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

Model 2 record and exact control

Model 2: spectral removal at fixed number cutoff › Witness, calibration, and record · lines 2114–2150

IV@1#fig:model2-record

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gravitationalscalaroperator / instrumenterror / restrictionsupport / scope
Ψ0=Ωg⊗Coh⁡(v∗)\Psi_0=\Omega_g\otimes\operatorname{Coh}(v_*)
Ψa=Coh⁡(az∗)⊗Coh⁡(v∗)\Psi_a=\operatorname{Coh}(az_*)\otimes\operatorname{Coh}(v_*)

scalar factor identical

f∗=bψ∗,d∗=∫bψ∗2>0f_*=b\psi_*,\qquad d_*=\int b\psi_*^2>0
AR,M(2)=Ig⊗F0,M+λΠMBRΠMA^{(2)}_{R,M}=I_g\otimes F_{0,M}+\lambda\Pi_M B_R\Pi_M
ΔR,M≥c2−eM−eR(M)\Delta_{R,M}\ge c_2-e_M-e_R(M)
eMe_M from coherent number tails
eR(M)e_R(M) from spectral generator convergence
λ=0:U=Ig⊗eiτF0,M,Δp=0\lambda=0:\quad U=I_g\otimes e^{i\tau F_{0,M}},\quad \Delta p=0
scalar-only compression of the free term
total-number compression of the free scalar term
would introduce gravitational-number dependence

Coherent displacement is not claimed to commute with ΠM\Pi_M.

Model 2 record and exact control. A gravitational displacement at fixed scalar preparation gives a positive bilinear witness. The calibrated record includes separate spectral and coherent number-tail errors. Scalar-only compression of the free term preserves exact equality at ; total-number compression would not preserve that factorization.

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