Neutral Signature CSI Spaces in Four Dimensions
Bibliographic record
Abstract
Scalar curvature invariants are scalars formed by the contraction of the Riemann tensor and its covariant derivatives. The main motivation for studying scalar curvature invariants is that they can be used to classify certain spaces uniquely. For example, the I-non-degenerate spaces in Lorentzian signature. Lorentzian metrics that fail to be I-non-degenerate are Kundt metrics and have a very special structure. In this thesis we study pseudo-Riemannian spaces with the property that all of their scalar curvature invariants vanish (VSI spaces) or are constant (CSI spaces). These spaces include pseudo-Riemannian Kundt metrics. VSI and CSI spaces are not only of interest from a mathematical standpoint but also have applications to current theoretical physics. In particular, we focus on studying VSI and CSI spaces in four-dimensional neutral signature. We construct new, very general, classes of CSI and VSI pseudo-Riemannian spaces.
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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 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".