FINDING CONFORMAL KILLING VECTORS FROM THE INVARIANT CLASSIFICATION SCHEME
Bibliographic record
Abstract
The invariant classification (Karlhede classification)1 of a particular spacetime fixes (up to isotropy) an intrinsic tetrad for the spacetime, in terms of the Riemann tensor and its derivatives. Exploiting this tetrad, it has been shown how to determine the number of Killing vectors which exist 2, and also whether a proper homothetic Killing vector exists 3. The first part of the talk outlined a procedure for finding explicitly homothetic and Killing vectors by exploiting the symmetry properties of the intrinsic tetrad 4,5. In general, it is not always possible to use this same tetrad to investigate proper conformal Killing vectors by the same methods. In this talk it was suggested to modify the invariant classification procedure so that only conformally invariant conditions are used for fixing the tetrad in terms of the Riemann tensor and its derivatives. This would mean that the existence of proper conformal Killing vectors could be deduced directly from the modified invariant classification scheme, and then found explicitly 6.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".