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IndisputableMonolith.Physics.Wavefunction_Collapse3_FromJCost

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Packages a J-cost-based domain cost, a strictly positive canonical collapse threshold, and an inhabited certificate for three-way wavefunction collapse in Recognition Science. Measurement and decoherence workers in the RS stack would cite the certificate and the nonnegativity facts. The module is mostly definitional, with short positivity and evaluation lemmas over the imported cost layer.

claimA domain cost built from the Recognition $J$-functional, together with a canonical threshold $\tau>0$ and an inhabited certificate that the collapse-from-$J$ package (nonnegative domain cost, positive threshold, evaluation identity) is available for three-component wavefunction collapse.

background

Recognition Science treats measurement-style collapse as a cost threshold crossing rather than an extra postulate. The cost layer supplies the unique $J$-functional $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law; Constants supplies the RS-native tick scale. This physics module lifts those primitives into a domain cost on configuration data and a single positive threshold used as the collapse gate.

Sibling definitions introduce domainCost (nonnegative, with an evaluation identity at equality cases), canonicalThreshold (strictly positive), and a certificate bundle that packages those facts. The local setting is therefore: collapse is declared when the domain cost meets or exceeds the canonical threshold, with all inequalities traced to $J$ rather than to an ad hoc Born-rule axiom.

proof idea

Definition-and-certificate module, not a deep derivation. Domain cost is defined from the imported $J$-cost; nonnegativity and the on-equality evaluation identity are short lemmas. The canonical threshold is a positive constant (positivity proved directly). The certificate type bundles those properties; inhabitation is a constructor application assembling the proved facts. No multi-step forcing argument lives here.

why it matters in Recognition Science

Gives the physics stack a named, checkable collapse-from-$J$ package instead of an informal measurement story. Downstream consumers (none linked in the current graph) can require the certificate rather than re-proving cost nonnegativity and threshold positivity. Ties collapse to the same $J$ that the forcing chain isolates at T5, so measurement structure stays inside the RS cost calculus rather than floating as an independent axiom. The three-way naming marks the intended use for three-component / spatial-$D=3$ collapse bookkeeping aligned with the T8 dimension step.

scope and limits

depends on (2)

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declarations in this module (8)