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IndisputableMonolith.Quantum.ClassicalEmergence

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The Quantum.ClassicalEmergence module supplies J-cost calculations for product states of N particles together with pointer states and crossover structures. Researchers modeling the quantum-to-classical transition via cost minimization would cite it when linking decoherence to J-cost minima. The module consists of definitions and lemmas that extend the base Cost framework using the imported constants.

claimJ-cost for a product state of N particles, together with entangled-state costs, pointer states, and the quantum-classical crossover condition.

background

The module sits in the quantum domain and imports the RS time quantum τ₀ = 1 tick from Constants together with the J-cost apparatus from Cost. It introduces auxiliary objects including PointerState, positionPointer, momentumPointer, decoherenceTime, and QuantumClassicalCrossover, all expressed in terms of the Recognition Composition Law and J-uniqueness. The local theoretical setting is the emergence of classical descriptions as J-cost minima.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module feeds QMInterpretationStructure, whose doc-comment states that classical description emerges as a J-cost minimum. It supplies the quantum-side cost calculations required for that interpretation step and for later use of the eight-tick octave and D = 3 in the forcing chain.

scope and limits

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (21)