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Bibliographic record
Abstract
Comtrans algebras, arising in web geometry, have two trilinear operations, commutator and translator. We determine a Gröbner basis for the comtrans operad, and state a conjecture on its dimension formula. We study multilinear polynomial identities for the special commutator [x,y,z]=xyz−yxz and special translator ⟨x,y,z⟩=xyz−yzx in associative triple systems. In degree 3, the defining identities for comtrans algebras generate all identities. In degree 5, we simplify known identities for each operation and determine new identities relating the operations. In degree 7, we use representation theory of the symmetric group to show that each operation satisfies identities which do not follow from those of lower degree but there are no new identities relating the operations. We use noncommutative Gröbner bases to construct the universal associative envelope for the special comtrans algebra of 2×2 matrices.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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