IndisputableMonolith.Physics.RS_PHY_Structural_004
Structural physics module that packages a nonnegative domain cost functional together with a strictly positive canonical threshold, then wraps both in an inhabited certificate. Physicists citing RS structural claims use it as a named bundle rather than re-proving the two inequalities. The argument is definitional plus elementary positivity from the imported cost layer.
claimDefine a domain cost $C$ with $C \ge 0$ at every admissible point, a canonical threshold $\theta > 0$, and an inhabited certificate packing both facts as the RS structural claim 004 bundle.
background
Recognition Science measures mismatch with a J-cost built from the unique solution of the Recognition Composition Law. The Cost import supplies that cost layer; Constants supplies the RS-native tick $\tau_0 = 1$.
This module sits in the Physics structural series. It introduces a domain-level cost (evaluation of the cost on a structural domain) and a canonical threshold against which that cost is compared. Nonnegativity of the domain cost and positivity of the threshold are the two elementary facts the certificate records.
No forcing-chain step (T5–T8) is re-derived here; the module only freezes the cost/threshold pair into a named, checkable bundle for downstream physics lemmas.
proof idea
Definition module with short positivity lemmas. Domain cost is defined by evaluating the imported cost; equality-at-a-point and nonnegativity are immediate from the Cost API. The canonical threshold is a positive constant (positivity proved by a one-line arithmetic or constant lemma). The certificate structure packs the two propositions; inhabitation is by constructing the pair of proofs.
why it matters in Recognition Science
Gives the Physics layer a single named certificate (structural claim 004) for “domain cost is nonnegative and the canonical threshold is positive.” Downstream consumers can depend on the certificate rather than re-importing Cost and re-proving the two inequalities. No used-by edges are recorded yet, so the module is presently a leaf packaging step inside the structural series, not a forcing-chain landmark (T5 J-uniqueness, T6 $\varphi$, T7 eight-tick, T8 $D=3$).
scope and limits
- Does not derive the J-cost uniqueness or the Recognition Composition Law.
- Does not fix numerical values of masses, alpha, or rung gaps.
- Does not prove any dynamical or evolutionary equation.
- Does not connect the threshold to Berry creation or dream-fraction bounds.
- Does not assert forcing-chain steps T5–T8.