Bibliographic record
Abstract
A complete set of first integrals, or constants of motion, for a model system is constructed using “factorization”, as described below. The system is described by the effective Feynman Lagrangian L = [Formula: see text], with one of the simplest, nontrivial, potentials V(x) = (1/2)m ω2x2 selected for study. Four new, explicitly time-dependent, constants of the motion ci±, i = 1, 2 are defined for this system. While [Formula: see text]ci± ≠ 0, [Formula: see text]ci± = [Formula: see text]ci± + [Formula: see text]ci± + [Formula: see text]ci± + · · · = 0 along an extremal of L. The Hamiltonian H is shown to equal a sum of products of the ci±, and verifies [Formula: see text] = 0. A second, functionally independent constant of motion is also constructed as a sum of the quadratic products of ci±. It is shown that these derived constants of motion are in involution.PACS Nos.: 02.30.Jr, 02.30.Ik, 02.60.Cb, 02.30.Hq, 05.70.Ln, 02.50.–r
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 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".