Claims of paleodata periodicity are many and controversial so that, for example, superimposing Phanerozoic (0–541 My) mass-extinction periods renders life on Earth impossible. This period hunt coincided with the modernization of geochronology which now ties geological timescales to orbital frequencies. Such tuneup simplifies energy-band (variance-) stratification of information contents, enabling separation of astronomical signal from any harmonics. Variance-based spectral analysis techniques can achieve this, such as the Gauss–Vaníček method favored by astronomers for resilience with even extreme data gaps. I thus show on diverse data (geomagnetic polarity, cratering, extinction episodes) that many-body subharmonic entrainment causes the Earth to respond to its astronomical forcing resonantly, so that the 2π-phase-shifted axial precession p=26 ky, and its Pi=2πp/i; i=1,…,n harmonics, are resonantly responsible for virtually all paleodata periods. This resonantly quasiperiodic nature of strata is shown co-triggered by the p’/4-lockstep to the p’=41-ky obliquity (also 2π-phase-shifted, to P’=3.5-My superperiod). For verification, residuals analysis after suppressing 2πp (and thus Pi, too) in the current polarity-reversals GPTS-95 timescale’s calibration extending to end-Campanian (0–83 My) successfully detected weak signals of Earth-Mars planetary resonances, reported previously from older epochs. The only significant intrinsic residual signal is 26.5-My Rampino period — carrier wave of crushing deflections that, during Transformative Resonant Events (TRE), decimate strata to quasiperiodicity — co-responsible for polarity reversals and whose detection confirms geomagnetism overall ergodicity. The (2πp, Pi) resonant response of the Earth to orbital forcing is the long-sought, energy-transfer mechanism of the Milankovitch theory — now a special case (applicable to the current episode) of Earth-Moon-Sun system resonant dynamics springing from the 1–40 My very long band. Fundamental system properties — 2π-phase-shift, ¼ lockstep to a forcer, and discrete time translation symmetry (multiplied or halved periods) — previously were thought typical of a discrete time crystal, which here then appears unremarkable.