IndisputableMonolith.Physics.WaveFunctionCollapseFromJCost
Links quantum measurement to the recognition cost J: a superposition carries strictly positive J-cost, while a definite measurement outcome sits at J-equilibrium (cost zero). Physicists deriving collapse from the RS cost functional would cite this module. The argument is definitional plus elementary inequalities on J, not a deep analytic construction.
claimBefore measurement, a superposition state has strictly positive recognition cost $J>0$. A measurement basis has finite cardinality; each definite outcome is a $J$-equilibrium ($J=0$). The module packages this as a wave-function-collapse certificate: collapse is the passage from positive-cost superposition to zero-cost eigenstate under the RS cost $J(x)=(x+x^{-1})/2-1$.
background
Recognition Science treats the unique cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$) as the sole source of physical selection. The forcing chain fixes $J$ at T5; the Recognition Composition Law then governs products and ratios. In that language a pure eigenstate is an equilibrium of $J$ (cost zero), while any nontrivial superposition is a nonequilibrium configuration.
This module sits in the Physics layer and imports only the Cost core. It introduces a finite measurement basis, a count of basis elements, and the elementary claims that superposition carries positive cost and that a recorded outcome is at equilibrium. The local setting is therefore kinematic: cost comparison before and after selection, not a dynamical Schrödinger evolution.
proof idea
Definition-heavy module with short supporting lemmas. Measurement bases and their cardinalities are introduced as data. The key inequality superposition_has_cost follows from strict convexity (or the unique minimum) of $J$ at the identity: any nontrivial mixture lies off the minimum. measurement_outcome_equilibrium records that a definite basis vector saturates $J=0$. WaveFunctionCollapseCert and its witness bundle these facts into a single certificate object. No heavy analysis; the structure is definitions plus direct appeals to Cost properties of $J$.
why it matters in Recognition Science
Gives the RS reading of wave-function collapse: measurement is cost minimization under $J$, not an extra postulate. It ties the Born-rule setting to the same $J$ fixed by T5 and used for masses, $\alpha$, and the eight-tick structure elsewhere in the monolith. Downstream consumers (none linked yet in the graph) would be Born-rule or decoherence developments that need a certified positive-cost-to-equilibrium step. The module therefore closes a conceptual gap between the abstract cost functional and laboratory measurement language, while remaining elementary enough to stay fully proved.
scope and limits
- Does not derive the Born probability weights from J.
- Does not supply unitary or open-system dynamics between preparations.
- Does not prove uniqueness of the measurement basis.
- Does not address relativistic or field-theoretic measurement.
- Does not connect to the eight-tick octave or D=3 forcing steps.