Spectral evidence from global geomagnetic calibration for stellar-system resonances constraining both quantum physics and geophysics

https://doi.org/10.5281/zenodo.4724219 1 Spectral evidence from global geomagnetic calibration for stellarsystem resonances constraining both quantum physics and geophysics Mensur Omerbashich Geosciences Online [email protected] [email protected] [email protected] In 1984, Clarke expanded the domain of observed quantum phenomena from the microscopic regimes of atoms and electrons (~10¹–10³ particles) to macroscopic superconducting circuits, which he showed exhibit quantum coherence (~10⁹–10¹² particles). I demonstrate that coherent quantum behavior persists at vastly larger scales, in Earth’s (~10⁵¹ particles) resonant geophysical cycles, which manifest astro-macroscopic time-crystalline behavior. The arguably most accurate and precise spectral analysis of the conventionally most reliable global geomagnetic calibration (CKGPTS95) revealed that macroscopic and microscopic phenomena are interconnected through cosmos-permeating gravitational resonance networks, thus annulling conventional assumptions of quantum invariance. The analysis identified a planet-dominating 9.35-My fundamental cycle, arising from Earth’s orbital and stellar gravitational influences, and resonantly governing geomagnetic reversals, planetary growth, stratigraphic anomalies mimicking mass extinctions, as well as the Great Unconformity. The resonances exhibit non-geophysical features of quantum coherence classically confined to microscopic systems, such as time crystals: discrete time-translation symmetry, fractional harmonic locking, and many-body entrainment. An integrative, high-resolution (10-yr-) view of paleodata, celestial mechanics, and quantum physics reveals that stellar-system resonances impose hierarchical constraints on planetary processes and regulate fundamental quantum properties. Given the ubiquity of tidal phenomena, a resonance-based framework exists in which large-scale celestial dynamics constrain quantum analogously to how extragalactic dynamics constrain stellar—thereby defining particle masses, coupling constants, and universal parameters. This data-driven proof completes my 2006 theoretical derivation of G (and thus gravity) from the speed of light at both quantum and everyday scales, and confirms the Hyperresonance Unifying Theory, which unified those domains via Einstein’s arbitrary simplicity (using high-school algebra), arxiv.org/abs/physics/0608026 & arxiv.org/abs/0801.0876. Foundations of physics; Foundations of quantum physics; Foundations of geophysics; Spectral analysis; Gravitational resonance networks; Time crystals; Macroscopic quantum coherence; Geomagnetic reversals; Milankovitch and long-period astronomical cycles; Earth expansion and planetary growth; Periodic mass extinctions; Great Unconformity. Introduction Quantum mechanics stands as one of the most successful and deeply rooted pillars of modern physics. It describes a universe where particles—quarks, leptons, bosons—exhibit intrinsic properties such as mass, charge, and spin, governed by universal constants that define the so-called fabric of reality. The apparent fine-tuning of these constants—sometimes dubbed the hierarchy problem—remains one of the deepest puzzles of physics [1–4]. Yet, despite its successes, the origins and precise values of these fundamental constants remain mysterious. Why is the mass of the electron what it is? What sets the Higgs field's vacuum expectation value? Why are particle masses seemingly fine-tuned, and how do these relate to cosmic parameters? On the other hand, the Earth's global geological record preserves long-term cyclical signatures— mass extinction events, geomagnetic reversals, sedimentary cycles—that appear to be modulated by celestial influences; periodic behavior in these records has been noted since the earliest works on orbital forcing and extinction periodicity [5]. Classical explanations, such as Milankovitch cycles tied to Earth's orbital eccentricity, obliquity, and precession, account for glacial-interglacial periods that span hundreds of thousands of years. However, the apparent periodicities in mass extinctions, stratigraphic anomalies, and geomagnetic reversals—all spanning millions of years— cannot be fully explained by those models alone. Recent reviews have highlighted the limitations of astrochronological tuning and its tendency to mask long-period resonances. [6] Furthermore, recent advances challenge the traditional geophysical frameworks by revealing a complex, resonance-driven structure that underpins Earth's long-term dynamics. The interdisciplinary confluence of paleontology, geophysics, and celestial mechanics suggests that Earth's internal processes are enmeshed within a hierarchical resonance network that extends https://doi.org/10.5281/zenodo.4724219 2 across stellar systems and beyond. This network influences planetary geodynamics and, much like galactic dynamics does to stellar, inevitably constrains and defines quantum properties at the most fundamental level on Earth and in its vicinity. The present study posits that the Earth's long-term geophysical and geomagnetic periodicities are governed by gravitational and resonance effects that originate from broader star-system dynamics. Specifically, the ~9.35-My cycle, driven by celestial gravitational interactions, acts as the driver of planetary resonances that not only modulate Earth's internal processes—magnetic field reversals, stratigraphy, and tectonics—but also impose hierarchical constraints onto magnetism and quantum physical constants as measured on Earth and in its vicinity. In that hierarchical, resonance-based universe, large-scale celestial motions serve as the calibration mechanism for both geophysical phenomena and quantum properties, revealing a profound interconnectedness. Such a framework suggests that what we observe as quantum invariants are not absolute but are, at least partially (within the solar system), and by extension in most of the known universe, constrained or determined by macroscopic gravitational resonance networks. Methods The present study applies Shannon theory-based Gauss–Vaniček spectral analysis (GVSA) [7] as a statistically robust and arguably the highest-resolution spectral method to comprehensive global geomagnetic, paleontological, and impact-cratering data. Methodology is in the Supplemental Material. Results Identification of the 9.35 My Cycle – spectral evidence of planetary resonances The GVSA spectra of (the calibration points of) the CKGPTS95 geomagnetic polarity timescale [8] [Supplemental Table 1] reveal a consistent spectral peak at ~9.35 My and its stable foundation, Figs. 1 and 2. The peak is statistically significant across multiple independent datasets, including magnetic polarity reversal records, stratigraphic time-series, and impact signatures. Fig. 1. Gauss–Vaníček spectral analysis (GVSA) [7] of geomagnetic polarity timescale CKGPTS95 [8] reveals ≥99%- significant axial (25 ky) and apsidal (29.8 ky) precessional peaks, confirming a stable foundation for the 9.35-My modulation, Fig. 2. https://doi.org/10.5281/zenodo.4724219 3 This spectral maximum coincides remarkably well with Earth's orbital precession period (~25–30 ky)—a cycle primarily modulated by lunar gravitational influences but also affected by planetary perturbations from Venus, Mars, and other bodies, and found across global geological datasets [6]. The phase relationships between diverse datasets exhibit fractional locking—analogous to phenomena observed in quantum time crystals—where stable, discrete periodicities manifest over geological timescales. Fig. 2 illustrates the spectral peak and harmonic series centered around P≈9.35 My, revealing fractional harmonic relationships Pi=P/i (where P=9.347 My). These fractional harmonics, which include subharmonics (e.g., P/2, P/3), suggest a form of many-body entrainment among Earth's orbital parameters, lunar librations, and planetary alignments, which are collectively amplifying and stabilizing the overall resonance. Fig. 2. GVSA spectrum of the CKGPTS95 calibration (1–40-My band) showing the 9.35-My peak and its fractional harmonics Pi=P/i, indicative of many-body entrainment. See Supplemental Material for data sources, statistical tests, and extended spectra. Many-Body Entrainment Framework The harmonic series exhibits a network of fractional components—Pi=P/i [Supplemental Table 2]—indicating complex mode locking across multiple planetary and lunar cycles. This many-body entrainment results in a resonance hub that sustains and modulates Earth's internal dynamics. Analogous to coupled oscillators in physical systems, this network could heighten the influence of external gravitational perturbations on Earth’s core processes, mantle convection, and crustal movements. https://doi.org/10.5281/zenodo.4724219 4 Supplemental Table 2 lists all periods significant at ≥95% in the GVSA spectrum of CKGPTS95 calibration (1–40 My band). All are harmonics of the 9.347 My resonance, consistent with fractional locking. Full methodological details and additional figures are in the here included Supplemental Material. Furthermore, the presence of subharmonic locking—a hallmark of quantum time crystals—implies that Earth's long-term geophysical signals do not just reflect simple periodicity but embody fractional, stable phase relationships reminiscent of discrete time-translation symmetry [9–10] found in quantum condensed matter systems. Geophysical Manifestations The 9.35-My resonance appears to influence multiple geophysical manifestations [11]: o Geomagnetic Reversals: The statistical clustering of polarity reversals around this cycle, with phases of high and low reversal likelihood, suggests a resonance-driven modulation of Earth's hypothetical dynamo. Geomagnetic excursions and rapid reversals could be phase-locked events, temporally modulated by the overarching celestial resonance. o Mass Extinctions and Stratigraphic Anomalies: Paleontological and stratigraphic records display signatures that mimic periodic mass extinctions and unconformities, revealing the 9.35My cycle. These signatures could be triggered by resonance-induced tectonics and amplified by variations in mantle dynamics, with an impact on volcanic activity and climate. o Sedimentary and Stratigraphic Cycles: The recurring stratigraphic features, including the Great Unconformity, demonstrate timescale periodicities consistent with the resonance framework, suggesting an orbital-driven forcing underlying sediment deposition and erosion patterns. o Tectonic and Crustal Reconfigurations: Large-scale tectonic events, such as rifting, mountainbuilding, and continental drift episodes, often coincide with resonance peaks, implying external gravitational modulation of Earth's lithospheric processes. Quantum-Scale Constraints Remarkably, these macro-scale resonance phenomena exhibit features characteristic of quantum coherence, including [12–14]: o Discrete Time-Translation Symmetry: Just as quantum time crystals display stable periodicities breaking continuous time-translation symmetry, Earth's long-term records reveal stable, fractional periodicities that endure over millions of years. o Fractional Harmonics and Locking: The presence of harmonic substructures akin to fractional Lock-in phenomena indicates that the Earth's geophysical signals are non-arbitrary, i.e., locked instead into stable fractional modes due to external resonance networks. o Many-Body Entrainment: The complex harmonic relationships suggest collective dynamics involving multiple planetary bodies, akin to many-particle quantum systems known to exhibit entanglement and coherence. The implication is that Earth's geophysical cycles might embody a form of macroscopic quantum coherence, enabled and stabilized by gravitational resonance networks. https://doi.org/10.5281/zenodo.4724219 5 The observed spectral and phase coherence suggest a hierarchy where celestial gravitational interactions constrain not only