Isometric Dilations of Non-Commuting Finite Rank <i>n</i>-Tuples
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Bibliographic record
Abstract
Abstract A contractive n -tuple A = ( A 1,…, A n ) has a minimal joint isometric dilation S = ( S 1 ,…, S n ) where the S i ’s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra generated by S is completely described in terms of the properties of A . This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra is always hyper-reflexive. In the last section, we describe similarity invariants. In particular, an n -tuple B of d × d matrices is similar to an irreducible n -tuple A if and only if a certain finite set of polynomials vanish on B .
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it