Formes quadratiques ternaires représantant tous les entiers impairs
Bibliographic record
Abstract
En 1993, Conway et Schneeberger fournirent un critère simple permettant de déterminer\nsi une forme quadratique donnée représente tous les entiers positifs ; le théorème\ndes 15. Dans ce mémoire, nous nous intéressons à un problème analogue, soit la recherche\nd’un critère similaire permettant de détecter si une forme quadratique en trois\nvariables représente tous les entiers impairs. On débute donc par une introduction générale\nà la théorie des formes quadratiques, notamment en deux variables, puis on\nexpose différents points de vue sous lesquels on peut les considérer. On décrit ensuite\nle théorème des 15 et ses généralisations, en soulignant les techniques utilisées dans la\npreuve de Bhargava. Enfin, on démontre deux théorèmes qui fournissent des critères\npermettant de déterminer si une forme quadratique ternaire représente tous les entiers\nimpairs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.048 | 0.008 |
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 source (direct Gemma or distilled Codex), 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".