NeutralWindow
plain-language theorem explainer
NeutralWindow encodes a local minimum region of the J-cost landscape in complex configuration space, with fields for center state, width, cost value, and minimality flag; this models the stable pointer states selected by decoherence. Researchers deriving the preferred basis from Recognition Science cost functions would cite it when linking environment interactions to classical emergence. The declaration is a direct structure definition that introduces the type without further reduction.
Claim. A neutral window is a tuple $(c, w, J_c, m)$ where $c$ is a center state in the complex plane, $w$ is the width of the stable interval, $J_c$ is the value of the J-cost at the center, and $m$ is a boolean recording whether the center is a local minimum of the J-cost.
background
J-cost is the non-negative cost of a recognition event, defined as Cost.Jcost of the state (ObserverForcing.cost). In the module setting, pointer states arise as the configurations that minimize this cost under environment coupling, so that superpositions incur higher J-cost while definite states sit at local minima. The upstream LedgerFactorization.of supplies the underlying multiplicative structure on positive ratios that induces the cost function, while IntegrationGap.A fixes the active edge count at D=3. The module QF-003 frames the entire construction as the mechanism by which decoherence drives systems into these minima.
proof idea
Structure definition that directly introduces the NeutralWindow type with four fields: center of type ℂ, width of type ℝ, cost_at_center of type ℝ, and is_local_minimum of type Bool. No lemmas or tactics are applied; the declaration itself supplies the mathematical object used downstream.
why it matters
It supplies the core definition consumed by ClaimBoundaries.C3_scope in the Z-Pattern Death and Survival section. The declaration fills the QF-003 target that pointer states are exactly the neutral windows of the J-cost landscape. Within the Recognition framework this anchors the emergence of classicality to the T5 J-uniqueness property, since only states at local J-cost minima survive environment interactions without cost increase.
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