On the spectrum of critical sets in latin squares of order 2<sup><i>n</i></sup>
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Bibliographic record
Abstract
Abstract Suppose that L is a latin square of order m and P ⊑ L is a partial latin square. If L is the only latin square of order m which contains P , and no proper subset of P has this property, then P is a critical set of L . The critical set spectrum problem is to determine, for a given m , the set of integers t for which there exists a latin square of order m with a critical set of size t . We outline a partial solution to the critical set spectrum problem for latin squares of order 2 n . The back circulant latin square of even order m has a well‐known critical set of size m 2 /4, and this is the smallest known critical set for a latin square of order m . The abelian 2‐group of order 2 n has a critical set of size 4 n ‐3 n , and this is the largest known critical set for a latin square of order 2 n . We construct a set of latin squares with associated critical sets which are intermediate between the back circulant latin square of order 2 n and the abelian 2‐group of order 2 n . © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 25–43, 2008
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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 | 0.002 | 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)
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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