SPECTRAL DISTRIBUTION ANALYSIS OF RANDOM INTERACTIONS WITH J-SYMMETRY AND ITS EXTENSIONS
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 (Jz 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 Ec(m,J) and spectral variances σ2(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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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".