BCSSuperconductorCert
plain-language theorem explainer
BCSSuperconductorCert packages the certification that a J-cost model matches BCS superconductivity through five parameters, zero cost at unit ratio, and reciprocity symmetry. Materials modelers in Recognition Science cite it when linking Cooper-pair formation to the J-cost minimum at r=1. The definition is a plain record whose fields are the cardinality statement on BCSParameter together with the ground-state and symmetry conditions on Jcost.
Claim. The structure asserts that the BCS parameter set has cardinality five, that the J-cost function satisfies $J(1)=0$, and that $J(r)=J(r^{-1})$ for all positive real $r$.
background
Recognition Science models BCS superconductivity by identifying Cooper-pair formation with the minimum of the J-cost function. The J-cost J(r) measures the recognition defect between signals whose ratio is r, and the module shows that J(1)=0 corresponds to the paired state with anti-correlated signals. BCSParameter is the inductive enumeration of the five standard observables: energy gap, coherence length, London depth, critical temperature, and critical field.
proof idea
BCSSuperconductorCert is introduced as a structure whose three fields are the cardinality equality, the ground-state equation, and the universal quantification over positive reals. No lemmas are applied inside the declaration itself; the fields stand as the defining properties.
why it matters
The structure provides the type for the concrete certificate bcsSuperconductorCert, which populates the fields from bcsParameterCount, bcs_ground_state, and cooper_pair_symmetry. It anchors the BCS mechanism inside the Recognition framework by tying the J-cost minimum and reciprocity to the standard superconductor parameters, consistent with the J-uniqueness property and the recognition composition law.
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