Bibliographic record
Abstract
Consider a model of partially directed paths from the origin in the square lattice, constrained to the region between the Y -axis and the line Y = qX , and ending in a vertex in this line (with coordinates of the form ( N , Nq ), and where q > 0 is an integer). Such paths are bargraph paths in a q -wedge. In this paper the adsorption of bargraph paths in the line Y = qX is examined. This model has generating function g q ( t , z ) where t is the edge generating variable and z is the generating variable of visits of the path to the line Y = qX . It is proven that the model undergoes an adsorption transition at the critical value of z q and that z q is given asymptotically by In other words, z q / q is given to decaying terms. Moreover, adsorbing bargraph paths in a 1/ p -wedge between the Y -axis and the line Y = (1/ p ) X , where p > 0 is an integer, are also considered. In these models it is shown that z 1/ p ≃ p 2 /2 log p 2 for large p .
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".