IndisputableMonolith.Physics.WaveFunctionCollapseFromJCost
This module shows that quantum superpositions carry positive J-cost before any measurement occurs, supplying a cost-based account of wave function collapse inside Recognition Science. Foundations researchers working on quantum measurement would cite the results to connect recognition cost to observed outcomes. The module imports the Cost library and assembles definitions for bases together with theorems establishing cost positivity and equilibrium after measurement.
claimLet $J$ denote the recognition cost $J(x) = (x + x^{-1})/2 - 1$. For any superposition state prior to measurement, $J > 0$. Measurement selects an outcome that minimizes this cost, with the process certified by an explicit predicate on the chosen basis.
background
Recognition Science obtains all physics from a single functional equation whose solution yields the J-cost function and the Recognition Composition Law. The present module sits in the Physics domain and imports the Cost module to apply that cost to quantum states. It introduces MeasurementBasis as the discrete set of admissible outcomes together with the count of such bases, then defines the predicate that a superposition carries positive cost and the certificate that collapse has occurred once an equilibrium outcome is reached.
proof idea
This is a definition-and-theorem module rather than a single proof. It opens with basis and count definitions, states the core claim that superpositions incur positive J-cost, proves an equilibrium property for post-measurement states, and packages the whole argument inside the WaveFunctionCollapseCert predicate. All steps rest directly on the J-cost primitives supplied by the imported Cost module.
why it matters in Recognition Science
The module supplies the Recognition Science treatment of the quantum measurement problem by deriving collapse from positive pre-measurement J-cost. It thereby fills a required step between the J-uniqueness result (T5) and the emergence of classical outcomes, even though the current graph shows no explicit downstream users. The DOC_COMMENT states the central claim: before measurement, superposition has positive recognition cost.
scope and limits
- Does not derive Born-rule probabilities.
- Does not treat entangled or multi-particle states.
- Does not compute explicit collapse times or rates.
- Does not address relativistic or field-theoretic extensions.