Sums of squares and moment problems in equivariant situations
Bibliographic record
Abstract
We begin a systematic study of positivity and moment problems in an equivariant setting. Given a reductive group G G over R \mathbb {R} acting on an affine R \mathbb {R} -variety V V , we consider the induced dual action on the coordinate ring R [ V ] \mathbb {R}[V] and on the linear dual space of R [ V ] \mathbb {R}[V] . In this setting, given an invariant closed semialgebraic subset K K of V ( R ) V(\mathbb R) , we study the problem of representation of invariant nonnegative polynomials on K K by invariant sums of squares, and the closely related problem of representation of invariant linear functionals on R [ V ] \mathbb {R}[V] by invariant measures supported on K K . To this end, we analyse the relation between quadratic modules of R [ V ] \mathbb {R}[V] and associated quadratic modules of the (finitely generated) subring R [ V ] G \mathbb {R}[V]^G of invariant polynomials. We apply our resu
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.015 | 0.001 |
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".