fixes the RS-native tick $\tau_0=1$.
This module sits in the Physics structural layer. It lifts the scalar cost to a domain-level functional domainCost, records evaluation identity and nonnegativity, and names a positive canonicalThreshold against which structural recognition events are compared.
The certificate type bundles those objects so downstream structural claims can assume a single inhabited witness rather than re-proving cost and threshold facts inline.
proof idea
Definition module with thin lemmas. Domain cost is defined from the imported Cost primitives; domainCost_at_eq is an evaluation identity; domainCost_nonneg follows from nonnegativity of the underlying cost. Canonical threshold is a positive constant (positivity is a one-line inequality). The certificate record packages these facts; cert_inhabited builds a concrete inhabitant.
why it matters in Recognition Science
Structural certificate RS-PHY-010 needs a fixed nonnegative cost and a positive threshold before any comparison or forcing step can run. This module is that interface: cost, threshold, and an inhabited cert so later physics lemmas do not re-open the Cost layer.
No downstream edges are recorded yet in the mirror graph, so the module presently closes a local structural obligation rather than feeding a named parent theorem. It aligns with the cost side of the forcing chain (T5 J-uniqueness) without itself proving uniqueness or the eight-tick/D=3 steps.
scope and limits
- Does not prove J-uniqueness or the Recognition Composition Law.
- Does not derive mass, alpha, or other RS constants.
- Does not assert physical units beyond RS-native cost/threshold.
- Does not supply dynamics or time evolution; only static cost and threshold.
- Does not record downstream consumers in the current graph.