Why this work is in the frame
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Bibliographic record
Abstract
ABSTRACT We consider playing the game of Tic‐Tac‐Toe on block designs BIBD and transversal designs TD. Players take turns choosing points and the first player to complete a block wins the game. We show that triple systems, BIBD, are a first‐player win if and only if . Further, we show that for , TD is a first‐player win if and only if . We also consider a weak version of the game, called Maker–Breaker, in which the second player wins if they can stop the first player from winning. In this case, we adapt known bounds for when either the first or second player can win on BIBD and TD, and show that for Maker–Breaker, BIBD is a first‐player win if and only if . We show that TD is a second‐player win, and so the second player can force a draw in the regular game by playing the same strategy.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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