From eons to epochs: multifractal geological time and the compound multifractal - Poisson process
Bibliographic record
Abstract
Geological time is punctuated by events that define biostrata and the Geological Time Scale’s (GTS) hierarchy of eons, eras, periods, epochs, ages. Paleotemperatures and macroevolution rates, have already indicated that the range ≈ 1 Myr to (at least) several hundred Myrs is a scaling (hence hierarchical) “megaclimate” regime. We apply analysis techniques including Haar fluctuations, structure functions, trace moment and extended self-similarity to the temporal density of the boundary events (ρ( t )) of two global and four zonal series. We show that ρ( t ) itself is a new paleoindicator and we determine the fundamental multifractal exponents characterizing the mean fluctuations, the intermittency and the degree of multifractality. The strong intermittency allows us to show that the (largest) megaclimate scale is at least ≈ 0.5 Gyr. We find that the tail of the probability distribution of the intervals (“gaps”) between boundaries is also scaling with an exponent q D ≈ 3.3 indicating huge variability with occasional very large gaps such that it’s third order statistical moment barely converges. The scaling in time implies that record incompleteness increases with its resolution (the “Resolution Sadler effect”), while scaling in probability space implies that incompleteness increases with sample length (the “Length Sadler effect”). The density description of event boundaries is only a useful characterization over time intervals long enough for there to be typically one or more events. In order to model the full range of scales and densities, we introduce a compound multifractal - Poisson process in which the subordinating multifractal process determines the probability of a Poisson event and that this new process is close to the observed statistics. Scaling changes our understanding of life and the planet and it is needed for unbiasing many statistical paleobiological and geological analyses, including unbiasing spectral analysis of the bulk of geodata that are derived from paleoclimatic and paleoenvironmental archives.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".