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
We study a bichromatic version of the well-known k-set problem : given two sets R and B of points of total size n and an integer k , how many subsets of the form (R ∩ h ) ∪ ( B ∖ h ) can have size exactly k over all halfspaces h ? In the dual, the problem is asymptotically equivalent to determining the worst-case combinatorial complexity of the k-level in an arrangement of n halfspaces . Disproving an earlier conjecture by Linhart [1993], we present the first nontrivial upper bound for all k ≪ n in two dimensions: O ( nk 1/3 + n 5/6−ϵ k 2/3+2 ϵ + k 2 ) for any fixed ϵ<0. In three dimensions, we obtain the bound O ( nk 3/2 + n 0.5034 k 2.4932 + k 3 ). Incidentally, this also implies a new upper bound for the original k -set problem in four dimensions: O ( n 2 k 3/2 + n 1.5034 k 2.4932 + n k 3 ), which improves the best previous result for all k ≪ n 0.923 . Extensions to other cases, such as arrangements of disks, are also discussed.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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