Classification of Voronoi and Delone tiles of quasicrystals: II. Circular acceptance window of arbitrary size
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Bibliographic record
Abstract
In this paper we describe all the Voronoi and Delone tiles arising in tilings of point sets Σ(Ω) ('quasicrystals') built by the standard projection of the root lattice of type A4 onto a two-dimensional plane spanned by the roots of the Coxeter group H2 (dihedral group of order 10). The acceptance window Ω for Σ(Ω) is a disc of any radius 0 < r < ∞. There are 22 distinct sets VTj (j = 1, ..., 22) of Voronoi tiles and eight sets DTk (k = 1, ..., 8) of Delone tiles, up to a uniform scaling by a factor τn where τ = 1/2(1 + √5) is the golden ratio and n ∊ .
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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