Positive Rational Solutions to <i> x <sup>y</sup> </i> = <i> y <sup>mx</sup> </i> : A Number-Theoretic Excursion
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
Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsMichael A. BennettMIKE BENNETT studied mathematics at Dalhousie University and the University of British Columbia. He received his Ph.D. in 1993 as a student of David Boyd. After postdoctoral fellowships at Waterloo, Ann Arbor, and the Institute for Advanced Study, he was a faculty member at the University of Illinois, Urbana-Champaign until returning to Vancouver in 2001. He remains an unrepentant number theorist and favors the plucky underdog New York Yankees.Bruce ReznickBRUCE REZNICK got his degrees at Caltech (B.S.,1973) and Stanford (Ph.D.,1976) and has been at the University of Illinois, Urbana-Champaign since 1979. He is interested in combinatorial problems in number theory, analysis, algebra, and geometry, often involving polynomials. He continues, somehow, to root for the Chicago Cubs.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.002 |
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