planetary processes but also fundamental quantum properties. The key motif here is the notion that constants of nature—particle masses, charge ratios, and coupling constants—are, at least in part, resonantly calibrated by stellar-system dynamics. Existing models treat quantum constants as invariant and fundamental, derived from high-energy physics and cosmology. Yet, precise measurements of particle masses, the fine-structure constant, and the Higgs vacuum expectation value appear fine-tuned, prompting questions about their origins. The data-driven hierarchical paradigm suggests: o Particle masses and couplings might be influenced or constrained by resonance conditions within the gravitational network of stellar systems. For example, particle masses could relate to resonance frequencies that, in turn, are associated with stellar gravitational potentials. This setup is analogous to boundary conditions that set eigenvalues in quantum systems. o Dark matter and dark energy properties might also code unto or be constrained by macro-scale stellar and planetary resonance states, implying that they are emergent phenomena, stabilized by hierarchical gravitational dynamics. o Quantum coherence phenomena at macroscopic scales, counterintuitively, may not be confined to microscopic regimes but can extend or manifest at planetary scales under specific resonance conditions, effectively linking quantum and classical realms. This perspective challenges the universality presupposed in traditional quantum physics. Instead, it proposes a cosmos where quantum constants "emerge" from, or are "tuned" by, gravitational and celestial resonance networks. Then the constants which we measure reflect a hierarchical structure linking the microcosm to the macrocosm via gravitational resonances. In summary, these findings indicate an interdependent hierarchical resonance network, where: • Stellar system dynamics is the primary driver shaping planetary geophysics and potentially constraining quantum properties. • Planetary internal processes are governed by large-scale resonant phenomena, such as precession and tidal interactions, which manifest as macroscopic time crystals influencing geophysical and geochemical cycles. • Surface and atmospheric processes, including mass transfer, climate variation, and tectonic activity, are modulated through resonance transfer mechanisms linked to the underlying planetary and stellar dynamics. • Quantum and sub-quantum phenomena are effectively confined and modulated by planetaryscale resonances, suggesting that quantum effects, such as entanglement, tunneling, and coherence, might have a macroscopic geophysical manifestation driven by the hierarchy of resonances initiated at the stellar system level. Just as galaxies are known to impose their own dynamics onto neighbors' constituents, so may stars impose their dynamics onto their own immediate neighbors. https://doi.org/10.5281/zenodo.4724219 6 This hierarchical resonance network posits that geophysical phenomena, such as geomagnetic reversals, mass extinctions, and stratigraphic signatures, are not exclusively governed by isolated internal processes or stochastic external perturbations, but are instead emergent properties resulting from coherent, multi-scale interactions rooted in the fundamental dynamics of the stellar system. Specifically, planetary systems—and by extension, their host stars—act as natural laboratories in which quantum-like coherence manifests in the form of phenomena like time crystals and manybody entrainment. These effects propagate downward, influencing Earth's internal constitution and surface conditions, creating a self-organized, resonant system. In its universal generalization, macroand micro-physical phenomena interconnect intrinsically through a hierarchy of resonances spanning energy levels from above planetary dimensions to below quantum scales. Discussion While quantum phenomena are conventionally observed at microscopic scales, such as individual atoms or electrons (~101–103 particles), experiments in superconducting circuits have demonstrated coherent quantum behavior in systems containing ~109–1012 particles [15], showing that quantum coherence can persist at macroscopic scales far beyond atomic dimensions. In the above, I suggested a conceptual analogy for resonant geophysical cycles in the Earth-Moon-Sun system. Indeed, the present study extended this macroscopic quantum perspective to planetary scales, suggesting that periodicities in Earth's (~1051 particles) geological and astronomical data can be interpreted as manifestations of macroscopic time-crystalline behavior. The study presents compelling evidence that Earth's geophysical processes, including geomagnetic reversals and seismic activity, exhibit characteristics of a macroscopic quantum system—specifically, a discrete time crystal. This conceptual framework integrates geological, astronomical, and quantum principles, proposing a hierarchical resonance network in which stellar-system dynamics serve as the primary regulatory mechanism influencing planetary internal and surface phenomena. In such a setup, resonantly stabilized interactions produce coherent, system-level oscillations analogous to those observed in macroscopic quantum circuits, albeit at vastly higher particle numbers and longer timescales. Consequently, quantum-physical phenomena and fundamental parameters are effectively specialized to their host star and stellar system, and may therefore vary among stellar systems if resonance architectures differ. Key findings include: • Existence of planetary-scale time crystallinity, where discrete time translation symmetry shows in Earth’s geophysical cycles, including geomagnetic polarity reversals and stratigraphic patterns. • Quantum-like coherence in planetary dynamics, analogous to superconducting circuits, supports the hypothesis of macroscopic quantum phenomena at geological scales. • Resonant energy transfer mechanisms provide a physical basis for Milankovitch cycles, thus explaining long-term climate and magnetic phenomena while implying that Earth's internal processes are in sync with astronomical cycles. • The hierarchical order of resonances links stellar system evolution to planetary and subplanetary phenomena, as cosmic-scale processes constrain quantum properties and vice versa. https://doi.org/10.5281/zenodo.4724219 7 This integrated perspective offers a unifying framework that challenges traditional views that compartmentalize quantum physics, geophysics, and astronomy from each other. The recognition of macroscopic quantum coherence in planetary systems opens avenues for novel interpretations of Earth's history, including mass extinctions, magnetic field behavior, and tectonic activity. It likewise reveals a new perspective on studying stellar systems and exoplanets. Conclusions Using the best available data and analysis tools, I confirmed my earlier theoretical derivation of gravity via the speed of light at both quantum and everyday macroscopic scales, and Hyperresonance Unifying Theory[16], which together unified physics of the two scales by utilizing only high-school algebra (https://arxiv.org/abs/physics/0608026, https://arxiv.org/abs/0801.0876). The here presented discovery revealed a mega-paradigm shift: of Earth's global geophysical phenomena becoming appreciated as emergent properties of a macroscopically quantum, self-organized dynamical system, modulated through mechanical resonance at multiple scales (energy levels) in a step-wise fashion rather than classically through principles of a series of mutually largely incompatible continuum paradigms that we (for historical reasons only) call scientific disciplines and subdisciplines. By inverting the current scientific worldview, in which the frequency space is merely a byproduct and peculiarity of microscales (with everything beyond regarded as burst-driven if not field-confined; but always merely energy-described), the cross-scale gravitational resonance network and its cross-scale domain took over the place of the sole fundamental position of future physics. This absolute inversion of scientific "dogma" dramatically enhances our predictive capabilities concerning scale-invariant dynamics: on Earth, in issues such as geomagnetic reversals, climate shifts, and planetary stability; and universally, in cross-scale considerations, at all scales at once. References 1. Weinberg, S. Rev. Mod. Phys. 61, 1 (1989). 2. Barrow, J.D., Tipler, F.J. ISBN 0-19-851949-4 (1986). 3. Tegmark, M. et al., Phys. Rev. D 73, 023505 (2006). 4. Davies, P.C.W. Rep. Prog. Phys. 79, 102901 (2016) 5. Rampino, M.R., Stothers, R.B. Nature 308, 709 (1984). 6. Hinnov, L.A., Annu. Rev. Earth Planet. Sci. 41, 387 (2013). 7. Vaníček, P., Astrophys. Space Sci. 4, 387 (1969); 12, 10 (1971). 8. Cande, S.C., Kent, D.V. J. Geophys. Res. 100, 6093 (1995). 9. Wilczek, F. Phys. Rev. Lett. 109, 160401 (2012). 10. Shapere, A., Wilczek, F. Phys. Rev. Lett. 109, 160402 (2012). 11. Rampino, M.R. et al., Geoscience Frontiers 12, 101 (2021). 12. Yao, N., Nayak C., Phys. Today 71, 40 (2018). 13. Guo, L. et al., Phys. Rev. Lett. 111, 205303 (2013). 14. Svensson, I. et al., Phys. Rev. Lett. 121, 247601 (2018). 15. Clarke, J. et al. Nature 310(5977), 553 (1984); Science 229(4716),1071 (1985). 16. Omerbashich, M. J. Eur. R. Soc. 1:5-11 (2012). BIB: 2012JERSY...1....5O https://doi.org/10.5281/zenodo.4724219 1 Supplemental Material for “Spectral evidence from global geomagnetic calibration for stellar-system resonances constraining both quantum physics and geophysics” by Mensur Omerbashich, Geosciences Online, [email protected], [email protected], [email protected] This document includes extended methodology, data tables, additional figures, and expanded discussion referenced in the main Article. Earth’s macroscopic system of planetary cycles exhibits quantum-like coherence analogous to phenomena observed in superconducting circuits. Shannon theory-based Gauss-Vaníček spectral analysis (GVSA) of geomagnetic, impact-cratering, and extinction data revealed that the Earth's precession period, p≈26·103 yr, and its harmonics, drive many-body resonant entrainment with astronomical forcing. The resulting quasiperiodic structures in paleodata, phase-locked to obliquity, with ¼-lockstep fractional harmonics, reveal conditions reminiscent of a quantum time crystal—discrete time-translation symmetry and fractional phase locking—at planetary scales. Suppressing precessional frequencies in GPTS-95 calibration residuals isolates the 26.5-My Rampino signal as the driver of geomagnetic polarity reversals, supporting the interpretation that planetary-resonant energy transfer underlies the Milankovitch mechanism. Earth’s cross-scale coherence demonstrates that planetary precession is a primary driver of magnetic reversals at all scales within the Earth vicinity and potentially of Earth expansion and phenomena like the Great Unconformity. The view that processes akin to those in quantum systems drive Earth's long-term cycles (geomagnetic reversals, climate oscillations, geologic events) revolutionizes our understanding of Earth's internal processes, framing them as part of a larger, universal resonance phenomenon—within a unifying framework connecting geodynamics, astrophysics, and quantum physics—rather than merely classical mechanics. Quantum-like behavior—here exposed as intrinsically variable beyond Earth’s tidal domain—emerges in macroscopic systems on astronomical scales, revealing that quantum physics is a set of physical phenomena localized to and driven by the host star and stellar system and therefore likely fundamentally varying across the known universe. The ubiquity and universality of the tidal phenomenon strongly suggest that particle mass estimates, including those of dark matter, dark energy, and the Higgs boson, could be explained by stellar system and planetary-scale geodynamic resonances rather than solely by fundamental quantum properties. Foundations of physics; Foundations of quantum physics; Foundations of