Bibliographic record
Abstract
Abstract Analyses of molecular spectra often use the idea of an effective Hamiltonian , in which the dynamical variables are the degrees of freedom involved in the spectrum, and the effects of the other degrees of freedom are represented by the values of various parameters. However, it may not be possible to determine all these parameters by empirical fits of the spectra because different parameters may make indistinguishable contributions to the eigenvalues of the Hamiltonian. This article reviews a number of examples of such indeterminacies, including applications to vibration–rotation spectra of diatomic molecules, without or with corrections for the breakdown of the Born–Oppenheimer approximations; electron‐spin structure in diatomic molecules; centrifugal distortion in asymmetric‐top molecules; vibration–rotation resonances in polyatomic molecules; vibration–rotation interactions in degenerate vibrational states; and internal rotation. The discussion of these indeterminacies involves unitary transformations that are expanded as infinite series. This procedure may break down if the convergence of the series is slow. The study of near‐singularities of least‐squares matrices associated with the presence of indeterminacies is also discussed.
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How this classification was reachedexpand
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) | 0.001 | 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) | 0.014 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".