einselection_from_jcost
plain-language theorem explainer
The environment selects pointer states by imposing J-cost penalties that drive high-cost superpositions to decohere rapidly while low-cost product states persist as the classical basis. Researchers modeling the quantum-to-classical transition via decoherence would cite this when linking Recognition Science cost minimization to einselection. The proof reduces the claim directly to the trivial proposition.
Claim. An environment with many degrees of freedom imposes a J-cost on system states such that high-cost entangled configurations decohere rapidly while low-cost product states survive as pointer states.
background
The module QF-011 derives classical emergence from many-body J-cost minimization. The cost function is the derived cost of a multiplicative recognizer's comparator on positive ratios, and the cost of any recognition event equals this J-cost value, which is non-negative. The environment is a structure carrying degrees of freedom, positive temperature, and interaction strength; the system is a nonempty collection of energy levels.
proof idea
The proof is a one-line wrapper that applies the trivial proposition.
why it matters
This fills the QF-011 proposition on classical emergence from many-body J-cost in the Recognition Science framework. It connects the J-cost defined via the multiplicative recognizer and observer forcing to the pointer states selected by the environment. No downstream uses are recorded, leaving open its integration with the full quantum-to-classical crossover.
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