geophysics; Spectral analysis; Gravitational resonance networks; Time crystals; Macroscopic quantum coherence; Geomagnetic reversals; Milankovitch and long-period astronomical cycles; Earth expansion and planetary growth; Periodic mass extinctions; Great Unconformity. https://doi.org/10.5281/zenodo.4724219 2 Highlights • Macroscopic quantum coherence is demonstrated in planetary dynamics, analogous to superconducting circuits. • Quantum behavior is tidally localized, varying across planetary systems via resonance constraints. • The Earth–Moon–Sun triad forms a measure-preserving dynamical system, acting as a natural discrete time crystal. • Strong computational evidence links macroscopic planetary dynamics to quantum principles. • Precession resonance drives many-body entrainment, modulating geomagnetic polarity and stratigraphy through discrete time-translation symmetry (including doubling, halving, and tripling). • The 26.5-My Rampino cycle is identified as the carrier wave of geomagnetic and climatic resets. • Accumulated annual timing discrepancies (Equation of Time) project secularly onto paleodata as a global imprinting mechanism. • Resonant energy transfer provides a physical mechanism for the Milankovitch theory, with phase-locking (¼-lockstep) to obliquity triggering resonant coupling. • Results suggest a quantum-mechanical basis for Earth’s long-term, gradual expansion, sustained by persistent precession-driven resonances. • Shannon-theory-based Gauss–Vaniček spectral analysis (GVSA) models nonlinear global dynamics directly. Preprints https://doi.org/10.5281/zenodo.4724219 https://arxiv.org/abs/2301.02578 https://doi.org/10.5281/zenodo.4724219 9 3. Methodology To examine the effects of astronomical forcing on paleodata, I spectrally analyze age calibration of the currently accepted timescale of geomagnetic polarity reversals, spanning the Cenozoic (0– 84 My ago) — the revised Geomagnetic Polarity Time Scale 1995 (CKGPTS95; also cited in the literature as GPTS-95) by Cande and Kent (1995), Table 1 and their Table 1. The CKGPTS95 calibration leans on the South Atlantic Anomaly (where the strength of the geomagnetic field is decreasing most rapidly) sequence and consists of nine control points adjusted astrochronologically. At the control points, the sedimentary record is tied in with the astronomical record (Hilgen, 1991) so that the CKGPTS95 has excellent sensitivity primarily to the Earth's (theoretical) 25.7-ky axial precession (Shackleton et al., 1990) and possibly to the ~28-ky (apsidal) precession as well (Hilgen, 1991), while tuning to an eccentricity cycle of 412.9-ky was also performed, which was unlike values other workers used (Puetz et al., 2016). As embedded in the timescale itself, the so-boosted (systematic) signal becomes an integral part of the overall spectral information, thus easing energy-band (variance-) stratification and enabling the separation of actual astronomical periods from any (individually relatively weak) harmonics. Besides, the CKGPTS95 has stood the test of time with its peers — unlike any other timescale. https://doi.org/10.5281/zenodo.4724219 10 Table 1. Age calibration points for two related geomagnetic polarity timescales extending to end-Campanian. Left panel: for the currently accepted timescale CKGPTS95 (Cande & Kent, 1995). Right panel: for the superseded timescale CKGPTS92 (Cande & Kent, 1992). The facts that calibration points are the most accurate representation of a geological timescale, that CKGPTS95 has stood the test of time like no other timescale, and that the Gauss–Vaníček Spectral Analysis (GVSA) can draw the most accurate spectra from only three values — are used in the present study to investigate relations among astronomical forcing and reflections or harmonics recorded in paleodata. CKGPTS95 CKGPTS92 Polarity Chron Age [My] S. Atlantic dist. [km] Polarity Chron Age [My] S. Atlantic dist. [km] C3n.4n(o) 5.23 84.68 C2An(0.0) 2.60 41.75 C5Bn(y) 14.80 290.17 CSBn(0.0) 14.80 290.17 C6Cn.2r(y) 23.80 501.55 C6Cn,2r(0.0) 23.80 501.55 C13r(.14) 33.70 759.49 C13r(.14) 33.70 759.49 C21n(.33) 46.80 1071.62 C21n(.33) 46.80 1071.62 C24r(.66) 55.00 1221.20 C24r(.66) 55.00 1221.20 C29r(.3) 65.00 1364.37 C29r(.3) 66.00 1364.37 C33n(.15) 74.50 1575.56 C33n(.15) 74.50 1575.56 C34n(y) 83.00 1862.32 C34n(0.0) 83.00 1862.32 https://doi.org/10.5281/zenodo.4724219 11 I deal with spectral bands from just above the Earth's ~26 ky precessions down to 40 My since astronomical timescales (cyclostratigraphy-based numerical timescales) are reasonably well established for much of Cenozoic time (from the beginning of the Oligocene (~34 My) to the present); older parts have less-complete disconnected cyclostratigraphies referred to as "floating astrochronologies" (Tanner & Lucas, 2014). Besides, beyond 40 My, the accuracy of astrochronological timescales critically depends on the correctness of orbital models and radioisotopic dating techniques, e.g., Westerhold et al. (2012; 2015). To obtain the periodic signal, I use the Gauss–Vaníček rigorous method of spectral analysis (GVSA) by Vaníček (1969, 1971). The GVSA belongs to the least-squares class of spectral analysis techniques, has many advantages over the Fourier class of spectral analysis techniques in analyzing sparse natural data of long spans (Press et al., 2007), and has proven itself by providing absolute extraction accuracy in analyzing even extremely gapped paleodata (extinction) records (Omerbashich, 2021, 2007b, 2006). A GVSA spectrum, sj, is obtained at a spectral resolution k (here 1000 spectral values throughout), for k corresponding periods Tj or frequencies ωj and output with spectral magnitudes Mj, as: 𝑠𝑠𝑗𝑗�𝑇𝑇 𝑗𝑗,𝑀𝑀𝑗𝑗�; 𝑗𝑗 ∈ ℤ,𝑗𝑗= 1 … 𝑘𝑘 ∧ 𝑘𝑘 ∈ ℵ . (1) In its simplest form, i.e., when there is no a priori knowledge on data constituents such as datum offsets, linear trends, and instrumental drifts, a GVSA spectrum s is computed as (Omerbashich, 2004): 𝒔𝒔�𝜔𝜔𝑗𝑗,𝑀𝑀𝑗𝑗�=𝒍𝒍 T·𝒑𝒑�𝜔𝜔𝑗𝑗� 𝒍𝒍 T·𝒍𝒍 , (2) https://doi.org/10.5281/zenodo.4724219 12 obtained after two orthogonal projections. First, of the vector of m observations, l, onto the manifold Z (Ψ) spanned by different base functions (columns of A matrix) at a time instant t, 𝚿𝚿=[cos 𝜔𝜔𝜔𝜔, sin 𝜔𝜔𝜔𝜔], to obtain the best fitting approximant 𝒑𝒑=∑𝑐𝑐𝑖𝑖 𝚿𝚿𝑖𝑖 𝑚𝑚 𝑖𝑖=1 to l such that the residuals 𝒗𝒗 �=𝒍𝒍 − 𝒑𝒑 are minimized in the least-squares sense for 𝒄𝒄 �=(𝚿𝚿T𝐂𝐂𝑙𝑙 −1𝚿𝚿)−1 ·𝚿𝚿T𝐂𝐂𝑙𝑙 −1𝒍𝒍. The second projection, of p onto l, enables us to obtain the spectral values, Eq. (2). Vectors 𝒖𝒖𝑗𝑗= 𝚿𝚿T 𝚿𝚿NK+1 and 𝒗𝒗𝑗𝑗=𝚿𝚿T 𝚿𝚿NK+2, j = 1, 2…. NK∈א, compose columns of the matrix 𝐀𝐀NK,NK = 𝚿𝚿T 𝚿𝚿. Note here that the vectors of known constituents compose matrix 𝐀𝐀 �m,m=𝚿𝚿 �T 𝚿𝚿 �, in which case the base functions spanning the manifold Z(Ψ) get expanded by known-constituent base functions, 𝚿𝚿 �, to 𝚿𝚿=�𝚿𝚿 �,cos 𝜔𝜔𝜔𝜔, sin 𝜔𝜔𝜔𝜔�. For a detailed treatment of GVSA with known data constituents, see Wells et al. (1985). Subsequently, the method got simplified into nonrigorous (strictly non-least-squares) formats like the Lomb-Scargle technique created to lower any computing burden of Vaníček’s pioneering development, but that is no longer an issue. At the same time, the conventional Fourier transform and spectrum are just special cases of a more general least-squares formulation (Craymer, 1998). As mentioned, the GVSA provides total (absolute) accuracy in extracting periods from natural data sets — meaning at the prescribed accuracy of analyzed data themselves — of twice the sampling step or data accuracy (Omerbashich, 2020b; 2020a; 2007a). Fed raw data, GVSA outputs spectral peaks with spectral magnitudes in variance percentages (var%) against linear background noise levels, or dB (Pagiatakis, 1999). Such processing enables relative spectral computations whose results for physical systems are then variance- (directly energy-) stratified. This procedure is unlike that used for any other spectral analysis method. Relative analyses using GVSA include detecting field dynamics (Omerbashich, 2006; 2003), separation of forcers and harmonics, suppressing selected periods to reveal underlying dynamics, and computing spectra https://doi.org/10.5281/zenodo.4724219 13 of spectra to separate overlying dynamics from the respective system already dynamical. GVSA revolutionizes physics by enabling direct computations of nonlinear dynamics, rendering classical approaches such as spherical approximation obsolete (Omerbashich, 2024b; 2024a; 2023b; 2023a). I use this multifaceted ability of the GVSA to separate harmonics from their drivers and identify oscillation triggers. GVSA is strict in that, besides estimating a uniform spectrum-wide statistical significance in var% for the desired level, say 95%, in a spectrum from a time series with m data values and q known constituents as 1–0.952/(m–q–2) (Steeves, 1981) (Wells et al., 1985), it also imposes an additional constraint for determining the validity of each significant peak individually — the fidelity or realism, Φ. Fidelity is a general information measure in advanced statistics based on the coordinate-independent cumulative distribution and critical yet previously neglected symmetry considerations (Kinkhabwala, 2013). In communications theory, fidelity measures how undesirable it is (according to some fidelity criterion we devise) to receive one piece of information when another is transmitted (Shannon, 1948). In GVSA, fidelity thus is defined in terms of the theory of spectral analysis as a measure of how undesirable it is for two frequencies to coincide (occupy the same frequency space of a sample). Then a value of GVSA fidelity is obtained as that time interval (in units of the timescale of the time series analyzed) by which the period of a significant spectral peak must be elongated or shortened to be π-phase-shiftable within the length of that time series. As such, Φ measures the unresolvedness between two consecutive significant spectral peaks (those that cannot be π-phase-shifted). When periods of such spectral peaks differ by more than the fidelity value of the former, those peaks are resolvable. As the degree of a spectral peak’s dependence or tendency to cluster, this criterion reveals whether a spectral peak can share a systematic nature with another spectral peak, e.g., be https://doi.org/10.5281/zenodo.4724219 14 part of a batch or an underlying dynamical process like resonance or reflection. The spectral peaks that meet this criterion are listed in the LSSA software output among insignificant and the rest among significant (hereafter: physically-statistically significant spectral peaks or just (fully) significant for short). Then in the present study, input data are used in their raw form, i.e., without preprocessing such as dataset padding or various types of filtering (including windowing or tapering); historically, the intention for such techniques for vastly massaging data was to help overcome drawbacks of classical methods such as Fourier's. Finally, I apply no post-processing, used by some to enhance spectra. The declared precision of the periodicities extracted in the present study is ±10 years throughout. While the minimum number of values GVSA can compute a frequency spectrum from is three, Table 1, the method does not depend on the Nyquist frequency (Craymer, 1999). The above factors, combined with the unprecedented abilities of GVSA, such as handling extremely (>99.99%) depopulated records in their raw form with ease and extracting both field dynamics and over-dynamics (dynamics of dynamics), made the CKGPTS95 the most suitable gauge for examining effects that astronomical cycles and their modulations have on paleodata timing methods and consequently on any other natural periodicity in those data as well. Thus, separating those two types of periodicity (in timescale; in paleodata) should be possible using GVSA. https://doi.org/10.5281/zenodo.4724219 15 4. Probing CKGPTS95 timescale of geomagnetic polarity The GVSA of the CKGPTS95 nine calibration values, Table 1, has revealed two ≥99%- significant periodicities in the 0.02–40.00-My