coherence_collapse_cert
plain-language theorem explainer
The coherence collapse certificate asserts that recognition action equals twice residual rate action for all angles, that Born weights are positive, that sin squared plus cos squared equals one, and that the mesoscopic coherence mass lies below one nanogram. Physicists modeling quantum measurement via gravitational collapse would cite it to separate Recognition Science predictions from Penrose-Diósi models. The proof is a direct structure instantiation that assembles four prior lemmas.
Claim. The structure CoherenceCollapseCert holds: for all angles θ, recognition action θ equals twice rate action θ; for all C, born weight C is positive; for all θ, sin²θ + cos²θ = 1; and m_coh_kg < 10^{-9} kg.
background
Recognition Science models gravitational collapse through recognition cost J along paths. Recognition action C integrates J(r(t)) dt over a path γ, while residual rate action A equals -ln(sin θ_s) for geodesic separation angle θ_s. The central identity C = 2A connects gravitational coherence to quantum measurement outcomes.
proof idea
The proof constructs the CoherenceCollapseCert structure by direct assignment: C_is_2A receives the theorem C_equals_2A, born_positive receives born_weight_pos, normalization receives born_normalization, and threshold_nanogram receives a norm_num tactic after unfolding m_coh_kg. Each field is supplied by an upstream lemma in the same module.
why it matters
This certificate completes the formalization of the C = 2A identity in the gravity-coherence paper, packaging the Born rule emergence and the mesoscopic threshold m_coh ≈ 0.2 ng. It supplies a sharp distinguisher: Recognition Science predicts collapse rate plateaus after orthogonality, unlike Penrose-Diósi models. The result anchors coherence collapse predictions within the Recognition framework.
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