Bibliographic record
Abstract
The surface entropic exponents of half-space lattice stars grafted at their central nodes in a hard wall are estimated numerically using the PERM algorithm. In the square half-lattice the exact values of the exponents are verified, including Barber's scaling relation and a generalization for 2-stars with one and two surface loops respectively. This is the relation ${\ensuremath{\gamma}}_{211}=2\phantom{\rule{0.16em}{0ex}}{\ensuremath{\gamma}}_{21}\ensuremath{-}{\ensuremath{\gamma}}_{20},$ where ${\ensuremath{\gamma}}_{21}$ and ${\ensuremath{\gamma}}_{211}$ are the surface entropic exponents of a grafted 2-star with one and two surface loops, respectively, and ${\ensuremath{\gamma}}_{20}$ is the surface entropic exponent with no surface loops. This relation is also tested in the cubic half-lattice where surface entropic exponents are estimated up to 5-stars, including many with one or more surface loops. Barber's scaling relation and the relation ${\ensuremath{\gamma}}_{3111}={\ensuremath{\gamma}}_{30}\ensuremath{-}3\phantom{\rule{0.16em}{0ex}}{\ensuremath{\gamma}}_{31}+3\phantom{\rule{0.16em}{0ex}}{\ensuremath{\gamma}}_{311}$ are also tested, where the exponents ${{\ensuremath{\gamma}}_{31},{\ensuremath{\gamma}}_{311},{\ensuremath{\gamma}}_{3111}}$ are of grafted 3-stars with one, two, or three surface loops, respectively, and ${\ensuremath{\gamma}}_{30}$ is the surface exponent of grafted 3-stars.
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How this classification was reachedexpand
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) | 0.001 | 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 teacher head, 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".