CoherenceCollapseCert
plain-language theorem explainer
CoherenceCollapseCert is a structure that records the four properties required to certify the recognition-gravity link: recognition action equals twice residual rate action for every angle, Born weights remain positive, the sine-cosine identity holds, and coherence mass stays below one nanogram. Researchers modeling objective collapse would reference it when contrasting the Recognition Science plateau after orthogonality against the continuing growth predicted by Penrose-Diósi. The structure is assembled by direct citation of the four component
Claim. A structure asserting that recognition action satisfies $C(θ) = 2A(θ)$ for all $θ$, where $A(θ) = -ln(sin θ)$ is the residual rate action, that Born weights $w(C) = e^{-C}$ are positive for all $C$, that $sin²θ + cos²θ = 1$ for all $θ$, and that the coherence mass threshold satisfies $m_{coh} < 10^{-9}$ kg.
background
The Gravity.CoherenceCollapse module formalizes the bridge between gravitational coherence collapse and the Born rule through recognition cost. Recognition action $C$ along a geodesic rotation is twice the residual rate action $A(θ_s) = -ln(sin θ_s)$. Born weight for an outcome with cost $C_I$ is defined as $exp(-C_I)$, which equals $sin²θ$ and therefore supplies the probability interpretation $|α|²$. The threshold mass $m_{coh} ≈ 2×10^{-13}$ kg marks the scale at which $A ≈ 1$, separating coherent quantum behavior from rapid classicalization.
proof idea
This is a structure definition whose fields are filled by four prior results in the same module. The equality field is supplied by the definition of recognition_action, positivity by the born_weight lemma, normalization by the trigonometric identity, and the mass bound by direct evaluation of m_coh_kg.
why it matters
The structure supplies the bundled properties that the coherence_collapse_cert theorem instantiates to assert the full set of predictions. It encodes the central C = 2A identity that derives the Born rule from recognition cost and distinguishes the Recognition Science plateau from Penrose-Diósi growth. The certificate closes the formal link between recognition action and mesoscopic gravity effects.
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