Recherche à voisinage variable de graphes extrémaux. 13. À propos de la maille
Bibliographic record
Abstract
Le systeme AutoGraphiX (AGX1 et AGX2) permet, parmi d'autres fonctions, la generation automatique de conjectures en theorie des graphes et, dans une version plus recente, la preuve automatique de conjectures simples. Afin d'illustrer ces fonctions et le type de resultats obtenus, nous etudions systematiquement ici des conjectures obtenues par ce systeme et de la forme $\underline{b}_{n} \, \le \, g \, \oplus \, i \, \le \, \overline{b}_{n}$ ou g designe la maille (ou longueur du plus petit cycle) du graphe G=(V, E), i un autre invariant choisi parmi le nombre de stabilite, le rayon, le diametre, le degre minimum, moyen ou maximum, et des fonctions de l'ordre n = |V| de G les meilleures possibles, enfin correspond a une des operations +,-,×,/. 48 telles conjectures sont obtenues: les plus simples sont demontrees automatiquement et les autres a la main. De plus 12 autres conjectures ouvertes et non encore etudiees sont soumises aux lecteurs.
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How this classification was reachedexpand
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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".