Basis Enumeration of Hyperplane Arrangements Up to Symmetries.
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Bibliographic record
Abstract
Given a symmetry group acting on the hyperplanes of an arrangement, our goal is to report a single basis from each orbit of bases induced by this group. In this paper we extend previous techniques for finding the (feasible) bases of polyhedra up to symmetry, and for computing the symmetry groups of polyhedra, to the setting of hyperplane arrangements. We present some preliminary experiments with a C++ implementation of these techniques called Basil. These results show substantial speedups compared to a previous polyhedra only system using the computer algebra system GAP. We also measure the speedup due to a Gram matrix invariant, and show that the overhead of symmetry testing, while substantial, is dominated by the savings in reduced pivoting.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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