tau_coh_s
plain-language theorem explainer
The definition tau_coh_s fixes the coherence time at 1 in Recognition Science units. It establishes the mesoscopic threshold for the C equals 2A identity that derives the Born rule from recognition costs along paths. Researchers in quantum gravity and measurement theory would reference it when scaling coherence times to one second for masses around 0.2 nanograms. The assignment is a direct constant definition.
Claim. The coherence time in the gravity-coherence model is defined by $τ_{coh} = 1$ (in seconds).
background
In the CoherenceCollapse module the recognition action C[γ] is the integral of J-cost along a path γ. The residual rate action A equals -ln(sin θ_s) where θ_s is the geodesic separation angle. The module proves the identity C = 2A and shows that Born probabilities emerge as P(I) = exp(-C_I) / sum exp(-C_J) which equals |α_I|^2. The constants m_coh_kg and tau_coh_s set the threshold m_coh ≈ 0.2 ng and τ ≈ 1 s when A ≈ 1.
proof idea
The declaration is a direct definition assigning the real number 1 to tau_coh_s. No upstream lemmas are invoked and no tactics are used.
why it matters
This constant realizes the mesoscopic time scale in the central C = 2A identity of the gravity-coherence paper. It pairs with m_coh_kg to fix the point where recognition action produces the Born rule. The definition supplies the τ ≈ 1 s estimate listed in the module's core results. It provides a fixed scale for coherence collapse calculations but leaves open the derivation of the exact value from the forcing chain.
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