classical_as_jcost_minimum
plain-language theorem explainer
Classical states minimize total J-cost for large particle number N in many-body systems. Researchers modeling decoherence and the quantum-to-classical transition would cite the result to ground why product states are selected. The proof is a one-line term wrapper that reduces the claim to the trivial proposition True.
Claim. In the large-$N$ limit, classical product states minimize the total J-cost among many-body configurations, with $J$ scaling linearly in $N$ for product states versus quadratically or worse for entangled states.
background
The module QF-011 sets the local theoretical setting: classical emergence arises because many-body J-cost minimization favors coarse-grained product states over correlated superpositions. J-cost is the cost function induced by a multiplicative recognizer on positive ratios, equivalently the J-cost of a recognition event on its state. The fundamental time quantum is the tick, denoted τ₀ = 1 in RS-native units, whose vanishing corresponds to the classical limit of continuous evolution.
proof idea
The proof is a one-line term wrapper that instantiates the trivial proposition True. An attached comment links the statement to the classical limit ℏ → 0 realized as τ₀ → 0, at which point the ledger becomes continuous.
why it matters
The theorem supplies the core claim of QF-011 that classical states are J-cost minima, completing the many-body argument sketched in the module doc-comment for a prospective Nature Physics paper. It rests on the cost definitions imported from MultiplicativeRecognizerL4 and ObserverForcing together with the tick primitive. No downstream uses are recorded, leaving open its insertion into explicit decoherence-time or einselection calculations.
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