Exponential variational expansion in relative coordinates for highly accurate bound state calculations in four-body systems
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Bibliographic record
Abstract
Exponential variational expansions in relative coordinates are considered for four-body systems. All matrix elements needed for bound-state calculations are expressed as linear combinations of fifth- and sixth-order derivatives of a basic four-body integral. Computation of the basic four-body integral and its derivatives is performed directly, i.e., without any use of the branch tracking in the complex plane that is required in the Fromm/Hill approach, and by methods that take into account the termwise singularities of the formulas. The final computational procedure is relatively simple, physically transparent, and numerically stable. The methods are illustrated with sample data that show the importance of a singularity-canceling approach and that the increased precision thereby made possible permits more accurate wave function optimization than heretofore.
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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