Classical freeness of orthosymplectic affine vertex superalgebras
Bibliographic record
Abstract
The question of when a vertex algebra is a quantization of the arc space of its associated scheme has recently received a lot of attention in both the mathematics and physics literature. This property was first studied by Tomoyuki Arakawa and Anne Moreau (see their paper in the references), and was given the name \lq\lq classical freeness" by Jethro van Ekeren and Reimundo Heluani [Comm. Math. Phys. 386 (2021), no. 1, pp. 495-550] in their work on chiral homology. Later, it was extended to vertex superalgebras by Hao Li [Eur. J. Math. 7 (2021), pp. 1689–1728]. In this note, we prove the classical freeness of the simple affine vertex superalgebra L n ( o s p m | 2 r ) L_n(\mathfrak {o}\mathfrak {s}\mathfrak {p}_{m|2r}) for all positive integers m , n , r m,n,r satisfying − m 2 + r + n + 1 > 0 -\frac {m}{2} + r +n+1 > 0 . In particular, it holds for the rational vertex superalgebras L n ( o s p 1 | 2 r ) L_n(\mathfrak {o}\mathfrak {s}\mathfrak {p}_{1|2r}) for all positive integers r , n r,n .
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".