Bibliographic record
Abstract
Given a tournament T=(V,A), with each subset X of V is associated the subtournament T[X]=(X,A∩(X×X)) of T induced by X. A subset I of V is an interval of T provided that for any a,b∈I and x∈V∖I, (a,x)∈A if and only if (b,x)∈A. For example, ∅, {x}, where x∈V, and V are intervals of T called \emph{trivial}. A tournament is indecomposable if all its intervals are trivial; otherwise, it is decomposable. Let T=(V,A) be an indecomposable tournament. The tournament T is \emph{critical} if for every x∈V, T[V∖{x}] is decomposable. It is \emph{partially critical} if there exists a proper subset X of V such that |X|≥3, T[X] is indecomposable and for every x∈V∖X, T[V∖{x}] is decomposable. The partially critical tournaments are characterized. Lastly, given an indecomposable tournament T=(V,A), consider a proper subset X of V such that |X|≥3 and T[X] is indecomposable. The partially critical support of T according to T[X] is the family of x∈V∖X such that T[V∖{x}] is indecomposable and T[V∖{x,y}] is decomposable for every y∈(V∖X)∖{x}. It is shown that the partially critical support contains at most three vertices. The indecomposable tournaments whose partially critical supports contain at least two vertices are characterized.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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 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".