Bibliographic record
Abstract
The goal of this paper is to study the geometry of the connected unit component of the four-dimensional real general linear Lie group four dimensional G 0 as a Lorentzian and flat affine manifold.As the group G 0 is also naturally equipped with a bi-invariant Hessian metric k + , relative to the natural bi-invariant flat affine structure ∇, we examine these structures and their relationships.The study of this space-time model (G 0 , k + , ∇) was initiated by the first author (A New Space Time Model), and the present paper is a complementary study of this one.We naively hope this work will be useful for studying our physical universe.Theorems 3 and 4 can help in understanding of quantum entanglement.The curvatures, tidal force, and Jacobi vector fields of (G 0 , k + ) are determined in Section 2. Subsection 2.5 discusses the causal structure of (G 0 , k + ), while Section 3 focuses on the developed map relative to ∇ in the sense of C. Ehresmann.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.026 | 0.009 |
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".