Extreme value attractors for star unimodal copulas
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Bibliographic record
Abstract
We determine maximum attractors for copulas star (or 2-) unimodal (about a point <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi mathvariant="normal">a</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">b</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∈</mml:mo> <mml:msup> <mml:mi mathvariant="normal">R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> ). If ( a , b )≠(1,1) these attractors form a two-parameter family of copulas extending that of Cuadras–Augé, whereas if ( a , b )=(1,1) they cover all maximum value copulas. We also examine the relationship between unimodality and Archimax copulas.
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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.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.003 |
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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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