On the Numerical Stability of the Precise Integration Time-Domain (PITD) Method
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Bibliographic record
Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this letter, the stability issue of the recently proposed 3-D precise integration time-domain (PITD) method is reinvestigated. It is found that the PITD is not unconditionally stable; its stability condition is strongly dependent on the preselected number of sub time-steps and sizes of numerical cells as well as the order of the approximation used. However, since the upper limit of time step is found to be proportional to the number of sub time-steps, the time step can be of a value much larger than the Courant–Friedrich–Levy limit of the conventional finite difference time domain. Numerical examples are presented to verify our analysis. </para>
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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 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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