Bibliographic record
Abstract
We present the first solution to finding τ -majorities on tree paths. Given a tree of n nodes, each with a label from [ 1 . . σ ] , and a fixed threshold 0 < τ < 1 , such a query gives two nodes u and v and asks for all the labels that appear more than τ ⋅ | P u v | times in the path P u v from u to v , where | P u v | denotes the number of nodes in P u v . Note that the answer to any query is of size up to 1 / τ . On a w -bit RAM, we obtain a linear-space data structure with O ( ( 1 / τ ) lg lg w σ ) query time, which is worst-case optimal for polylogarithmic-sized alphabets. We also describe two succinct-space solutions with query time O ( ( 1 / τ ) lg ⁎ n lg lg w σ ) . One uses 2 n H + 4 n + o ( n ) ( H + 1 ) bits, where H ≤ lg σ is the entropy of the label distribution; the other uses n H + O ( n ) + o ( n H ) bits. By using just o ( n lg σ ) extra bits, our succinct structures allow τ to be specified at query time. We obtain analogous results to find a τ -minority, that is, an element that appears between 1 and τ ⋅ | P u v | times in P u v .
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.016 | 0.004 |
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".