SPECTRAL DISTRIBUTION ANALYSIS OF RANDOM INTERACTIONS WITH J-SYMMETRY AND ITS EXTENSIONS
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Bibliographic record
Abstract
Spectral distribution theory, based on average-fluctuation separation and trace propagation, is applied in the analysis of some properties of a system of m (identical) nucleons in shell model j-orbits with random interactions preserving angular momentum J-symmetry. Employing the bivariate Gaussian form with Edgeworth corrections for fixed E (energy) and M (J z eigenvalue) density of states ρ(E,M), analytical results, in the form of expansions to order [J(J+1)] 2 , are derived for energy centroids E c (m,J) and spectral variances σ 2 (m,J). They are used to study distribution of spectral widths, J=0 preponderance in energy centroids, lower order cross correlations in states with different J's and so on. Also, an expansion is obtained for occupation probabilities over spaces with fixed M. All the results obtained with spectral distribution theory compare well with those obtained recently using quite different methods. In addition, using trace propagation methods, a regular feature, that they are nearly constant, of spectral variances generated by random interactions is demonstrated using several examples. These open a new window to study regular structures generated by random interactions.
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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) | 0.000 | 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