PointerState
plain-language theorem explainer
PointerState structures a classical observable with its J-cost selection reason in the Recognition Science model of decoherence. Researchers deriving classical emergence from many-body interactions cite it when building position and momentum pointer states. The definition is a direct structure with two string fields that carries no proof obligations and directly supports downstream instantiations.
Claim. A pointer state is a pair $(o, r)$ where $o$ is a classical observable (position, momentum, etc.) and $r$ is a string asserting that $o$ is selected because it minimizes total J-cost under local environmental interaction.
background
The module QF-011 derives classical emergence from many-body J-cost minimization: single-particle superpositions carry low cost while correlated many-body states scale as $N^2$. Upstream, cost is the derived cost of a multiplicative recognizer comparator or the J-cost of a recognition event; Position is simply the real line. The local setting treats the environment as a J-cost regulator that selects product states for large $N$.
proof idea
This is a structure definition that introduces the PointerState type with fields observable and selection_reason. No lemmas or tactics are applied; it functions as a data carrier for the downstream definitions positionPointer and momentumPointer.
why it matters
The structure supplies the type used by positionPointer and momentumPointer, which instantiate the einselection claim that the environment selects J-cost minima. It fills the QF-011 step in the Recognition Science chain by grounding decoherence in cost minimization, consistent with J-uniqueness and the eight-tick octave. It leaves open the quantitative scaling of J-cost for realistic many-body environments.
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