Axiomatic formulations of the Hohenberg-Kohn functional
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Bibliographic record
Abstract
Properties of the Hohenberg-Kohn functional are considered. In particular, the Hohenberg-Kohn functional should (a) give correct results in the variational principle and should be (b) continuous, (c) convex, and (d) size consistent. All of these properties are satisfied by the Legendre-transform functional (equivalently, the density matrix constrained search functional) and, moreover, this is the only functional that possesses all these properties. Not only that, but the Legendre-transform functional is determined uniquely by requiring (a), (b), and either (c) or (d). This shows how an ``axiomatic'' approach to constructing the Hohenberg-Kohn functional leads naturally to the Legendre-transform functional. Among all functionals consistent with the variational principle, the Legendre-transform functional is the smallest. One corollary to this approach is a simple proof of the equivalence of the Legendre-transform and density-matrix constrained search functionals. For completeness, the Appendix shows that ensemble-$v$-representable densities lie dense in the set of $N$-representable densities.
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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