Partial clones containing all Boolean monotone self-dual partial\n functions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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