Bibliographic record
Abstract
Let T be a neutral Tannakian category over a field of characteristic zero with unit object 1, and equipped with a filtration W • similar to the weight filtration on mixed motives.Let M be an object of T , and u(M) ⊂ W -1 Hom(M, M) the Lie algebra of the kernel of the natural surjection from the fundamental group of M to the fundamental group of Gr W M. A result of Deligne gives a characterization of u(M) in terms of the extensions 0 → W p M → M → M/W p M → 0: it states that u(M) is the smallest subobject of W -1 Hom(M, M) such that the sum of the aforementioned extensions, considered as extensions of 1 by W -1 Hom(M, M), is the pushforward of an extension of 1 by u(M).We study each of the abovementioned extensions individually in relation to u(M).Among other things, we obtain a refinement of Deligne's result, where we give a sufficient condition for when an individual extension 0 → W p M → M → M/W p M → 0 is the pushforward of an extension of 1 by u(M).In the second half of the paper, we give an application to mixed motives whose unipotent radical of the motivic Galois group is as large as possible (i.e., with u(M) = W -1 Hom(M, M)).Using Grothendieck's formalism of extensions panachées we prove a classification result for such motives.Specializing to the category of mixed Tate motives we obtain a classification result for 3-dimensional mixed Tate motives over ޑ with three weights and large unipotent radicals.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".