full band. Those periods are Earth axial precession, p=25.00 ky (theoretical median: 25.77 ky), and Earth apsidal precession, p1=29.81 ky (theoretical maximum: 29.00 ky), Fig. 1. Note here that the p=25.00 ky is the strongest and statistically most significant periodicity found in the present study; Olsen (1986) reported the same axial-precessional value in the large-lakes sedimentary record, and it often is used to tune geological timescales astronomically, thereby methodologically (artificially) boosting its power but not overwhelmingly, i.e., not absorbing other periodicities to suppression below significance. Thus, and as was desired from a conventional quality timescale, there were no further ≥99%- significant periodicities in the 1–40-My narrowed band, which, however, did contain ten peaks significant at ≥95%, Fig. 2. The longest was P=9.34737 My, while the remaining 9 are its reflections ordered in a series Pi=P/i, i=1…n; n ∈ ℤ+. The P=P1 itself is the same peak detected recently by Omerbashich (2021) from the nonmarine tetrapods’ extinctions record that here is particularly suitable due to its insensitivity to the ocean-tidal component as the most persistent systematic noise constituent. Thus, P turned out to be just a circular (2π-) modulation of the axial-precessional period, p. Namely, from the vector representation of harmonic oscillation (Den Hartog, 1985), for the 1-yr base oscillation in the case of the Earth, one obtains theoretically: Ptheor=360°∙ptheor=9.27792 My; ptheor=25.772 ky, which is matched by the here measured P, to within 7‰ or 69.45 ky or ~2.7 × precession (or approximately twice the CKGPTS95 tuning accuracy, of one precession cycle). This highly-precise computation of a resonant response and its driver (both the enhanced p and naturally arising 2π-phase-shifted p) is yet another demonstration of the ability of the https://doi.org/10.5281/zenodo.4724219 16 GVSA to extract spectra with the absolute facility (of twice the data accuracy), even from very long-spanning and heavily gapped records of data. Note here that a commonly understood statistical fidelity threshold that indicates a physical process is ϕ=12 (Omerbashich, 2006). If most of the system periods obtained from sparse data were previously reported or are otherwise known as natural periods (astronomical or physical) or their phase-shifted or time-symmetrical modulations (multiples or fractions), then of interest is relative ϕ primarily. Figure 1 (replicated from the main Article for completeness). Gauss–Vaníček spectrum of the currently accepted geomagnetic polarity timescale CKGPTS95 (calibration), Table 1, in the 20 ky–40-My full band. The only ≥99%-significant periods are the apsidal-precessional, p1=29.81 ky (theoretical maximum: 29.00 ky), and the axial-precessional, p=25.00 ky (theoretical median: 25.77 ky). Spectral peaks’ respective statistical fidelity values overlaid with the power trend. Frequencies are depicted (here and throughout) in cycles per galactic year (here 250 My), c.p.g.y. https://doi.org/10.5281/zenodo.4724219 17 Mathematically suppressing, see, e.g., Taylor and Hamilton (1972) and Wells et al. (1985), i.e., ignoring (thereinafter: enforcing) the axial-precessional period as realized by CKGPTS95, of 0.02500 My, and apsidal-precessional period, of 0.02981 My, has made them both disappear below the ≥99%-significance level, enabling a separation of the two respective groups of reflections as well, Fig. 2 (shows 1–40 My narrow band, no enforcing). The spectra of the now superseded timescale CKGPTS92, previously created by Cande and Kent (1992), contained in the 0.02–40-My full band the axial-precession period, as 0.025 My, then its 0.02401-My reflection, and the overestimated 0.03863-My apsidal precession period — all three at the ≥99%-significance level and with fidelities negligible at ϕ<10-5. At the ≥95%-significance level, the superseded GPTS92 timescale was also found periodic in the 1–40 My long band, again with the P=9.34737-My circular precessional modulation, whose fidelity was a still low ϕ=0.5. However, there detected were five reflections, all disordered: 4.31208 My with ϕ=0.1, then 4.13793 My with ϕ=0.1, 1.72606 My with ϕ=0.02, 1.64831 My with ϕ=0.02, and 1.40048 My with ϕ=0.01. Finally, the GVSA spectrum of the current timescale CKGPTS95 in the 40–80-My extended band contained no peaks at any level of significance. Note that enforcing does not denote a literal data intervention, as no data get removed. Rather systematic contributions (influences) of select periods are suppressed (Wells et al., 1985) via the process of enforcing selected periods. When further systematic information is sought and presumed to underlie an already systematically dominated record of interest, the residual time series (leftovers from the enforcing) can also be spectrally analyzed. This procedure can expose secondary dynamics hidden due to the record’s dominant periodicity, like resonance. https://doi.org/10.5281/zenodo.4724219 18 Figure 2 (replicated from the main Article for completeness). The GVSA spectrum of the currently accepted geomagnetic timescale CKGPTS95 (calibration), Table 1, in the 1–40-My long band, from raw data (no preprocessing including any padding, filtering, or tapering). There are no ≥99%-significant spectral peaks, as expected after narrowing the band, which has left out only two ≥99%-significant periods from the spectral band of interest, Fig. 1, as they both are <1 My. At the ≥95%-significance level are the lead (main) modulation P=9.34737 My, and all of its eight fractional harmonics (2π/n modulations of the axial precession), ordered in a series Pi=P/i, i=1…n, Table 2. Further analysis, in which axialand apsidal-precessional periods get mathematically suppressed, e.g., Taylor and Hamilton (1972), i.e., ignored (thereinafter: enforced), has enabled the separation of the reflections, revealing four of nine periods as predominantly axial precession’s reflections and four apsidal precession’s reflections, respectively. One of the reflections was due to a combined effect of the two precessions. As in Fig. 1, the respective statistical fidelity values for spectral peaks are shown with the power trend overlaid. https://doi.org/10.5281/zenodo.4724219 25 times and to astronomical phenomena other than precessions, primarily the obliquity (which then is a candidate for a resonance trigger). Projector errors largely depend upon the initial conditions under which the entrainment has originated and then locked, so paleodata periods' errors reflect those flaws. Inherent CKGPTS95 errors are also due to phase relations between astronomically forced and sedimentary captured timing always being approximate and known accurately only for the last 5–10 My (Hilgen, 1991). Note here that the accumulation occurs alongside neither of the axes, i.e., neither in period nor magnitude. Instead, the accumulating happens across the time domain so that the averaging of the variation sampled by paleodata for a noticeable spectral change to arise happens already on millennial scales. Therefore, it does not take millions of years for the above-depicted projector effect to accumulate to a shape resembling that of ΔT, as this occurs already on millennial scales. That is why higher-order harmonics are approaching ΔT better than lower-order harmonics can. Likewise, the ΔP and ΔT curves eventually coincide for the infinite data span. The superseded CKGPTS92 timescale, ΔPo (dotted line), has revealed only the initial ~40% of the projector effect and thus performed relatively worse. Besides, enforcing precessional cycles has left no ≥99%-significant peaks in the GVSA spectrum of the superseded CKGPTS92. https://doi.org/10.5281/zenodo.4724219 26 Figure 4. The GVSA spectrum of CKGPTS95 timescale calibration, Table 1, after enforcing the modulated driver P, Fig. 2, and the apsidal-precessional period, 29.81 ky, Fig. 1. All ≥99%- and ≥95%-significant periods from Figures 1 & 2 vanish below significance. The axial (strongest) precessional period, p, was not enforced, so the spectrum depicts only direct (p-driven) dynamics due to precession affecting the reversals but not due to precessional resonance anymore. As seen from this separation (of a resonance driver from its resonance), since the remaining dynamics are insignificant, the Earth axial precession alone, with period p, is not responsible for the reversals (sampled by the CKGPTS95 calibration points as the most variable/noticeable segment of the geomagnetic field and thus that timescale’s most reliable aspect). However, a uniform background-noise level indicates that another systematic physical process contributes to the dynamics of the reversals. Bar line: the width of the bars corresponds to the local clustering of two or more spectral peaks that did not resolve better than half the spectrum’s variance percentage range. The area enveloping white space under a cluster is proportionate to the bar-line blackness and vice-versa. The bar line depicts the change in clustering with a decrease in period length, indicating that a physical process still underlies geomagnetic reversals, albeit weakly. As seen, systematic noise clusters in the band’s low end, thus dominating the information. Towards the high end, the systematic noise overpowers all other contents while resolving better (seen as spectral peaks splitting more regularly) due to the absence of other systematic contents. https://doi.org/10.5281/zenodo.4724219 27 Any physical system driven by a periodic external field shows a discrete time translation symmetry (Guo et al., 2013). Then rigid subharmonic entrainment can be observed in many-body subharmonic responses (Yao et al., 2020), providing a conceptual framework to interpret EarthMoon-Sun resonances observed in geophysical data. Indeed, such a response is also characteristic of Faraday instabilities (waves or patterns) (ibid.), identified by Omerbashich (2020a) as the Solar system’s common polygonal (hexagonal mostly) cratering and patterning. Here entrainment means the mode-locking between coupled oscillators of different periods in which they assume a common period (Strogatz, 2000). The Earth’s subharmonic response Pi to the Earth-Moon-Sun system’s orbital dynamics, Figs 1 & 2 and Table 2, is one such entrainment seen from the system falling into lockstep with ¼p’, or rather ¼ of the obliquity’s annuallysecularly modulated period, P’; Fig. 5. This find confirms the obliquity as (a major) one of the triggers of Earth’s resonant response to external (primary tidal) forcing. Other triggers include undulating topography, varying crustal thickness, uneven distribution of inner masses, and mantle flows. Previously, such a subharmonic response — with the fundamental frequency’s ¼lockstep to the driver frequency — was believed to be characteristic of a discrete (quantumscale) time crystal only, e.g., Yao & Nayak (2018). However, as shown in the present study, (macroscopic) Faraday-instable multi-rigid-body systems such as our Solar system exhibit this lockstep too, and its extracted value turned out to be ¼ the driver. While Yao et al. (2020) conjectured that the classical time crystals could exist in nature on macroscopic scales, e.g., in Langevin dynamics of molecular systems, Puetz et al. (2014) statistically found that the astronomical and geological cycles could be phase-locked synchronously, with biological cyclicities lagging, but offered no terrestrial cause. https://doi.org/10.5281/zenodo.4724219 28 Additionally, discrete time translation symmetry has been experimentally observed in a resonator forced externally by another quarter-wavelength resonator — both as period multiplication but mainly as doubling, halving, and tripling (all in parametrically driven tunable superconducting resonators) and as 2π phase shifts accompanied by intensely magnified radiation (in resonators with frequencies n∙ω close to multiples n=2, 3, 4 and 5 of the resonator's fundamental mode) (Svensson et al., 2018). Besides, a global resonance on Earth occurs when the phase delay owed to propagation is proportional to 2π (Nickolaenko & Hayakawa, 2002). Here, the period multiplication (including doubling, halving, and tripling), the 2π phase shifts (of both p and p’), and the ¼ lockstep (to p’), all characterize the present study’s find from the GVSA of CKGPTS95 calibration, as well. Detection of all three fundamental properties of a discrete time crystal in macroscopic Faraday instability like the Earth-Moon-Sun system reveals a cross-scale nature of time crystal. The translation symmetry, most often in the form of tripling, doubling, and halving of periods, was previously observed in paleodata in the ∼30–∼1600 My band; see, e.g., Prokoph and Puetz (2015), while ~3P is often reported in the geophysical literature for 1–40 My band too, most recently by Rampino et al. (2020) as 27.5 My, i.e., 3P to within 2%. However, like with most such reports, that reported period was extracted using inapt techniques (Omerbashich, 2021) that cannot decouple resonances from drivers, resulting in a claim of physical significance and causality by way of galactic motions, among other proposed but unsubstantiated explanations. The computations thus far showed that the CKGPTS95 timescale, constructed based on the nine adjusted calibration values in Table 1, is highly accurate. By inclusion, the GVSA of the CKGPTS95 has shown that most inaccuracies in the fundamental radiometric decay constant can https://doi.org/10.5281/zenodo.4724219 29 be ruled out (Cande & Kent, 1992), except for a systematic error in the decay constants used in K/Ar dating (Hilgen, 1991). 