Bibliographic record
Abstract
In this thesis, we investigate mathematical constructions related to holography principle from physics, organized into three main parts. Firstly, we introduce the concept of quadratic duality for chiral algebras, extending the construction from associative algebras. We establish its relationship with the Maurer-Cartan equation, bridging it with physical intuition.Secondly, we define the notion of a vertex operator algebra (VOA) in a (pseudo)-tensor category. Specifically, we study a βγ VOA in the Deligne category. This construction provides a rigorous mathematical definition for the large N vertex algebra relevant to holography. Thirdly, we analyze the structure of the higher dimensional Laurent series, which are analog of the 1d Laurent series C((z)). Here, the derived structure becomes crucial, distinguishing it from the 1d case. We compute the A∞ structure on the cohomology and explore various variations of this model. These A∞/L∞ algebraic structures can define certain (vertex) Poisson algebra. As a consequence of the holography conjecture, the vertex Poisson algebra is isomorphic to the one constructed from the βγ system in the Deligne Category. We provide several checks of this conjecture.
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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 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".