How Ambiguous Is the Local Kinetic Energy?<sup>†</sup>
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Bibliographic record
Abstract
The local kinetic energy and the closely related local electronic stress tensor are commonly used to elucidate chemical bonding patterns, especially for covalent bonds. We use three different approaches-transformation properties of the stress tensor, quasiprobability distributions, and the virial theorem from density-functional theory-to clarify the inherent ambiguity in these quantities, discussing the implications for analyses based on the local kinetic energy and stress tensor. An expansive-but not universal-family of local kinetic energy forms that includes the most common choices and is suitable for both chemical-bonding and atoms-in-molecule analysis is derived. A family of local electronic stress tensors is also derived. Several local kinetic energy functions that are mathematically justified, but unlikely to be conceptually useful, are derived. The implications of these forms for atoms-in-molecule analysis are discussed.
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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 | 0.001 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| 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 it