Bibliographic record
Abstract
We classify central extensions of Artin-Schelter regular algebras of global dimension atmost 3, generated by elements of degree 1. Let 𝐴 be a quadratic Artin-Schelter regular algebra generated by degree 1 elements over a field 𝑘, and let 𝐷 be an extension of 𝐴 by a central element 𝑧, such that 𝐴 ≅ 𝐷/⟨𝑧⟩. The study by Le Bruyn, S.P. Smith, Van den Bergh “Central extensions of three dimensional Artin-Schelter regular algebra” is cited as the primary source of information in this thesis. Le Bruyn et al. used the fact that the quadratic algebras under specific conditions are Koszul to analyze the central extensions of three dimensional Artin-Schelter regular algebras. Adopting the same facts, we identify central extensions of one dimensional and two dimensional Artin-Schelter regular algebra generated by degree 1 elements.
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How this classification was reachedexpand
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) | 0.001 | 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) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".