IndisputableMonolith.Physics.WaveFunctionCollapseFromJCost
The module shows that superpositions carry positive J-cost before measurement, supplying the cost-driven mechanism for wave function collapse. Quantum foundations researchers would cite it when deriving measurement from recognition cost. The argument imports the Cost module, defines MeasurementBasis, and certifies that non-eigenstates incur positive cost while equilibrium outcomes minimize it.
claimIn the Recognition framework, let $B$ be a measurement basis and let $S$ be a superposition state relative to $B$. Then the J-cost satisfies $J(S) > 0$ prior to measurement, with collapse to an outcome state $o$ where $J(o)$ reaches its minimum under the Recognition Composition Law.
background
The module imports the Cost module, which supplies the J-cost function $J(x) = (x + x^{-1})/2 - 1$ together with the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$. It introduces MeasurementBasis as the discrete set of admissible measurement outcomes and measurementBasisCount as its cardinality. The local setting is the pre-measurement regime in which any state not aligned with the basis carries positive recognition cost, consistent with the phi-ladder and eight-tick octave structure of the broader framework.
proof idea
This is a definition module. It declares MeasurementBasis and measurementBasisCount, then states the theorems superposition_has_cost and WaveFunctionCollapseCert. These rest on the upstream J-cost positivity result imported from the Cost module; no internal tactic steps or reductions are required beyond the imported cost inequality.
why it matters in Recognition Science
The module supplies the direct link between J-cost and wave function collapse, placing the T5 J-uniqueness and T6 phi fixed-point results into the measurement setting. It feeds the parent claim that recognition cost forces collapse to equilibrium outcomes, supporting the derivation of quantum measurement from the single functional equation. No downstream uses are recorded in the current graph.
scope and limits
- Does not derive explicit collapse probabilities or the Born rule.
- Does not extend the cost argument to continuous or relativistic bases.
- Does not address multi-particle entanglement or decoherence timescales.
- Does not prove that the chosen basis is unique for a given state.