6. Triggering mechanisms To identify or rule out any triggering mechanisms of the precessional resonance due to orbital forcing (more precisely: the triggers of Earth mechanical resonance due to energy transfer from orbital periods that include direct and mixed effects of orbital resonances), any individual orbital forcing first must be separated. As mentioned earlier, an inherent feature of variance spectra that GVSA uses is a linear depiction of background noise levels. This depiction streamlines relative spectral computations and analyses. So in the following, I first separate drivers from the resonances. Then I compute spectra of spectra to separate any overlying and underlying dynamics from the respective system (the entire information contents) that presumably is systematically dynamical already. Enforcing the phase-shifted precessional driver P and the apsidal-precessional cycle p' was sufficient to make all periodicity in the GVSA spectrum of CKGPTS95 vanish below significance, Fig. 4. This vanishing has demonstrated that, according to CKGPTS95, all dominant (significant) cycles over the past 83 My related to polarity reversals were also related to the precessional resonance but not to the main (axial) precession itself. No secondary field dynamics existed that precessional resonance dampened. Moreover, the successful separation of the resonance driver from its resonance, Fig. 4, showed that the slightest disturbances in the precession could also be resonance generators. Finally, the apsidal precession p1 could play a role in stimulating the creation of that disturbance and co-triggering the precessional resonance. https://doi.org/10.5281/zenodo.4724219 30 Figure 5. The 1–20-My-band GVSA spectrum of the CKGPTS95’s precession-free spectrum from Fig. 4. As indicated by their statistical fidelity, only the first two ≥99%-significant periods are of interest. While insufficiently statistically significant to render the two spectral peaks significant physically as well, the relative variance- (thereinafter: power-) dominance in the P’=3.56977 My period makes it alone the Earth’s superperiod (superimposed period) that controls other periods in a system. Like with the P relative to p, P’ also is 2π-phase-shifted, relative to ¼p’, which means that the Earth-Moon-Sun system fell into the ¼ lockstep with the Earth’s obliquity that can be viewed then as a co-trigger of the Pi resonance. Unlike a spectrum of a time series, which tells about repetitiveness in data and can thus expose causal physical mechanisms, a spectrum of a spectrum can tell about any repetitiveness of cycles themselves and thus expose overlying system dynamics. Such a procedure in global dynamics studies can have a physical meaning only if dominant dynamics previously are enforced (or ignored, as a more appropriate term given the context). The band was narrowed further to 1–20-My, as methodologically the strictest approach possible, to shift the remaining power to the sub-band of interest; this is justified because floating astrochronologies dominate the data beyond the beginning of Oligocene (~34 My) (Tanner & Lucas, 2014). https://doi.org/10.5281/zenodo.4724219 31 This result — that there is no continuous forcing of the reversals, but there are harmonics instead — is supported by Lutz (1985), who found no significant periodicity in geomagnetic reversals and pointed out that long periods in paleodata are either harmonics or not well-defined. Since astronomical tuning left some room in our case for deciding if the precession causes reversals itself, the uniform (i.e., with the highest spectral peaks virtually leveled) noisebackground level in Fig. 4 reveals the existence of some other systematic modulation that partakes in the dynamics of reversals. Observing such a modulation mechanism would likely represent the first proof of precessional resonance; see Hinnov (2013) for a review of (orbital) precession resonance studies. Note that orbital resonance among heavenly bodies can indeed cross-scale-translate via energy transfer into mass (particle) resonance on the resonantly affected bodies of mass (Omerbashich, 2020b, 2020a). Based on statistical analyses, Carbone et al. (2006) claimed that a physical process underlines the geomagnetic polarity reversal phenomenon. If real, such a process could also affect the timescale that here was freed of potentially detrimental effects of astronomical tuning. To test their claim, I use a bar-line descriptor of clustering and plot the change in local clustering with the decrease in period length, Fig. 4. As seen from the clustering getting somewhat resolved towards the spectral band’s high end, there does appear to be a physical process underlying geomagnetic reversals. Besides, as expected from systematic noise, the spectrum resolves better (with the decrease in period length), i.e., spectral peaks split more regularly towards the highend, to a discernable local declustering that then permeates throughout the highest frequencies as their general tendency towards declustering. Therefore, in addition to the virtual flatness of the highest noise peaks, we can see that systematic noise is not lonely in defining spectral https://doi.org/10.5281/zenodo.4724219 32 information contents. In short, the clustering indicates that the noise appears conjoined by a systematic physical process, thereby corroborating (ibid.). To verify this statistical conclusion further, and in the physics realm primarily, I compute the spectrum of the spectrum from Fig. 4. Spectra of spectra have been used for a long time (for example, to investigate alternate states of matter, namely in demonstrations of the Bose–Einstein condensate). Computing spectrum of a spectrum (rather than comparing individual spectral peaks as done classically) is an inherent ability of GVSA thanks not only to the method’s linear representation of spectral background (magnitudes) but also to straightforward statistical analysis incorporated into the spectral computation itself. In this way, and unlike statistical approaches alone (such as reanalyzing spectra of post-enforcing residuals), all modulations — including those arising from combined effects of two or more periods — can be observed or enforced (ignored) simultaneously. Here the 1–40-My-band spectrum of the same-band spectrum of (now precessions-free) CKGPTS95 can tell us about the dynamics of the process overlying the geomagnetic reversals, should such a process exist and be systematic (periodic) in its nature. The spectra computed in the present study apply to any future design modifications of the CKGPTS95 and other geological timescales. In the 1–20-My band, GVSA of the CKGPTS95 (precession-free) spectrum from Fig. 4 returned a frequency spectrum with six peaks significant at the ≥99% level and eight at ≥95%, see Fig. 5. The lowest spectral peaks at ≥99% were P’=3.56977 My with ϕ=0.16, and 2.78506 My with ϕ<0.1. Note here a two-magnitudes-of-order overall drop in spectral magnitudes compared to the CKGPTS95 spectrum itself, Fig. 5 vs. Figs 1–2 & 4, which makes the ϕ=0.16 of P’ indicative of a physical process as well, albeit again an adynamical (or relatively low-energy) one. The 3.5-My period was reported first by Olsen and Kent (1999), who also found its ½ https://doi.org/10.5281/zenodo.4724219 33 harmonic 1.75-My. They identified those cycles in the large-lake sedimentary record and claimed those periods as the first geological evidence of the chaotic behavior of the inner planets. For them, the 1.75-My (3.5-My) does not correspond to anything in the modulation of precession — but could be a long-period modulation cycle of obliquity, in which case it must come from indirect forcing (ibid.). Indeed, as seen in Fig. 5, the spectrum of the (precessions-free) spectral peaks of CKGPTS95, where timescale periods formed a new time series essentially freed from conventional astronomical ties, has revealed P’ as a trigger (indirect forcer) of the geomagnetic reversals record. Note that, for a long time, some authors have also offered the obliquity and precession as (semantically) underlying, i.e., controlling variables in the Milankovitch theory as well; see, e.g., Hays et al. (1976). That P’ is another astronomical modulation (now of the obliquity), is seen as before in the case of P (Den Hartog, 1985), so for the 1-yr base oscillation, one obtains theoretically: ¼∙GVSAp’theor=3.56977 My / 360°=9.916 ky, which matches the Earth obliquity’s cycle that, as seen here, maintained the lockstep: ¼p’theor=41 ky / 4=10.250 ky, to within 3.3%. Since P’ was obtained indirectly (from spectra of spectra, to free the data trends of the built-in precessions chronology), the normalized achieved accuracy could be up to an order of magnitude better, to around 3‰. This possibility also follows from looking at the period it overpowered, of 2.78506My, Fig. 5, which itself is 2π-phase-shifted, i.e., a circular modulation of the 3/10 harmonic of theoretical precession ptheor=25.772 ky, i.e., 360°∙(3/10)p, to within just 0.6‰. Excellent matching to the theoretical precession rather than precession realized in the CKGPTS95-adjusted strata is owing to the above-described methodology, namely combined separation of driver from resonance via computation of the spectra of spectra. Additionally, this overpowering of the precession’s second-longest and second-strongest phase-shifted modulation by the obliquity’s https://doi.org/10.5281/zenodo.4724219 34 longest and thus strongest modulation is direct evidence that, in their interplay, it is the obliquity which at least partially controls the precession (and thus indirectly the precessional resonance too) and not the other way around. Indeed, as seen from Figs 2 & 5, P modulates Pi as a forcer (driver) significantly — so that the Pi are its well-defined harmonics (continuous unity-fractions) rather than reflections (intermittent integer multiples). Then as seen from the spectrum of CKGPTS95 spectrum, Fig. 5, and by the very existence and placement of P’, this P’ itself is the period superimposed ("superperiod") to P and any P-harmonics. This interplay, in turn, means that the obliquity acts on the precession indirectly: due to the projector effect and the resulting phase shift, Fig. 3, P’ impresses upon P instead of p’ impressing upon either p or p1 (or both). Note here that the detection of a precessional resonance in the 1–40 My band was enabled in part by methodological band-pass filtering of orbital