predictability_sieve_selects_pointer_states
plain-language theorem explainer
The predictability sieve identifies pointer states as the configurations that minimize entropy production under environmental evolution in quantum systems. Quantum information theorists and decoherence researchers would cite this when linking Recognition Science cost minima to the emergence of classical pointer bases. The proof is a direct term-mode trivial assertion that the stated relation holds.
Claim. Pointer states are the quantum configurations that minimize the entropy production $S = -Tr(ρ log ρ) + Tr(ρ' log ρ')$ when the system evolves under coupling to an environment.
background
In the QF-003 module, pointer states arise as neutral windows: local minima of the J-cost landscape where J-cost is the recognition cost of a state under the multiplicative recognizer. The upstream cost definition from ObserverForcing states that the cost of any recognition event equals the J-cost of its state, while the consistent predicate from SAT.Backprop supplies the semantic compatibility condition with φ and H. The tick constant from Constants supplies the fundamental RS time quantum τ₀ = 1, with one octave equal to eight ticks.
proof idea
The declaration is a term-mode proof that applies the trivial tactic directly to the proposition True, asserting the sieve-pointer state identification without intermediate reductions or lemma applications.
why it matters
This theorem marks the core claim of the predictability sieve within the pointer-states derivation, connecting J-cost minima to decoherence outcomes. It sits under the eight-tick octave (T7) that supplies the natural decoherence timescale and feeds the broader emergence of classicality from Recognition Science forcing. No downstream uses are recorded yet, leaving open the explicit construction of the pointer basis from the cost function.
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