Multibox strategy for constructing highly accurate bound-state wave functions for three-body systems
Why this work is in the frame
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Bibliographic record
Abstract
Variational, multibox approach is proposed to construct extremely accurate, bound-state wave functions for arbitrary three-body systems. The high efficiency of our present approach is based on an optimal choice of nonlinear parameters in the exponential basis functions. The proposed method is very flexible, since the final wave function can also include a large number of separately optimized cluster fragments. The wave functions obtained are very compact and highly accurate. Such wave functions can be used to compute various bound state properties for different three-body systems. The proposed approach has been successfully tested on a large number of actual systems. It is shown that the present approach can be used to solve various three-body problems with, in principle, arbitrary precision. In particular, the long-standing problem of highly accurate determination of the weakly bound (1,1) states in the $\mathrm{dd}\ensuremath{\mu}$ and $\mathrm{dt}\ensuremath{\mu}$ muonic molecular ions has finally been solved. The determined binding energies are $\ensuremath{-}1.9749880880\ifmmode\pm\else\textpm\fi{}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} \mathrm{eV}$ and $\ensuremath{-}0.66033874\ifmmode\pm\else\textpm\fi{}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8} \mathrm{eV},$ respectively.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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