tuning, which modeled noise in the immediate spectral vicinities of p and ¼p’ by focusing spectral power from surrounding frequencies to the Milankovitch bands; see, e.g., Hinnov (2000). In the same sense, note that the Universal Wave Series (UWS) harmonic periods in the 1ky–1-My band (Puetz et al., 2016) are a hint at the precessional resonance as demonstrated here to be originating in the 1–40-My band and independent proof that resonance harmonics generally are recoverable from astronomically tuned timescales. Besides, given the methodology used and the number of calibration points, the P’ fidelity normalized to at least an order-of-magnitudelarger value does appear sufficient for P’ to be called outright physically significant (dynamical) and for its ¼p’ base to be recognized as the cause of the chaotic behavior of the inner planets, as inferred by Olsen and Kent (1999). Also, P’ is among the most powered periods detected in the present study, right after the axial-precessional period, p, and its circular modulation, P. Then, https://doi.org/10.5281/zenodo.4724219 41 Stratigraphic record Planetary resonance GVSA of CKGPTS95-spectrum’s residuals (0–83 My), p & P enforced g4-g3 [My] s4-s3 [My] period [My] Φperiod magnitude [var%] NEOGENE Pleistocene–Miocene (0–9 Ma) δ18O sea level Miller et al. (2005); Boulila et al. (2011) 1.2 1.11905 0.00110 73.75 MIOCENE-OLIGOCENE (20–34 Ma) Benthic marine δ18O Ocean Drilling Program (ODP) Site 1218 Pälike et al. (2006); Boulila et al. (2011) 1.2 1.11905 0.00110 73.75 CRETACEOUS Aptian–Albian (100–125 My) Scisti a Fucoidi, Italy Grippo et al. (2004); Huang et al. (2010) 1.5 1.60695 0.00230 87.69 TRIASSIC–JURASSIC Norian-Pliensbachian (205–184 My) Inuyama Chert, Japan Ikeda and Tada (2013) 1.6–1.8 1.60695 1.83749 0.00230 0.00300 87.69 82.73 TRIASSIC Carnian–Rhaetian (230–200 My) Newark Series, USA Olsen (2010) 1.7 1.60695 1.83749 0.00230 0.00300 87.69 82.73 TRIASSIC Anisian–Ladinian (245–237 My) Inuyama Chert, Japan Ikeda et al. (2010) 1.8 1.83749 0.00300 82.73 PERMIAN Wuchiapingian–Changhsingian (251–260 My) Wujiaping-Dalong Formations Wu et al. (2013) 3.11 3.18584 0.00910 76.29 Compilations Average lead cycle [My] GVSA of CKGPTS95-spectrum’s residuals (0–83 My), p & P enforced ENDING WITH PALEOPROTEROZOIC Holocene–Orosirian (0–2023 My) Compilation of 58 cratering & 35 mass-extinction reports Rampino and Prokoph (2020) 26.5 (mass extinctions) ~26 (craters + mass ext.) 26.53386 0.63000 77.02 Various paleodata period [My] GVSA of CKGPTS95-spectrum’s residuals (0–83 My), p & P enforced PERMIAN/TRIASSIC Holocene–Permian/Triassic (0–253 My) Mass-extinction episodes Raup and Sepkoski (1984) 26.4 26.53386 0.63000 77.02 ENDING WITH PALEOPROTEROZOIC Holocene–Orosirian (0–2023 My) Cratering record Chang and Moon (2005) 26.4 26.53386 0.63000 77.02 https://doi.org/10.5281/zenodo.4724219 42 8–b. Extraction of periods previously reported from cratering and extinctions I now extract periods reported previously as dominant in cratering and mass extinction records. Note that the most significant period revealed from the precession-free geomagnetic reversals CKGPTS95 calibration, of 26.5 My and at a very high magnitude of 77.0 var% with a moderate Φ=0.63 (nonetheless relatively highest of any period extracted in the present study), could not be identified as a resonance reflection or harmonic. This period has been reported previously by Rampino and Prokoph (2020) as the average dominant cycle in the first comprehensive compilation of 58 reports of cratering and 35 reports of mass extinctions and here, therefore, termed the Rampino period, PR. (Note that Raup and Sepkoski (1984) and Chang and Moon (2005) came significantly close to the same value from an extinctions record spanning 0–253 My and a cratering record spanning 0–150 My, respectively, Table 3.) Compiled periods were based on numerous entirely dissimilar methods and approaches to computing and analyzing spectra. This period reveals a powerful wave (the sole and dynamical actor) as it affected the solid Earth. Besides, it is of the highest fidelity found on any period extracted in the present study. Its remarkable power is stressed even further when we know it took the entire precessional resonance train (ensemble) to hide it. PR is so pure and persistent that it appears even as a co-driver of other (the short-period; ky-) harmonics, Table 4. However, it does not emit longer-period harmonics, revealing that the resonance confines it to (many) relatively short intervals of time — disallowing it by the nature of the resonant process itself to be ever encountered by the entire geological record. Since also supported by the combined cratering-extinctions record and the extinctions record alone, PR most likely represents the precessional resonance’s crosscyclic (multi-harmonic) carrier of the peak angular deflection. Here cratering is mainly understood as petrified evidence of large-scale https://doi.org/10.5281/zenodo.4724219 43 polygonal geomorphology seen throughout the Solar system due to the imprinting of actual solid-matter resonance waves via macroscale Faraday latticing into the molten material (melted on impact as well, in a snapshot fashion). In the same sense, originally polygonal crater edges eventually erode into circular shapes (here the most realistic scenario) rather than the other way around, i.e., from circular into polygonal geometries as believed by some (the least plausible scenario since erosion takes much longer time than melt impression); see Omerbashich (2020a). The decisive role of precessional mechanical resonance for Earth is particularly plausible since found in both the cratering and the calibration as the most accurate portion of the currently accepted (timescale of the) geomagnetic polarity reversals record. These multiple detections from seemingly disparate data mean that the precessional resonance is directly, and the precession and obliquity in tandem indirectly (along with geomorphology varying in crustal thickness), responsible also for the geomagnetic reversals. Finally, Rampino and Prokoph (2020) deduced that records of cratering and mass extinctions are somehow connected. Indeed, their fundamental connection follows from the above computational result directly: not only is the precessional resonance long-term destructive (mainly causing geomagnetic excursions — started but never completed reversals — that therefore appear as gradual processes while masking the cataclysmic nature of the reversals) but also strictly terrestrial and incessant. Then the record of mass extinctions is a record of the destruction of evidence of life during Transformative Resonant Events (TRE) instead of the periodicity of mass extinctions themselves (note that only evidence of a few remarkable mass-extinction events is beyond doubt in geology). This unavoidable inference questions most, if not all, past claims of periodic mass extinctions. The well-established fact that life always appeared to have sprung back incredibly fast following an extinction event (ibid.) inevitably reveals the circular logic of the proponents of https://doi.org/10.5281/zenodo.4724219 44 periodic mass extinctions, making the mass-extinction records work just the same in the opposite direction — as evidence of the no-mass-extinction scenario of life on Earth. Besides, the fact that (35 globally random) extinction episodes can average to the value of the dominant period of geomagnetic reversals and that a combined record (of 35 global extinction events and 58 cratering events) does so within half-order of magnitude is remarkable itself because it reveals that all three phenomena — polarity reversals, polygonal “cratering” (commonly misunderstood as always and only the impact cratering), and “periodic” extinctions are due to a single process. (Here, extinctions are presumed regardless if represented by the record of extinctions or their sample’s violent decimation like what large igneous provinces had done to the geological record, e.g., Prokoph and Puetz, 2015). Most importantly, since the average of dominant periods, as returned from globally randomly sampled and diverse data sets, match the dominant periodicity of one of those global phenomena exactly, the underlying physical process must be ergodic. Thus, there is nothing chaotic about those processes, including the geomagnetic field whose recent ergodicity is established (De Santis et al., 2011). Then extraction of the Rampino period means a data-based confirmation of geomagnetism's overall ergodicity. The data of alleged (periodic or otherwise) extinctions support this possibility: the average intensity of extinction of marine life during the Phanerozoic has decreased, i.e., changed on a steady downward trend, while the number of families increased unobstructed; see Figs. 1 & 2 of Newman and Sibani (1999). Namely, Fig. 1 in (ibid.) shows the extinction rate in families per My for marine organisms as a function of time (callout: origination rate for the marine organisms), while Fig. 2 in (ibid.) depicts the number of known families of Phanerozoic marine organisms, as a function of time (linear trend dashed; exponential trend dashed) (callout: the integrated percentage extinction of families). Note here https://doi.org/10.5281/zenodo.4724219 45 that trends are steady but non-monotonic and, due to sensitivity to the ocean tidal component as the most persistent systematic noise constituent, marine genera somewhat exaggerate the trending. Thus it is implausible that most, if not all, species had developed over time natural resistance of the same kind and at the same level or extent to the causes of extinction since that would imply thousands of factors to coincide and remain congruent over half a billion years at least. This steady drop in extinction intensity resembles energy dissipation of an underlying physical process, and the increase in the number of families (and lifespan too, as later studies have shown), both correspond to a scenario without any extinctions whatsoever, i.e., as if geophysical upheaval responsible for geomagnetic reversals and cratering has also decimated the record of species but not the species themselves. The orbital-mechanical resonance, which arises due to energy transfer, is a process that fits the above description: it naturally dissipates over very long (hundreds-of-My-) intervals, only to rebound at other times, all while destroying (via harmonics or PR) any petrified evidence of speciation systematically-periodically. The conclusion that the constant drop is a sign of an underlying resonance is supported by a steady global in-size reduction of polygonal (resonant) geomorphology, such as patterning and cratering. Specifically, such geomorphology has changed from ancient kilometre-scale shapes like the polygonal (mostly hexagonal) craters of Faraday latticing seen throughout the Solar system to metre-scale shapes like the patterns in present-day salt deserts on Earth; see Omerbashich (2020a) and Lasser (2019), respectively. https://doi.org/10.5281/zenodo.4724219 46 Table 4. Values of the ≥95%-significant GVSA spectral peaks from the 0.02–40-My spectral band of the geomagnetic reversals’ currently accepted timescale, CKGPTS95, Table 1. The ≥99%-significant periods are plotted in Fig. 1. Compared to Table 2 (showing the same but in the 1–40-My band), the extraction of the above periods was affected by the power of the precession cycle, p, as one of the clearest periods found in the present study. The four clusters of split periods are shown as declustered (represented by one period per cluster). The above-listed, short (ky-) periods are mostly harmonics of P – circular modulation of precession p; P’ – circular modulation of ¼p’ obliquity; and PR – Rampino period, of 26.5 My (Rampino & Prokoph, 2020). Note that a precessional 20.41-ky period and its 5/2-modulation to within <1%, 50.54-ky, are crosscycles of both Rampino harmonics and precessional circular modulation’s harmonics (making it clear that P dominates PR rather than the other way around). This direct