rate_action
plain-language theorem explainer
The residual rate action A for a two-branch geodesic rotation equals -ln(sin θ_s) where θ_s is the separation angle. Researchers modeling coherence collapse and the emergence of the Born rule cite this definition when connecting recognition costs to gravitational rates. It is supplied as a direct functional definition in the CoherenceCollapse module.
Claim. The residual rate action is given by $A(θ_s) = -ln(sin θ_s)$ for separation angle $0 < θ_s < π/2$.
background
The CoherenceCollapse module formalizes the connection between gravitational collapse and quantum measurement through recognition cost. Recognition action C along a geodesic rotation is twice the residual rate action A, with the central identity C = 2A. Residual rate action A is the quantity defined here.
proof idea
The declaration is a one-line definition that sets rate_action θ_s to the negative of the real logarithm of the sine of θ_s.
why it matters
This definition is the foundation for the C = 2A identity proved in C_equals_2A and used in CoherenceCollapseCert. It enables born_weight_is_sin_sq showing born_weight equals sin²(θ_s). The framework predicts collapse rate plateaus after orthogonality, distinguishing RS from Penrose-Diósi models, and supports Born rule emergence from recognition costs. It touches the mesoscopic threshold m_coh ≈ 0.2 ng for A ≈ 1.
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