A completely bounded non-commutative Choquet boundary for operator\n spaces
Bibliographic record
Abstract
We develop a completely bounded counterpart to the non-commutative Choquet\nboundary of an operator space. We show how the class of completely bounded\nlinear maps is too large to accommodate our purposes. To overcome this\nobstacle, we isolate the subset of completely bounded linear maps on an\noperator space admitting a dilation of the same norm which is multiplicative on\nthe generated $C^*$-algebra. We view such maps as analogues of the familiar\nunital completely contractive maps, and we exhibit many of their structural\nproperties. Of particular interest to us are those maps which are extremal with\nrespect to a natural dilation order. We establish the existence of extremals\nand show that they have a certain unique extension property. In particular,\nthey give rise to $*$-homomorphisms which we use to associate to any\nrepresentation of an operator space an entire scale of $C^*$-envelopes. We\nconjecture that these $C^*$-envelopes are all $*$-isomorphic, and verify this\nin some important cases.\n
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.005 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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".