IndisputableMonolith.Physics.WaveFunctionCollapseFromJCost
The module shows that superpositions carry positive J-cost before measurement and derives wave function collapse in the Recognition Science setting. Quantum foundations researchers would cite the WaveFunctionCollapseCert to connect measurement to the cost functional. The module defines a measurement basis, proves cost positivity and outcome equilibrium, then certifies collapse.
claimDefines MeasurementBasis and certifies that $J($superposition$) > 0$ forces collapse to an equilibrium outcome minimizing recognition cost.
background
The module sits inside Recognition Science, where physics follows from the single J-functional obeying the composition law. It imports the Cost module that supplies the definition of J-cost. The module documentation states the core claim: before measurement, superposition has positive recognition cost. It introduces MeasurementBasis as the discrete set of possible outcomes together with the count function and the equilibrium property.
proof idea
This is a definition-and-theorem module. It first defines MeasurementBasis and measurementBasisCount, then proves superposition_has_cost, establishes measurement_outcome_equilibrium, and packages the results into the WaveFunctionCollapseCert.
why it matters in Recognition Science
The module supplies the WaveFunctionCollapseCert that feeds derivations of quantum measurement from J-cost. It connects directly to the J-uniqueness step in the forcing chain and supplies the cost-based mechanism for collapse. No downstream uses are listed.
scope and limits
- Does not derive explicit wave-function forms.
- Does not treat relativistic or field-theoretic cases.
- Does not compute numerical cost values for specific states.
- Does not address multi-particle entanglement.