MeasurementBasis
plain-language theorem explainer
MeasurementBasis enumerates the five standard quantum measurement bases in the Recognition Science model of wave function collapse. Researchers working on J-cost minimization for measurement outcomes cite this enumeration to fix the basis cardinality at five. The declaration is an inductive type definition with five constructors that automatically derives Fintype.
Claim. Let $B$ be the set of measurement bases with five elements: position, momentum, spin, energy, angular momentum.
background
The module models quantum measurement as selection of the J-cost minimum from a superposition treated as a recognition cost distribution. Before measurement Jcost r exceeds zero for r not equal to one; after measurement the system reaches equilibrium at Jcost 1 equals zero. The module states that five basis types realize configDim D equals five.
proof idea
This is the inductive definition of the five basis constructors with automatic derivation of DecidableEq, Repr, BEq and Fintype. No lemmas are applied and no proof body exists.
why it matters
The definition supplies the basis set required by the downstream measurementBasisCount theorem asserting cardinality five and by the WaveFunctionCollapseCert structure packaging five_bases together with superposition_cost and measurement_equilibrium. It realizes the module's claim that five bases correspond to configDim D equals five in the J-cost treatment of collapse, where the Born rule arises from cost weighting.
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