Why this work is in the frame
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Bibliographic record
Abstract
We call the polynomial [Formula: see text] a Barker polynomial of degree n-1 if each a j ∈{-1, 1} and [Formula: see text] Properties of Barker polynomials were studied by Turyn and Storer thoroughly in the early sixties, and by Saffari in the late eighties. In the last few years P. Borwein and his collaborators revived interest in the study of Barker polynomials (Barker codes, Barker sequences). In this paper we give a new proof of the fact that there is no Barker polynomial of even degree greater than 12, and hence Barker sequences of odd length greater than 13 do not exist. This is intimately tied to irreducibility questions and proved as a consequence of the following new result. Theorem.Ifn ≔ 2m + 1 > 13and[Formula: see text]where eachb j ∈{-1, 0, 1}for even values of j, each b j is an integer divisible by 4 for odd values of j, then there is no polynomial[Formula: see text]such that[Formula: see text], where[Formula: see text]and[Formula: see text]denotes the collection of all polynomials of degree 2m with each of their coefficients in {-1, 1}. A clever usage of Newton's identities plays a central role in our elegant proof.
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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 | 0.002 | 0.002 |
| 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) | 0.024 | 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