K-Theory of Non-Commutative Spheres Arising from the Fourier Automorphism
Bibliographic record
Abstract
Abstract For a dense Gδ set of real parameters θ in [0, 1] (containing the rationals) it is shown that the group K0(Aθ ⋊σ ) is isomorphic to , where Aθ is the rotation C*-algebra generated by unitaries U, V satisfying VU = e2πiθUV and σ is the Fourier automorphism of Aθ defined by σ(U) = V, σ(V) = U−1. More precisely, an explicit basis for K0 consisting of nine canonical modules is given. (A slight generalization of this result is also obtained for certain separable continuous fields of unital C*-algebras over [0, 1].) The Connes Chern character ch: K0(Aθ ⋊σ ) → Hev (Aθ ⋊σ )* is shown to be injective for a dense Gδ set of parameters θ. The main computational tool in this paper is a group homomorphism T: K0(Aθ ⋊σ ) → obtained from the Connes Chern character by restricting the functionals in its codomain to a certain nine-dimensional subspace of Hev (Aθ ⋊σ ). The range of T is fully determined for each θ. (We conjecture that this subspace is all of Hev.)
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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 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".