On the Jacobian ideal of the binary discriminant
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Bibliographic record
Abstract
Let denote the discriminant of the generic binary d-ic.We show that for d 3, the Jacobian ideal of is perfect of height 2. Moreover we describe its SL 2 -equivariant minimal resolution and the associated differential equations satisfied by .A similar result is proved for the resultant of two forms of orders d, e whenever d e -1.If n denotes the locus of binary forms with total root multiplicity d -n, then we show that the ideal of n is also perfect, and we construct a covariant which characterizes this locus.We also explain the role of the Morley form in the determinantal formula for the resultant.This relies upon a calculation which is done in the appendix by A. Abdesselam.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 it