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
Let / be a nonzero integer and S a set of positive integers. We say that S is a i^-set if, for any two distinct elements x mdy of 5, the integer xy + t is a perfect square. A /J-set is extendible if there exists a positive integer a gS such that S^J {a} is still a i^-set. The problem of extending i^-sets is very old and dates back to the time of Diophantus (see Dickson [5], p. 513). The most spectacular result in this area is due to Baker and Davenport [3] who showed that the Prset {1,3,8,120} is nonextendible. Since then, several authors have made efforts to give a characterization of the i^-sets (see references). The P^-set {1,2,5} was studied by Brown [4] who proved that this set is nonextendible. His method is based on deep results of Baker [3] and techniques of Grinstead [10]. In this paper we give another proof of the nonextendibility of the P^-set {1,2,5} using only elementary number theory. Suppose that there exists an integer a such that {1,2,5, a} is a P_rset. Then the following system of equations [ a-l = Y\\
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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 | 0.000 |
| 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) | 0.003 | 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