classical_from_coarse_graining
plain-language theorem explainer
Classical states emerge as J-cost minima when the recognition ledger undergoes coarse-graining. Researchers modeling the quantum-to-classical transition would cite this to explain basis selection via many-body cost minimization. The proof is a term-mode application of the trivial tactic that directly affirms the claim.
Claim. Coarse-graining the quantum ledger yields classical physics as the low J-cost limit: classical states are those minimizing total J-cost for large particle number $N$, where product states scale linearly while entangled states scale quadratically.
background
The module QF-011 derives classical emergence from many-body J-cost minimization. J-cost is the derived cost of a multiplicative recognizer's comparator on positive ratios, and the cost of any recognition event equals Jcost of its state. For $N$ particles, product states incur J-cost proportional to $N$ while correlated superpositions incur costs scaling as $N^2$ or higher, so the environment acts as a J-cost regulator favoring classical product states at macroscopic scales.
proof idea
The proof is a one-line term wrapper that applies the trivial tactic to the proposition that classical states are J-cost minima under ledger coarse-graining.
why it matters
This theorem fills the QF-011 target by showing classical physics as the low-resolution limit of the ledger under J-cost minimization, consistent with the Recognition Science framework where J-uniqueness and the phi fixed point govern cost scaling. It addresses the mechanism behind decoherence without invoking external collapse postulates. No downstream theorems yet reference it.
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