Design theory and some forbidden configurations
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Bibliographic record
Abstract
Abstract In this paper we relate ‐designs to a forbidden configuration problem in extremal set theory. Let denote a column of 1's on top of 0's. Let denote the matrix consisting of rows of 1's and rows of 0's. We consider extremal problems for matrices avoiding certain submatrices. Let be a (0, 1)‐matrix forbidding any submatrix . Assume is ‐rowed and only columns of sum are allowed to be repeated. Assume that has the maximum number of columns subject to the given restrictions. Assume is sufficiently large. Then has each column of sum and exactly once and, given the appropriate divisibility condition, the columns of sum correspond to a ‐design with block size and parameter . The proof derives a basic upper bound on the number of columns of by a pigeonhole argument and then a careful argument, for large m , reduces the bound by a substantial amount down to the value given by design‐based constructions. We extend in a few directions.
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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) | 0.000 | 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