Recognizing the Farey–Stern–Brocot AF algebra
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In his 2008 paper published in the Canadian Journal of Mathematics, F. Boca investigates an AF algebra \mathfrak A , whose Bratteli diagram arises from the Farey–Stern–Brocot sequence. It turns out that \mathfrak A coincides with the AF algebra \mathfrak M_1 introduced in 1988 by the present author in a paper published in Advances in Mathematics. We give a procedure to recognize \mathfrak A among all finitely presented AF algebras whose Murray–von Neumann order of projections is a lattice. Further: (i) \mathfrak A is a *-subalgebra of Glimm universal algebra; (ii) tracial states of \mathfrak A correspond to Borel probability measures on the unit real interval; (iii) all primitive ideals of \mathfrak A are essential; (iv) the automorphism group of \mathfrak A has exactly two connected components.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it