Hierarchical recurrence domains wtih 129600 year unit across Earth-system evolution revealed by stratigraphic boundaries and climate records

Technical Summary: Hierarchical Recurrence Domains with 129,600-Year Unit Across Earth-System Evolution

Problem Statement
Earth-system variability manifests across a vast spectrum of temporal scales, from orbital cycles to deep-time geological transitions. While specific periodicities (e.g., Milankovitch cycles) are well-established in Quaternary records, signals identified from different geological records are rarely evaluated within a common statistical framework. Existing claims of long-period recurrence in fossil diversity, extinction, and tectonics remain difficult to validate due to finite, unevenly sampled, and chronologically uncertain records. Furthermore, analytical choices and candidate ranges often yield conflicting preferred periodicities. This study addresses the lack of a unified framework to compare candidate recurrence domains across multiple orders of magnitude, distinguishing between robust empirical signals, dataset-dependent optima, and conceptual timescales.

Methodology
The study developed a multiscale analytical framework to evaluate seven target temporal domains (P1–P7), ranging from 129.6 kyr to 16.79616 Gyr. These domains were derived from a hierarchical cycle theory based on conversion factors of 12 and 30, anchored by a 129,600-year unit.

• Data Sources: The analysis integrated discrete stratigraphic boundaries from the International Chronostratigraphic Chart (ICS) and continuous proxy records (benthic $\delta^{18}$O, reconstructed temperature, sea level, ice volume, atmospheric CO$_2$, magnetochron boundaries, and orbital solutions).
• Hierarchical Matching: Different ICS levels were matched to specific domains: Eonothem for P6 (1.399 Gyr), Erathem for P5 (466.56 Myr), System for P4 (46.656 Myr), and Stage for P3 (3.888 Myr) and P2 (1.296 Myr).
• Analytical Techniques:
  • Discrete Events (P2–P5): Candidate periods were tested against geological boundaries using circular phase alignment and a resultant-based fit score ($score_R$). Chronological robustness was assessed via 2,000 timing-uncertainty realizations (Monte Carlo sampling of boundary ages).
  • Continuous Records (P1, P2): Lomb–Scargle spectral analysis was applied to handle uneven sampling. Band-limited decomposition and filtering were used to isolate specific frequency bands (e.g., 80–150 kyr).
  • Significance Testing: Statistical significance was evaluated using surrogate datasets (randomly distributed events for discrete data; AR(1) autoregressive surrogates for continuous data). Both local $p$-values and candidate-set global $p$-values (accounting for multiple testing across predefined candidates) were calculated.
• Scope: P1–P5 were evaluated empirically. P6 (1.39968 Gyr) and P7 (16.79616 Gyr) were treated as conceptual higher-order groupings rather than formally validated periodicities.

Key Results
The analysis revealed a hierarchical spectrum of candidate timescales rather than a single universal geological clock:

1. ~100-kyr Domain (P1): Late Quaternary climate records (benthic $\delta^{18}$O, temperature, sea level, ice volume, CO$_2$) consistently supported an approximately 100-kyr recurrence. This signal was robust across proxies, remained significant after family-wise error-rate (FWER) correction, and showed a shift from 41-kyr dominance to 100-kyr dominance during the Mid-Pleistocene Transition.
2. ~1.2–1.4-Myr Domain (P2): Results were dataset-dependent. Cenozoic ICS Stage boundaries preferentially selected 1.2 Myr, whereas magnetochron boundaries favored ~1.30 Myr, and isotope records ($\delta^{13}$C, $\delta^{18}$O) favored ~1.40 Myr. No single period achieved statistical significance across all proxies.
3. ~3.5-Myr Domain (P3): Within the 2.5–5.0 Myr candidate set, ~3.5 Myr emerged as the best-fitting candidate. It was selected in 67% of uncertainty realizations over the full Phanerozoic and 100% of realizations in the restricted 0–80 Myr window. While it showed strong relative stability, it did not reach candidate-set global significance.
4. ~46.656-Myr Domain (P4): Among intermediate-scale candidates (30–60 Myr), ~46.656 Myr produced the highest median fit score and was selected as the best candidate in 96% of uncertainty realizations.
5. ~500-Myr Domain (P5): Among long-period candidates (300–600 Myr), ~500 Myr was the most robust fit, selected with a probability of 1.00 across uncertainty sampling. However, like the 46.656-Myr candidate, it did not achieve candidate-set global statistical significance ($p > 0.05$).
6. Conceptual Domains (P6 & P7): The ~1.39968-Gyr domain was retained as a conceptual grouping of the pre-Phanerozoic record (approx. 3 segments of ~1.34 Gyr). The ~16.79616-Gyr domain was treated as a cosmological-scale envelope. Neither was formally tested for periodicity.

Significance and Claims
The paper claims to provide a unified framework that distinguishes between:

• Strong cross-proxy signals: Specifically the ~100-kyr recurrence in Quaternary climate.
• Robust relative preferences: Stable rankings for ~3.5, ~46.656, and ~500 Myr candidates, even in the absence of strict statistical significance.
• Dataset-dependent optima: The variation in preferred periods at the ~1.2–1.4 Myr scale depending on the proxy used.
• Conceptual timescales: Higher-order organizational hypotheses for deep Earth history.

The author concludes that Earth-system variability is best described as a "hierarchical spectrum of recurrence domains" rather than a single periodic clock. The study emphasizes that while certain timescales show reproducible relative preferences, the evidence currently supports them as robust candidates for future evaluation using independent geological and geochemical records, rather than as definitive proof of universal physical forcing mechanisms. The framework allows for the systematic evaluation of candidate domains while accounting for chronological uncertainty and multiple-testing biases.