Bibliographic record
Abstract
In this thesis, we establish decomposition theorems for topological Azumaya algebras, and topological Azumaya algebras with involutions of the first kind. Decomposition of topological Azumaya algebras Let A be a topological Azumaya algebra of degree mn over a CW complex X. We prove that if m and n are relatively prime, m<n, and the dimension of X is in the stable range for GL(m,ℂ), then A can be decomposed as the tensor product of topological Azumaya algebras of degrees m and n. Moreover, if the dimension of X is outside of the stable range for GL(m,ℂ), then A may not have such a decomposition. Decomposition of topological Azumaya algebras with involution Let A be a topological Azumaya algebra of degree mn with an orthogonal involution over a CW complex X. We prove that if m and n are relatively prime, m<n, and the dimension of X is in the stable range for O(m,ℂ), then A can be decomposed as the tensor product of topological Azumaya algebras of degrees m and n with orthogonal involutions. Let A be a topological Azumaya algebra of degree 2mn with a symplectic involution over a CW complex X. We prove that if n is odd, and dim(X)≤7, then A can be decomposed as the tensor product of a topological Azumaya of degree 2m with a symplectic involution, and a topological Azumaya algebra of degree n with an orthogonal involution.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.004 | 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".