Neutral Signature CSI Spaces in Four Dimensions
Bibliographic record
Abstract
Scalar curvature invariants are scalars formed by the contraction of the Riemann tensor\nand its covariant derivatives. The main motivation for studying scalar curvature\ninvariants is that they can be used to classify certain spaces uniquely. For example,\nthe I-non-degenerate spaces in Lorentzian signature. Lorentzian metrics that fail to\nbe I-non-degenerate are Kundt metrics and have a very special structure.\nIn this thesis we study pseudo-Riemannian spaces with the property that all of\ntheir scalar curvature invariants vanish (VSI spaces) or are constant (CSI spaces).\nThese spaces include pseudo-Riemannian Kundt metrics. VSI and CSI spaces are not\nonly of interest from a mathematical standpoint but also have applications to current\ntheoretical physics.\nIn particular, we focus on studying VSI and CSI spaces in four-dimensional neutral\nsignature. We construct new, very general, classes of CSI and VSI pseudo-Riemannian\nspaces.
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How this classification was reachedexpand
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) | 0.001 | 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 teacher head, 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".