Ordered *-Semigroups and a C<sup>*</sup>-Correspondence for a Partial Isometry
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Bibliographic record
Abstract
Certain * -semigroups are associated with the universal C * -algebra generated by a partial isometry, which is itself the universal C * -algebra of a * -semigroup. A fundamental role for a * -structure on a semigroup is emphasized, and ordered and matricially ordered * -semigroups are introduced, along with their universal C * -algebras. The universal C *algebra generated by a partial isometry is isomorphic to a relative Cuntz-Pimsner C * -algebra of a C * -correspondence over the C * -algebra of a matricially ordered * -semigroup. One may view the C * -algebra of a partial isometry as the crossed product algebra associated with a dynamical system defined by a complete order map modelled by a partial isometry acting on a matricially ordered * -semigroup.
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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 | 0.006 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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