collapse_threshold
plain-language theorem explainer
collapse_threshold sets the recognition cost value at which accumulated J-cost forces a configuration into a definite state. Modal interpretations of quantum dynamics or recognition-based collapse models would cite it to replace the measurement postulate with a built-in threshold. The declaration is a direct constant definition with no computation or lemmas applied.
Claim. The collapse threshold is the real number defined by $τ := 1$, such that a configuration $c$ has a definite pointer precisely when its recognition cost satisfies $J(c) ≥ τ$.
background
In the Modal.Actualization module the Actualization operator A selects the J-minimizing configuration from the possibility set P(c), dual to the Possibility operator. Upstream, both IntegrationGap.A and Masses.Anchor.A fix the active edge count per tick at 1, satisfying the φ-power balance identity φ^(A − gap) · φ^gap = φ at D = 3. The J-cost itself is the function appearing in the T5 J-uniqueness step of the forcing chain.
proof idea
The declaration is a one-line definition that directly assigns the real number 1 to the collapse_threshold constant.
why it matters
This constant is used by has_definite_pointer to express the definiteness predicate and by collapse_automatic to prove that collapse occurs automatically via J-minimization once the threshold is crossed. It supplies the numerical anchor for the framework claim that superposition collapse is built into the dynamics rather than added as an axiom, consistent with the Recognition Composition Law and the eight-tick octave. No open scaffolding is closed here.
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