Bibliographic record
Abstract
In this paper we show the construction of 32 infinite series based on the law of decay of radioactive isotopes, which indicates that a radioactive parent isotope is reduced by 1/2 and 1/e of its initial value during each half-life and mean life, respectively. We found that the ratios among the values of the radioactive parent isotope and the radiogenic daughter isotope for each half-life’s and mean life’s decay can be used to construct 16 half-life related (or 2-related) and 16 mean life related (or e-related) infinite series. There are 8 divergent series, 4 previously known convergent series and 2 series converging to the Erdös-Borwein constant. The remaining 18 series are found to converge to 18 mathematical constants and the divergent and alternating mean life related series leads to another 2 mathematical constants. A few interesting mathematical relations exist among these convergent series and 5 sequences are also attained from the convergent half-life related series.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".