Adsorbing bargraph paths in a<i>q</i>-wedge
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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 gq(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 zq and that zq is given asymptotically by In other words, zq/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 z1/p ≃ p2/2 log p2 for large p.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it