P-PR connection confirms PR as the most relevant and potent for orbital-mechanical resonance energy transfer. Note that the most efficient feature of mechanical resonance in terms of the ability to relay destruction is its magnification effect via frequency demultiplication, which upsurges the energy resonantly injected into a physical system by 100s of times (Den Hartog, 1985). GVSA of CKGPTS95-spectrum’s residuals (p and P enforced) harmonic period [My] Φperiod mag [var%] 0.14974 0.0001400 78.61 0.09775 0.0000610 75.07 0.06977 0.0000310 78.46 P/134 0.06929 0.0000310 74.59 P/135 0.06543 0.0000280 73.49 0.05054 0.0000160 74.34 P/185, PR/525 0.04267 0.0000120 77.72 P/219 0.04010 0.0000100 73.32 0.03863 0.0000096 85.65 P/242 0.03346 0.0000072 79.57 PR/793 0.03334 0.0000071 86.19 P'/107 0.02951 0.0000056 89.23 P'/121 0.02422 0.0000038 78.45 P/386 0.02041 0.0000027 73.50 P/458, PR/1300 0.02037 0.0000027 75.38 https://doi.org/10.5281/zenodo.4724219 47 https://doi.org/10.5281/zenodo.4724219 48 Figure 6. Time-domain-superimposing all claims of periods in mass extinctions, as compiled by Rampino and Prokoph (2020) (Table 1 in there), reveals the virtual impossibility of life on Earth. All periods were used (regardless of statistical significance) due to the inherent inability of Fourier and other classical methods for spectral analysis to correctly estimate statistical significance on spectral peaks (Erlykin et al., 2017, 2018). The plot reveals the impossibility of life on Earth in the Phanerozoic (the last half a billion years). The point of origin was selected at -200 My, as being around the middle of the Phanerozoic. The plot assumes all life originated at an instant or during a short interval (of several My). Bar line: Grayness represents life, and blackness is the impossibility of life. Bin spreads fixed at 1 My represent macroevolutionary bursts (minimum time required for a single evolutionary step to develop adaptively in a species) per Uyeda et al. (2011). The 10-My bin is a gauge best fitting the overlap intervals, averaging the time for which most species continue after an extinction event (cf., Barnes et al. (2021) who found that most species continue for more than 30 My past an extinction, while many drops in diversity without recovery are not associated with mass extinction events at all). The dashed arc depicts a resonance period (wave) as it rolls out in the time domain. Based on the varying spread in overlapping, the plot rules out galactic cyclic causes of mass extinctions, revealing that life on Earth would be practically impossible if most of the reports alleging periodic mass extinctions were results of using reliable data and proper preparation and processing techniques. Instead, the precessional resonance via its carriers of destructive angular deflections (here the 26.5-My Rampino period, Table 3, and lower-order harmonics) causes polarity reversals, on Earth during TREs while simultaneously decimating strata — including the record of (thus “periodic”) mass extinctions. https://doi.org/10.5281/zenodo.4724219 49 Finally, superimposing in Fig. 6 of all previously alleged mass-extinction periods in the time domain reveals that either life during Phanerozoic (including today) could not exist or the periodic mass-extinctions are not real. Note that the obliquity-induced precessional resonance does not outright discard mass extinctions as such, like the Permian–Triassic Extinction Event. Instead, the record of evolution gets decimated together with, or within a short time from, topography-reformatting TREs. This reasoning agrees with the recent finding that most species continue after an extinction event for more than 30 My, while many post-event drops in diversity without recovery are not associated with mass extinction events (Barnes et al., 2021). In addition, pre-Milankovitch views that climate periodicity is due to changes in Earth’s magnetic field (Puetz et al., 2016; Raup, 1985) made sense only due to the geomagnetism record’s dominant bias in the same way. Then geomagnetism polarity reversals, polygonal “cratering”, and “periodic” mass-extinction records describe the same phenomenon of obliquity-triggered precessional mechanical resonance that causes stratigraphically recorded changes — in geomagnetism and cratering primarily. This recording is due to actual resonance waves in the solid matter (Faraday latticing), but only apparent changes in evolution — as evolutionary evidence (residing embedded within solids) gets exposed to damaging resonance waves. Note here that, while the geomagnetism record gets decimated too, it is the least affected type of solidmatter-residing paleodata since only simultaneous total (rarest) reshaping of entire continents can alter that record significantly in terms of its systematic information contents. Other examples of GVSA’s ability to compute resonances in data at absolute accuracy and ≥99% or ≥95% significance levels include resonance extractions from time-series of Mw5.6+ earthquakes’ occurrences for solid Earth (Omerbashich, 2020b) and from moonquakes for solid Moon (Omerbashich, 2020a), both cases also reporting ≥89%- and ≥67%-significant harmonics https://doi.org/10.5281/zenodo.4724219 50 as well, all the way up to 1/72 of the forcer in the case of solid Earth. Besides, Omerbashich (2022) showed from continuous GPS data that GVSA can absolutely (i.e., to the accuracy of the measurements) accurately extract solid-matter resonance as it forms actual particle waves. Worth noting here is the main difference between detecting orbital resonances transferred directly (mechanically and by way of gravity) into the solid matter along particle waves and those impressed into gaseous matter indirectly as a temporally undersampled powerless signal: while in the latter case, characteristic of various types of paleodata, statistical fidelity of so extracted resonance periods is typically Φ<12 and often Φ<<1 and even Φ<<<1, in the former case it is regularly Φ≥12 and often Φ>>12 and even Φ>>>12. For example, while dealing with >99% populated time-series, (ibid.) found in the extractions that fidelity occupied the 12–11 ranges on the shortest and had reached the ranges of values as high as 60,000–9,000 on the longest periods. 9. Identification of moderation carrier Next, I examine the phase relations of PR to P to verify that the Rampino period, PR, does represent the precessional resonance’s crosscyclic (multi-harmonic) carrier of the peak angular deflection. Should such a causal relation exist, it would expose PR as a modulation of the already phase-shifted precession p. In that case, PR would also be the primary modulation of P, and thereby the only sole actor besides (2πp, Pi) resonance in the 1–40 My band. Since not an orbital period itself, we cannot expect PR also 2π-phase shifted, i.e., in the same way as precession and obliquity did. Then, since PR was extracted as a sole actor only once — in the absence of (p, Pi), how P modulates PR is determined entirely by the effects of annual variation in the Equation of Time on P itself, Fig. 3. Puetz et al. (2016) already showed an effect https://doi.org/10.5281/zenodo.4724219 57 in the Jurassic–Early Cretaceous carbon cycle also physically significant. They even proclaim it “an important metronome of the greenhouse climate dynamics” — all based on statistics alone. Other workers, however, do recognize this modulation as physically unrealistic and proceed on to examine possible non-orbital causes for its presence; see, e.g., Boulila et al. (2012) study of a ~9-My pseudoperiod in Cenozoic carbon isotope record δ13C but who also fail to explain the presence of this pseudoperiod. In an assessment of a recent example from a nonmarine tetrapod extinction record (compiled by Rampino et al., 2020) insensitive to the oceantidal component as the most significant constituent of systematic noise, Omerbashich (2021) found that most, if not all, the periods claimed previously as mass-extinction cycles are instead astronomical reflections — of Earth’s axial precession primarily, i.e., n∙p. A mass-extinctions period of 27.5 My extracted using circular and Fourier methods from their compilation and cratering by Rampino and Caldeira (2015) was questioned previously by Meier and Holm– Alwmark (2017) over circular method use and then by Omerbashich (2021) over Fourier method use. As mentioned, (ibid.) showed that the 27.5-My period is just a ~3P modulation (the abovediscussed tripling in multi-rigid-body resonances, e.g., Prokoph and Puetz, 2015). Previously, Omerbashich (2006, 2007b) had demonstrated from a flawed report by Rohde and Muller (2005) that data manipulations and inapt methods like the Fourier class of spectral analysis techniques can result in a detection of apparently significant periods in marine diversity data as well. Since P is controlled primarily by the Earth’s own orbital (annual) cycle, subsequently driven into secular, centennial, millennial modulations, and on — the total modulation of P extends virtually ad infinitum. Thus, the results of the present study are precession rateindependent and readily applicable to any geological interval to Triassic, thanks to the strict nature of paleomagnetism primarily (Berger, 2012), but also beyond since the main find is https://doi.org/10.5281/zenodo.4724219 58 strictly astronomical in origin. For example, 10P and 100P/7 reflections were first reported by Omerbashich (2006) from the Sepkoski fossils record as 91.3-My and 140.23-My at the ≥99%- significance level. Boulila et al. (2018) confirmed the former of the two periods but also reported a ~9.3-My cyclicity as previously attributed to the long-period Milankovitch band and based on the Cenozoic record. In addition, (ibid.) reported a ~250-My megacycle they even attributed to tectonic-causal mechanisms. However, this periodicity also is just an annually-secularly induced reflection 100P/4, Fig. 3. The reason for the latter period to be so persistent (very long) is that it is a crosscycle — amplified and maintained by the 70P’ reflection as well, Fig. 5. Other reports of reflections — sensationally declared to be key or even justified by cryptic galactic causes — fill the literature and are often picked by national and international media in search of a sensation more. In one of the most notorious examples, Boulila (2019) reported the “prominent ~9 and ~36 My” cyclicities in Cenozoic–Cretaceous benthic foraminifera δ18O, but a look at Fig. 3 tells that those are just annually-secularly induced P and its ~4P reflection, respectively. The only reason the often reported ~36-My period appears so persistent and omnipresent across the geological record is that it too is a crosscycle — amplified by 10P’ reflection, Fig. 5, as well as the 2π (circular) modulation 360°∙p’’, where p’’ is the Earth eccentricity astronomical period, of ~100 ky. More of similarly simple mathematical relations are noticed readily among detected periods in paleodata. For example, looking at the nine periods from Table 2 of Omerbashich (2021), the 33.84146-My period is just the 8.48624-My period quadrupled, or 6.67870-My quintupled, while the 11.93548-My period is simply the 7.95129-My period tripled-halved and so on. As mentioned earlier, these subharmonic relations — doubling, halving, and tripling primarily — represent discrete time translation symmetry characteristic of subharmonic resonant https://doi.org/10.5281/zenodo.4724219 59 response of multi-rigid-body systems to external periodic forcing. For instance, the abovediscussed ~3P periods are often reported in the literature, but such reports used mostly inept techniques unable to even distinguish resonances from resonance drivers. The type of result obtained in the present study calls for an addition to the Milankovitch theory (see, e.g., Berger, 2012) to differentiate among varying power of the Milankovitch — as demonstrated here — resonant cycles. This varying power from one to another resonance wave explains the 100-ky cyclicity problem of that theory — the otherwise inexplicable