Instrumental Eigenmode Spectroscopy of a Holographic Einstein–Dilaton Bulk Using Optical Clocks

An instrument-level protocol is specified to test whether optical-clock time series exhibitan auditable response to bulk eigenmode perturbations of a frozen Einstein–Dilaton background under an ex-ante, no-feedback sweep. An integrated temporal dictionary, tint(ϵ;n) =τR zdstzsrc exp[−(A(z) + ϵΦn(z))]dz, is recomputed over a fixed list of perturbation amplitudes ϵand eigenmodes Φn(z). For each (n,ϵ), a sliding-window analysis reports SNR and demodulatedphase coherence at a pre-registered target frequency. At ϵ = 0 (control), all mode labels areidentical by construction (same dictionary). At ϵ = 0.02 (first nonzero perturbation), the dictionary becomes mode-dependent and yields mode-dependent phase-coherence structure underthe same fixed decision rule.