Bibliographic record
Abstract
One of the most fundamental facts in topos theory is the internal parameterization of subtoposes: the bijective correspondence between subtoposes and Lawvere-Tierney topologies.In this paper, we introduce a new but elementary concept, "a local state classifier," and give an analogous internal parameterization of hyperconnected quotients (i.e., hyperconnected geometric morphisms from a topos).As a corollary, we obtain a solution to the Boolean case of the first problem of Lawvere's open problems.Contents 1 Introduction 263 2 Hyperconnected geometric morphism 268 3 Local state classifier 270 4 Internal parameterization of hyperconnected quotients 291 5 Examples and Applications 297 6 Conclusions and future works 303 A Internal semilattices and the universal filter 304 B Existence theorem for a local state classifier 309The author would like to thank Ryu Hasegawa and Hisashi Aratake for their suggestions and support, and Yuta Yamamoto and Haruya Minoura for their useful discussions.I would like to express deep
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".