Features of gravity–Yang-Mills hierarchies in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>dimensions
Bibliographic record
Abstract
Higher-dimensional, direct analogues of the usual $d=4$ Einstein--Yang-Mills (EYM) systems are studied. They feature single members of both the gravitational and the Yang-Mills hierarchies in $d=4p$-dimensional spacetimes, both consisting of $2p$-form curvature terms only. This enables us to probe the effects of higher order gravitational terms, which in the presence of the usual Einstein term would be masked. Regular and black hole solutions are constructed in $2p+2\ensuremath{\le}d\ensuremath{\le}4p$, in which dimensions the total mass-energy is finite, generalizing the familiar Bartnik-McKinnon solutions in EYM theory for $p=1$. In $d=4p$, this similarity is complete. In the special case of $d=2p+1$, just beyond the finite energy range of $d$, exact solutions in closed form are found. Finally, $d=2p+1$ purely gravitational systems, whose solutions generalize the static $d=3$ BTZ solutions, are discussed.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".