Highly accurate calculation of the auxiliary functions of the fourth order and five-body integrals
Bibliographic record
Abstract
General theory and analytical formulae suitable for numerical calculations of the fourth order auxiliary functions A4(k, ℓ, m, n, a, b, c, d) are presented. The auxiliary functions of the fourth order A4(k, ℓ, m, n, a, b, c, d) are of great interest in various applications, e.g., they can be used to solve a number of five- and many-body problems in atomic, molecular and nuclear physics. The obtained analytical formulae have been extensively tested in actual calculations of the A4(k, ℓ, m, n, a, b, c, d) functions and one-centre five-body integrals I5. Numerical computations of the ground bound state in the Be atom with the use of Hylleraas variational expansion are briefly discussed. The one-centre, five-body integrals I5 can also be useful to determine the general five-body integrals .
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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) | 0.000 | 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 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".