Bibliographic record
Abstract
Introduction: glimpses of the theory beneath Monstrous Moonshine When you are collecting mushrooms, you only see the mushroom itself.But if you are a mycologist, you know that the real mushroom is in the earth.There's an enormous thing down there, and you just see the fruit, the body that you eat.In mathematics, the upper part of the mushroom corresponds to theorems that you see, but you don't see the things that are below, that is: problems, conjectures, mistakes, ideas, etc. V. I. Arnold [17] What my experience of mathematical work has taught me again and again, is that the proof always springs from the insight, and not the other way around -and that the insight itself has its source, first and foremost, in a delicate and obstinate feeling of the relevant entities and concepts and their mutual relations.The guiding thread is the inner coherence of the image which gradually emerges from the mist, as well as its consonance with what is known or foreshadowed from other sources -and it guides all the more surely as the 'exigence' of coherence is stronger and more delicate.A. Grothendieck. 1Interesting events (e.g.wars) always happen whenever different realisations of the same thing confront one another.When clarity and precision are added to the mix, we call this mathematics.In particular, the most exciting and significant moments in mathematics occur when we discover that seemingly unrelated phenomena are shadows cast by the same beast.This book studies one who has been recently awakened.In 1978, John McKay made an intriguing observation: 196 884 ≈ 196 883.Monstrous Moonshine is the collection of questions (and a few answers) that it directly inspired.No one back then could have guessed the riches to which it would lead.But in actual fact, Moonshine (albeit non-Monstrous) really began long ago. Modular functionsUp to topological equivalence (homeomorphism), every compact surface is uniquely specified by its genus: a sphere is genus 0, a torus genus 1, etc.However, a (real) surface can be made into a complex curve by giving it more structure.For a sphere, up to 1 Translated in Geometric Galois Actions 1, edited by L.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.043 | 0.009 |
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".