momentumPointer
plain-language theorem explainer
Momentum qualifies as a pointer state in homogeneous environments under the Recognition Science J-cost model. Researchers modeling decoherence and the emergence of classical observables would cite this definition when building the preferred basis for translation-invariant systems. The definition is a direct record construction that populates the PointerState structure with the observable label and the interaction-invariance rationale.
Claim. The momentum pointer state is the structure with observable equal to momentum and selection reason given by translation-invariant interactions favoring momentum states.
background
PointerState records a classical observable together with its selection reason; in RS these are the states that minimize total J-cost under environmental interaction. The module sets classical emergence as the outcome of many-body J-cost minimization: product states scale linearly with particle number while entangled states scale quadratically, so the environment selects the lower-cost classical basis. Upstream, cost is the derived cost of a multiplicative recognizer comparator on positive ratios and also the J-cost of any recognition event.
proof idea
The definition is a direct record construction that instantiates the PointerState structure with the supplied observable string and selection-reason string.
why it matters
This definition supplies one concrete element of the pointer basis used to construct the einselection mechanism in the classical-emergence development. It fills the QF-011 target by exhibiting how homogeneous environments impose J-cost that selects momentum as a stable observable. It touches the open question of explicit J-cost evaluation for concrete observables before the full many-body scaling can be applied.
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