On the generation of discrete figures with connectivity constraints
Why this work is in the frame
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Bibliographic record
Abstract
This paper addresses a generalization of polyominoes called ( a , b )- connected discrete figures , where a and b represent the connectivity of the foreground ( i.e. black pixels ) and background ( i.e. white pixels ), respectively. Formally, a finite set of pixels P is ( a , b )-connected if P is a -connected and P is b -connected. By adapting a combinatorial structure enumeration algorithm by J. L. Martin and employing breadth-first search ordering on the pixels of the figures, we sequentially generate all ( a , b )-connected discrete figures up to size n = 18, utilizing minimal storage space. This paper presents an extended version of the research presented at the 2022 GASCom conference.
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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 | 0.001 |
| 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