ON THE AREA OF THE FUNDAMENTAL REGION OF A BINARY FORM ASSOCIATED WITH ALGEBRAIC TRIGONOMETRIC QUANTITIES
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Bibliographic record
Abstract
Let F ( x , y ) be a binary form of degree at least 3 and non-zero discriminant. We estimate the area A F bounded by the curve | F ( x , y ) | = 1 for four families of binary forms. The first two families that we are interested in are homogenizations of minimal polynomials of 2 cos ( 2 π n ) and 2 sin ( 2 π n ) , which we denote by Ψ n ( x , y ) and Π n ( x , y ) , respectively. The remaining two families of binary forms that we consider are homogenizations of Chebyshev polynomials of the first and second kinds, denoted as T n ( x , y ) and U n ( x , y ) , respectively.
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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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| 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) | 0.001 | 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 it