Why this work is in the frame
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Bibliographic record
Abstract
Abstract Let = { a 0 + a 1 z + · · · + a n –1 z n –1 : a j ∈ ﹛0, 1﹜¯﹜, whose elements are called zero- one polynomials and correspond naturally to the 2 n subsets of [ n ] := ﹛0, 1, … , n – 1﹜. We also let = ﹛α( z ) ∈ : α(1) = m ﹜, whose elements correspond to the subsets of [ n ] of size m , and let , whose elements are the zero-one polynomials of degree exactly n . Many researchers have studied norms of polynomials with restricted coefficients. Using ‖α‖ p to denote the usual L p norm of α on the unit circle, one easily sees that α( z ) = a 0 + a 1 z +· · ·+ a N z N ∈ ℝ[ z ] satisfies and , where . If α( z ) ∈ , say α( z ) = z β1 + · · · + z β m where β 1 < · · · < β m , then c k is the number of times k appears as a difference β i – β j . The condition that α ∈ satisfies c k ∈ ﹛0, 1﹜ for 1 ≤ k ≤ n – 1 is thus equivalent to the condition that ﹛β 1 , … , β m ﹜ is a Sidon set (meaning all differences of pairs of elements are distinct). In this paper, we find the average of over α ∈ , α ∈ , and α ∈ . We further show that our expression for the average of over yields a new proof of the known result: if m = o ( n 1/4 ) and B ( n , m ) denotes the number of Sidon sets of size m in [ n ], then almost all subsets of [ n ] of size m are Sidon, in the sense that .
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.017 | 0.001 |
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