OMITTING TYPES, BOUNDED WIDTH AND THE ABILITY TO COUNT
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Bibliographic record
Abstract
We say that a finite algebra 𝔸 = 〈A; F〉 has the ability to count if there are subalgebras C of 𝔸 3 and Z of 𝔸 such that the structure 〈A; C, Z〉 has the ability to count in the sense of Feder and Vardi. We show that for a core relational structure A the following conditions are equivalent: (i) the variety generated by the algebra 𝔸 associated to A contains an algebra with the ability to count; (ii) 𝔸 2 has the ability to count; (iii) the variety generated by 𝔸 admits the unary or affine type. As a consequence, for CSP's of finite signature, the bounded width conjectures stated in Feder–Vardi [10], Larose–Zádori [17] and Bulatov [5] are identical.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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