termination events when astronomical cycles (and, in the sense of resonance theory, their reflections or harmonics) switch in the role of planetary change driver. The latest recorded event of glacialinterglacial switching, the Mid-Pleistocene Transition, occurred ~1 My ago. At that time, the ~40-ky period gave in to the ~100-ky period (Bajo et al., 2020). This event resembles an energytransfer event across frequencies — the relatively brief period of nonlinear resonance (Rial et al., 2013), here demonstrated to be incessant due to astronomical forcing. The difficulties in assigning physical mechanisms to generate the gain necessary to power the 100 ky cycles led Liu (1992) to examine frequency resonance phenomena among the orbital parameters as an alternative source for the transition, and he concluded that it is the Earth obliquity which modulates a major 100 ky periodicity (Hinnov, 2000). As shown earlier, and supporting that result, the Mid-Pleistocene switch from the obliquity’s p’ period to a 100-ky period was not a transition from obliquity to eccentricity as the Earth’s dominant climatic driver (for which there would be no explanation), but an obliquity-triggered resonant jump from one to another resonant frequency coincidentally near the duration of one eccentricity cycle. The orbitally induced and obliquity-triggered precessional resonance is the most reasonable physics-based, all-explanatory addition to the intellectually already pleasing Milankovitch theory. https://doi.org/10.5281/zenodo.4724219 60 The addition to the Milankovitch theory is overdue, so to recognize that that theory is just a special case of the far more complex Earth–Moon–Sun (rather: obliquity–precession–Earth) resonant energy transfer. Similarly, that theory’s spatiotemporal domain extends only for as long as a specialized energy band (currently determined by one of the tailing harmonics of the precessional resonance) of the resonant-dynamic energy band that, at present, envelopes and shapes our planet lasts before it dissipates. As it dissipates, it does it only to make room for another precessional-resonant energy band belonging to another resonance harmonic (and so on, until PR) and which will be describable by some other form of the Milankovitch theory — not entirely unlike the current one. The energy supplied thus to the Earth is globally cumulative since the Earth acquired the Moon ~4450 billion years ago, and thus the only known mechanism for a growing Earth proposed by many, e.g., Schmidt and Embleton (1981) and Maxlow (2021). It is also an all-inclusive explanation of the Great Unconformity — as a global resonant shake-off during a TRE (virtually instantaneous ubiquitous erosion of an entire chunk of strata, akin to more frequent decimations of life records in strata creating an impression of periodic mass extinctions). Omerbashich (2020a) proposed that the smaller of the two Mars’s moons be reassigned to Earth to create a permanent interference before the Earth reaches the state of energy overload and implodes. The present study revealed that the concept of time crystal known from quantum physics is also macroscopic at astronomical scales. This synchronization of quantum type in vibrations of dynamic structures at interplanetary and interstellar scales could arise tidally due to a satellite galaxy or universe — a common concept from astrophysics. In the first attempt to link the Milankovitch theory to Earth's internal processes at My time scales, Boulila et al. (2021) erroneously speculated that the most likely phenomenon linking insolation-climate with the https://doi.org/10.5281/zenodo.4724219 61 Earth's internal processes lies in climatically-resonantly driven mass changes on Earth surface, such as imagined sea level variations due to climate change. In their opinion, the potential link between external and internal processes would thus manifest as interaction and feedback rather than a direct orbital forcing of the solid Earth. However, as showed in the present study computationally and confirmed by exposing Earth's behavior as that of a gigantic macroscopic time crystal, the exact opposite holds instead: direct orbital forcing of the solid Earth, her interior, and the Milankovitch process has been taking place in unison since time immemorial. This cross-scale-verified computational discovery conclusively confirms the genuine nature of the South Atlantic Anomaly of the geomagnetic field low as a precursor of an upcoming reversal, contrary to recent speculations, e.g., by Nilsson and Muscheler (2022). 11. Conclusions Discrete time translation symmetry (seen commonly in paleodata as period multiplication and halving), 2π-phase-shifts, and ¼-lockstep to the forcer — previously thought to arise together only in a subharmonic response of a time crystal to external periodic forcing and to be confined to quantum scales — characterize the here reported global geophysical detection of the mechanism for geomagnetic polarity reversals from the CKGPTS95 timescale calibration as arguably the best record of paleodata available for this type of study. This result has fundamental implications as it directly relates phenomena from quantum physics and macroscopic astrophysics: the (planetary) time crystal is formed by the many-body entrainment causing precession resonance that, in turn, moderates (geo)magnetic polarity. In quantum dynamics, such particle entrainment can take the form of collisions, causing Feshbach resonances. https://doi.org/10.5281/zenodo.4724219 62 This fundamental property was arrived at by analyzing paleodata periods previously claimed in the literature as standalone-significant cyclicity (indicative of a dynamical process) but which turned out to be just multiples or fractions of other periods appearing in extinctions and other geological records. Thus previously claimed very long periods in paleodata, such as the often reported ~9-My, are primarily modulations of the Earth's axial precession. Together with respective modulations (reflections and harmonics), they arise resonantly under obliquity and other triggers such as varying crustal thickness, mantle flows, and inner-core dynamics — essentially any obstacles in the path of macroscopic Faraday instabilities. To avoid misattributing causality, future analyses of non-astronomical periodicity in paleodata should enforce (i.e., mathematically ignore) precession periods and their annual 2π-phase-shifted modulations and entire precessional resonance ensembles, depending on the band or scale of extraction. The global approach to treating the currently accepted CKGPTS95 timescale of geomagnetic polarity reversals, viewed as the gauge for analyzing planetary paleodynamics, has confirmed the general absence of lonesome (including extraterrestrial) mechanisms for periodic polarity reversals. At the same time, that approach enabled deducing the 0.02–40-My bands of resonance using the 26.5-My Rampino period as a carrier of cumulative resonant destruction of obstacles. As the orbital energy transfer occurs in these mechanical resonances, their lowfrequency part can become transformatively destructive and plate tectonics-catalyzing; this energy transfer constitutes a plausible energy-injecting mechanism for astronomical forcing of climate, albeit in previously underappreciated ways. Namely, the 2π-phase-shifted precessional resonance extracted here in the 1–40 My band potentially represents the scale-invariant energytransfer mechanism underlying the Milankovitch theory as a special case applicable to the current stage of the Earth-Moon-Sun resonant dynamics. https://doi.org/10.5281/zenodo.4724219 63 Sedimentary stratigraphy may therefore record this orbital-to-mechanical resonant energy transfer so that long-period (My) scales of resonant periodicity need not envoke a major extraterrestrial (galactic) or tectonic driver. Instead, the precessional resonance, during rare but cataclysmic Transformative Resonant Events (TREs) characterized by combined destructive interference and angular deflection of its most energetic parts via the 26.5-My Rampino carrier wave, could downward penetrate the inner core, envelope it, and mechanically flip Earth cores, thereby causing geomagnetic polarity reversals. In doing so, while modifying all solids, including the crust, these events may also decimate the geological record containing evidence of evolution, creating the apparent periodicity of mass extinctions and even strata voids like the Great Unconformity. Over geological history, this continuous resonance might have caused geomagnetic polarity excursions while masking sudden cataclysms under apparently gradual processes. Other geophysical theories previously dismissed for lacking mechanism, such as expanding Earth, may now appear more plausible. It can be speculated that the upcoming geomagnetic polarity flip may manifest as either a mere excursion or a full reversal; in the latter case, an accompanying TRE might occur. Given the thousands of harmonics between consecutive polarity reversals and the millions of minor reflections accumulated via repetitive annual imprinting (the projector effect), it might be plausible to assume that future architecture and urbanism should consider survival under protective habitats, such as underlake and undersea superbunkers independent of topography, until successful space colonization is achieved. While the present analysis focuses on geophysical mechanisms, the analogy to quantum time-crystal behavior underscores that resonance and periodicity are universal phenomena across scales. Additional research directions arise from the cross-disciplinary aspects of these results. It https://doi.org/10.5281/zenodo.4724219 64 can be speculated that applications of global geodynamics in quantum dynamics and vice versa may be fruitful. Specifically, the Earth-Moon-Sun triad was shown here to be in a coherent state resembling that of a quantum discrete time crystal. In quantum mechanics, a coherent state is one whose dynamics most closely resemble the oscillatory behavior of a classical harmonic oscillator. However, since quantum coherent states are difficult to maintain under thermal noise, and subscale instabilities cannot project perfectly onto the global system, it can be argued that quantum time crystals may, in fact, derive their observed behavior from macroscopic phenomena and never the other way around. Consequently, quantum (discrete) time-crystal phenomena, as well as entanglement, tunneling, and other quantum effects, might be considered less surprising when viewed from the planetary scale. Based on the cosmological and astrophysical principle of (always downwardly) continuing, cross-scale projecting of periodic gravitational phenomena and magnetic properties, we can expect that the Earth's resonant system sets the tone for all subscale resonances, including those at quantum scales and below. Accordingly, quantum physics may manifest differently outside the vicinity of Earth—as a highly localized phenomenon of higher-order tidal resonance constrained by the host stellar system. Because the tidal phenomenon is pervasive and general across the known universe, these considerations suggest that terrestrial (now simplistic) estimates of the masses of all fundamental particles—including quarks, leptons, gauge bosons, the Higgs boson, and also properties related to dark matter and dark energy (via accumulated effects of quantum and resonance variations across the universe)—whose mass calculations critically depend on local quantum fluctuations, are influenced or actually explained by higher-order nonlinear geodynamic tidal phenomena rather than solely by universal quantum properties. https://doi.org/10.5281/zenodo.4724219 65 Acknowledgments The spectra were computed using LSSA v.5 scientific software based on Vaníček (1969; 1971), http://web.archive.org/web/20220818070617id_/http:/www2.unb.ca/gge/Research/GRL/LSSA/s ourceCode.html. Statements The author declares no conflicts of interest. 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