Generalized derivations and general relativity
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra [Formula: see text]. Such a derivation, introduced by Brešar in 1991, is given by a linear mapping [Formula: see text] such that there exists a usual derivation, d, of [Formula: see text] satisfying the generalized Leibniz rule u(ab) = u(a)b + ad(b) for all [Formula: see text]. The generalized geometry “is tested” in the case of the algebra of smooth functions on a manifold. We then apply this machinery to study generalized general relativity. We define the Einstein–Hilbert action and deduce from it Einstein’s field equations. We show that for a special class of metrics containing, besides the usual metric components, only one nonzero term, the action reduces to the O’Hanlon action that is the Brans–Dicke action with potential and with the parameter ω equal to zero. We also show that the generalized Einstein equations (with zero energy–stress tensor) are equivalent to those of the Kaluza–Klein theory satisfying a “modified cylinder condition” and having a noncompact extra dimension. This opens a possibility to consider Kaluza–Klein models with a noncompact extra dimension that remains invisible for a macroscopic observer. In our approach, this extra dimension is not an additional physical space–time dimension but appears because of the generalization of the derivation concept.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 it