Bibliographic record
Abstract
We derive the laws of superposition of multiple successive collinear Lorentz boosts by four different methods. The first method exploits the relation between the Pochhammers of 2 x 2 nonautonomous matrices and the symmetric functions. The second method proceeds by diagonalizing the Lorentz boost. The third method is based on the characteristics of the Pauli matrices. The fourth method makes use of the relativistic law of addition of multiple collinear velocities, as well as the polygonometric identities. We give expressions, for the laws of superposition, parametrized using velocity and rapidity, as well as expressions in compact, symmetric, and unified forms. We also give the expressions of the laws of superposition in the special case of identical boosts, both for finite boosts, and for infinitesimal boosts. These latter results provide insight into the relation between Galilean (classical) and Lorentzian (relativistic) velocities.PACS Nos.: 03.30.+p, 02.10.Yn, 02.10.Ox
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 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".