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Geometric Origin of the π/2 Phase Lag in Imaginary Quasi-Periodic Oscillations: A TVS23 Derivation

Authors: ACOSTA PADILLA, ALFREDO LUIS;

Geometric Origin of the π/2 Phase Lag in Imaginary Quasi-Periodic Oscillations: A TVS23 Derivation

Abstract

Bellavita et al. (2025, arXiv:2502.12283) discover imaginary QPOs in MAXI J1820+070 with an exact π/2 phase lag relative to standard QPO components, undetected in the power spectrum but clearly visible in the imaginary cross-spectrum. The authors fit the data successfully but leave the origin of the π/2 phase lag unexplained. We show that this phase lag is a geometric theorem of TVS23: in the dodecahedral elastic vacuum network V₂₃, the 19 transverse (EM) channels and 4 longitudinal (gravitational) channels are exactly π/2 out of phase by the geometry of the elastic tensor (C_iiii=12/5, C_ijij=4/5, ν=1/4). The imaginary QPO is the observational signature of the 4 gravitational channels. The frequency ratio ν_imag/ν_QPO = 1/√3 = 0.577 (observed: ~0.57), the energy threshold at ~2 keV ≈ E_vac = 1866 eV, and the universality across MAXI J1820, MAXI J1348, and Cygnus X-1 are all derived with zero free parameters.

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