Partial clones containing all Boolean monotone self-dual partial\n functions
Bibliographic record
Abstract
The study of partial clones on $\\mathbf{2}:=\\{0,1\\}$ was initiated by R. V.\nFreivald. In his fundamental paper published in 1966, Freivald showed, among\nother things, that the set of all monotone partial functions and the set of all\nself-dual partial functions are both maximal partial clones on $\\mathbf{2}$.\nSeveral papers dealing with intersections of maximal partial clones on\n$\\mathbf{2}$ have appeared after Freivald work. It is known that there are\ninfinitely many partial clones that contain the set of all monotone self-dual\npartial functions on $\\mathbf{2}$, and the problem of describing them all was\nposed by some authors. In this paper we show that the set of partial clones\nthat contain all monotone self-dual partial functions is of continuum\ncardinality on $\\mathbf{2}$.\n
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".