Generalized atmospheric sampling of self-avoiding walks
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Bibliographic record
Abstract
In this paper, we introduce a new Monte Carlo method for sampling lattice self-avoiding walks. The method, which we call 'GAS' (generalized atmospheric sampling), samples walks along weighted sequences by implementing elementary moves generated by the positive, negative and neutral atmospheric statistics of the walks. A realized sequence is weighted such that the average weight of states of length n is proportional to the number of self-avoiding walks from the origin cn. In addition, the method also self-tunes to sample from uniform distributions over walks of lengths in an interval [0, nmax]. We show how to implement GAS using both generalized and endpoint atmospheres of walks and analyse our data to obtain estimates of the growth constant and entropic exponent of self-avoiding walks in the square and cubic lattices.
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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