The Residual Character of Finitely Generated Varieties of Unary Algebras and Groupoids, and Applications to the Restricted Quackenbush Problem.
Bibliographic record
Abstract
The crux of this thesis is to study the Restricted Quackenbush Problem: if B is a finite algebra of finite type and V(B) is residually finite, must V(B) be residually <N, for some positive integer N? We show that the Restricted Quackenbush Problem is answered affirmatively with respect to unary algebras, a result first shown by Baldwin and Berman in 1975. Then we turn our attention to groupoids and show that all groupoids that generate residually finite varieties must satisfy an identity of the form k(x)≈x∗x, where k(x) is an identity of type {∗} that is not equal to x∗x. Due to this result, we focus on a particular class of idempotent groupoids, called absorbing groupoids. We show that if a certain property holds, with respect to absorbing groupoids, then the Restricted Quackenbush Problem is answered affirmately.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
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".