Rapid calculation of individual ion Madelung constants and their convergence to bulk values
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Bibliographic record
Abstract
The distinction between the single Madelung constant that characterizes bulk materials and the range of Madelung constants that exists for real (finite) materials is emphasized. Madelung constants are calculated using a fast algorithm to compute Coulomb sums. The weighted averages of the specific ion Madelung constants provide a measure of the electrostatic potential for any cluster of ions. The central ions’ Madelung constants in a succession of progressively larger structures with the same symmetry as the bulk converge rapidly to the bulk Madelung constant if all the precursors to the bulk are electrically neutral. If this condition is satisfied, convergence is faster than other methods and is simpler to implement than the classical Ewald method. Applications to surface science and to the conformations and energies of nanostructures are made possible by this approach.
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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