Bibliographic record
Abstract
Given a finite or infinite set S and a positive integer k, a {\em binary structure} B of base S and of rank k is a function (S×S)∖{(x,x); x∈S}⟶{0,…,k−1}. A subset X of S is an interval of B if for a,b∈X and x∈S∖X, B(a,x)=B(b,x) and B(x,a)=B(x,b). The family of intervals of B satisfies the following: ∅, B–– and {x}, where x∈B–– , are intervals of B; for every family F of intervals of B , the intersection of all the elements of F is an interval of B; given intervals X and Y of B, if X∩Y≠∅, then X∪Y is an interval of B; given intervals X and Y of B, if X∖Y≠∅, then Y∖X is an interval of B; for every up-directed family F of intervals of B, the union of all the elements of F is an interval of B. Given a set S, a family of subsets of S is weakly partitive if it satisfies the properties above. After suitably characterizing the elements of a weakly partitive family, we propose a new approach to establish the following \cite{I91}: Given a weakly partitive family I on a set S, there is a binary structure of base S and of rank ≤3 whose intervals are exactly the elements of I.
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.
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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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".