Bibliographic record
Abstract
Much progress has been made on the classification of simple C*-algebras via the Elliott invariant. A key component of this invariant is the K0-group. Thus, the range of this invariant is of interest to the classification project. In the stably finite case, the K0-group is an ordered group. If x is an element of an ordered group ⟨G; G+⟩ such that x ∉ G + but nx ≠ 0 and nx ∈ G+ for some natural number n, we say that G is strongly perforated and call x a perforation element. The sequel establishes the existence of several new, strongly perforated order structures which arise as the ordered K 0-groups of certain simple C*-algebras. These order structures include all previously known strongly perforated order structures arising in this manner. Also proved is the existence of unital *-homomorphisms between simple C*-algebras with strongly perforated ordered K0-groups which preserve perforation elements.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 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; both teacher heads agree on what is shown here.
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".