Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Spiral tilings, as appealing as they are for their aesthetics, have not been studied well mathematically. One of the difficulties in this area of tiling theory is providing a mathematical definition of spiral tilings. A recently published attempt at providing a formal definition distinguishes a so-called L-spiral tiling (L-tiling) and an S-spiral tiling (S-tiling), with the two types being characterized by special properties of tile set partitions. Based on these existing definitions, we investigate the spiral structure in periodic tilings. Unlike spiral tilings, periodic tilings lend themselves easily to a definition and have been well studied. We first prove that it is not possible for periodic tilings to be S-tilings. We then study a subset of periodic tilings that can be L-tilings. In particular, we demonstrate that there exist examples for each type of isohedral tilings (a subset of periodic monohedral tilings) that are L-spirable.
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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 | 0.001 | 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) | 0.003 | 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