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 the separation of astronomical signals from harmonics, e.g., using variance-based spectral analysis. I thus show on diverse data (geomagnetic polarity, cratering, extinction episodes) as a proxy of planetary paleodynamics that many-body subharmonic entrainment induces a resonant response of the Earth to astronomical forcing so that the 2π-phase-shifted axial precession p=26 ky, and its Pi=2πp/i; i=1,…,n harmonics, get resonantly responsible for virtually all paleodata periods. This resonantly quasiperiodic nature of strata is co-triggered by a 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 significant intrinsic residual signal is 26.5-My Rampino period — the carrier wave of crushing deflections co-responsible for transformative polarity reversals. While the (2πp, Pi) resonant response of the Earth to orbital forcing is the long-sought energy transfer mechanism of the Milankovitch theory, fundamental system properties — 2π-phase-shift, ¼ lockstep to a forcer, and the discrete time translation symmetry (multiplied or halved periods) — previously thought confined to (quantum) time crystal, here appear macroscopic, rendering the concept of time crystal unremarkable. In turn, such a surprising cross-scale outcome has confirmed the main result: that of planetary precession being a cataclysmic geodynamic phenomenon as claimed in the past, e.g., as the mechanism for Earth expansion; then a time crystal in quantum dynamics could be due to particle entrainment, such as the collisions resulting in Feshbach resonances.
The Sun reveals itself in the 386–2.439-nHz (1-mo–13-yr) band of polar (φsun>|70°|) fast (>700 km s^−1) solar wind’s decade-scale dynamics as a globally completely vibrating/resonating magnetoalternator and not just a proverbial engine anymore. Thus North–South separation of hourly-averaged, 1994–2008 Ulysses samplings of the <10 nT polar winds in ~1.6·10^7 –2.5·10^9-erg energies revealed spectral signatures of a ≥99%-significant Sun-borne global differential resonant activity, verified across disparate data. Confirming the Alfvén’s view on a Sun globally resonating under its Ps=~11-yr Schwabe mode, this Alfvén (a-mode) resonance (AR) comprising Rossby-like r-modes and cavity-confined R-modes, is governed by Ps at a remarkable ~25% field variance northside, a ~9-yr degeneration of Ps at ~20% southside, and a ~10-yr degeneration of Ps under equatorial mixing. While composing the PG∈~(88–100-yr) Gleissberg cycle, the 9–10–11-yr sector coupling also co-triggers AR, Pi=Ps/i, i=2…n, n ∈ א, imprinted in the fast winds at least to the order n=100. The overwhelming (anisotropy moderating) and deterministic (with Φ>>12 fidelity) AR is accompanied by a most useful symmetrical antiresonance, P(-), whose both N/S tailing harmonics P(-)17 are the well-known 154-day Rieger period, from which the couplings-freed Rieger resonance sprouts as wind’s own. Thus the Sun is a typical, ~3-dB-attenuated ring system of differentially rotating and contrarily vibrating conveyor belts and layers, with a continuous spectrum of modes, patterns complete in both parities, and resolution better than 81.3 nHz (S) and 55.6 nHz (N) in lowermost frequencies (≲2μHz in most modes). Unlike a resonating car engine that tries but fails to separate its fixed casing, the resonating free Sun exhausts the wind in a shake-off alongside the rotational axis. AR advances standard stellar models, agrees with laboratory experiments for enhanced studies of the Sun interior and heliosphere, and can explain the million-degree corona and solar abundance.
Sun–Jupiter decade-scale magnetic entanglement emerges from Wilcox Solar Observatory 1975-2021 N–S ≲150 μT mean-field data, as a global response of solar magnetic fields to the magnetar-type evolution of Jupiter ~2001–onward global magnetoactivity discovered recently in the 1–6 month (385.8–64.3 nHz) band of Rieger resonance. At extreme ≲20% field variance, the sudden Jovian deviation is so high it forced solar magnetoactivity devolution into inverse-matching response, at effectively moderate ≲1.5% mean-field variance. Thus as Jupiter magnetoactivity evolved sinusoidally, the Sun began mirror-compensating ~2002 (the epoch of Abbe number drop), reducing its magnetoactivity in decreasingly sinusoidal fashion to solar cycle 24 extreme minimum. For check, 2004-2021 WIND mission data revealed <0.5-var% (<5-dB) calm ≲50 nT interplanetary magnetic field at L1, slightly undulated by the Jupiter evolution impulse, thus excluding solar wind and Sun as impulse sources (confirmed by statistical fidelity waning down Jupiter–L1–Sun diffusion vector spaces, as 10^7–10^3–10^2). Magnetic tangling of stars and hot (<0.1 AU) Jupiters was blamed previously for observed star superflaring 10^2–10^7 times more energetic than the strongest solar flare. Accordingly, the Sun ante-impulse locking is a shock-absorbing mechanism — routine shutter-response to Jupiter recurrent phasing into the flare-brown-dwarf state — with which the Sun enters a grand minimum (sleep mode). As Jupiter intermittently becomes an indirect driver of Earth’s climate, the Sun prepares to discharge stored energy as a non-extinction ~10^32-erg superflare (currently overdue). The mechanism, in which warm/cold Jupiters too trigger (mild) superflares, possibly defends stars against incoming Jupiters.