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Manuscript IV@1 · IV.tex · figure · 351cb2d7

Model 1 record certificate

Model 1: a fixed detector and its contrast › An explicit positive detector coefficient · lines 1374–1405

IV@1#fig:model1-record

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gravitationalscalaroperator / instrumenterror / restrictionsupport / scope
Witness
φ∗=−12(A0)ijxixjη0,ϖ∗=0\varphi_*=-\tfrac12(A_0)_{ij}x^ix^j\eta_0,\quad \varpi_*=0
ψ¨∗(t0,0)=c0=∣A0∣2>0\ddot\psi_*(t_0,0)=c_0=|A_0|^2>0
small future support of f∗f_*
d∗=∫f∗ψ∗≥d0>0d_*=\int f_*\psi_*\ge d_0>0
Preparation
Ψ0=Coh⁡(0)⊗Coh⁡(z∗)\Psi_0=\operatorname{Coh}(0)\otimes\operatorname{Coh}(z_*)
Ψ∗=Coh⁡(1/2)⊗Coh⁡(z∗)\Psi_*=\operatorname{Coh}(1/\sqrt{2})\otimes\operatorname{Coh}(z_*)

same scalar factor; equal oscillator covariances

ΔQ=1, ΔΠ0=0\Delta Q=1,\ \Delta\Pi_0=0
Record
Δ⟨A(1)⟩=λd∗\Delta\langle A^{(1)}\rangle=\lambda d_*
∣Δpε∣≥c1−eε|\Delta p_\varepsilon|\ge c_1-e_\varepsilon
λ=0⇒U=Ig⊗Uϕ⇒Δp=0\lambda=0\Rightarrow U=I_g\otimes U_\phi\Rightarrow \Delta p=0

This contrast does not exclude every classical stochastic model.

Model 1 record certificate. A local Hessian choice produces a positive detector coefficient. Gravitational coherent displacement at fixed scalar preparation changes the generator mean by , yielding a calibrated positive Ramsey contrast after edge removal. At , the two records agree exactly.

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