Bibliographic record
Abstract
The title of this lecture alludes to Ribenboim’s delightful treatise on Fermat’s Last Theorem [Rib1]. Fifteen years after the publication of [Rib1], Andrew Wiles finally succeeded in solving Fermat’s 350-year-old conundrum. That same year, perhaps to console himself of Fermat’s demise, Ribenboim published a second book, this time on Catalan’s conjecture that there are no consecutive perfect powers other than 8 and 9. As we have learned at this Congress, Preda Mihailescu has just disposed of this conjecture as well. His breakthrough comes only 8 years after the publication of Ribenboim’s book on Catalan’s equation. Such is the magic of Ribenboim’s books: the age-old problems which they treat have invariably been solved, in comparatively short order! So it is with some eagerness that we await the publication of Ribenboim’s next tome (hoping it will be devoted to the Riemann Hypothesis, or the Birch and Swinnerton-Dyer conjecture...) This “fourteenth lecture” is meant as a tribute both to Ribenboim and to the spirit of Fermat: the fascination with concrete Diophantine problems, especially those that draw us, seemingly inexorably, to central topics in the subject (cyclotomic fields, elliptic curves, reciprocity laws, modular forms...)
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.051 | 0.031 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".