post_orthogonality_plateau
plain-language theorem explainer
This definition encodes the Recognition Science claim that residual rate action remains bounded after the orthogonality angle. Gravitational decoherence researchers would cite it to separate the model from Penrose-Diósi predictions of unbounded growth. The statement is a direct universal quantification that imposes an additive upper bound on the action over the closed interval from orthogonality to pi.
Claim. Let $A(θ)$ be the residual rate action for geodesic separation angle $θ$. Then $A(θ) ≤ A(π/2) + 1$ for every real $θ$ with $π/2 ≤ θ ≤ π$.
background
The module develops the coherence-collapse bridge between gravity and the Born rule, centered on the identity that recognition action equals twice the residual action. The residual rate action is the negative logarithm of the sine of the separation angle for two-branch geodesics. This definition extends the angle domain past orthogonality while imposing a uniform bound. It rests on the explicit rate-action formula that is positive for non-orthogonal separations.
proof idea
The declaration is a direct definition of the stated proposition. It applies the residual rate action function to the closed interval from orthogonality onward and asserts the additive bound without further reduction steps.
why it matters
The definition supplies the formal plateau statement that distinguishes Recognition Science collapse rates from Penrose-Diósi models. It supports the central C = 2A identity in the coherence-collapse framework and closes one prediction in the gravity-coherence paper. No downstream uses are recorded yet.
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