{"paper":{"title":"Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn-Sham theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Exact density-functional theory emerges as two parallel ensemble variational hierarchies linked by the Kohn-Sham mapping on a shared density class.","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.chem-ph","authors_text":"Nan Sheng","submitted_at":"2026-03-24T16:35:25Z","abstract_excerpt":"Exact density-functional theory is recast here as two parallel exact ensemble variational hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in exact noninteracting ensemble theory. The Kohn-Sham construction links the two on a common admissible density class. In this recasting, Levy-Lieb, Hohenberg-Kohn, and Kohn-Sham formulations appear as constrained specializations of broader ensemble variational structures. Fractional particle number and fractional occupations enter naturally in the same ensemble setting, while piecewise linea"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Exact density-functional theory is reconstructed here from its convex variational structure as two parallel exact ensemble hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in the exact noninteracting ensemble theory. The Kohn-Sham construction links the two on a common admissible density class.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the convex variational structure of the energy functional admits exact parallel ensemble hierarchies for both interacting and noninteracting systems whose densities coincide under the Kohn-Sham mapping without additional constraints that would invalidate the claimed consequences for fractional occupations and derivative discontinuities.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact DFT is reorganized as parallel interacting and noninteracting ensemble variational hierarchies whose geometry produces fractional particle numbers, piecewise linearity, and the derivative discontinuity as direct consequences.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Exact density-functional theory emerges as two parallel ensemble variational hierarchies linked by the Kohn-Sham mapping on a shared density class.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"15983ce21997aa16be1da51341e3b086d41a1810d76d084110ad698dd8abe49f"},"source":{"id":"2603.23399","kind":"arxiv","version":4},"verdict":{"id":"dd68a62f-b048-4153-b710-c3164535c369","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T00:09:54.328101Z","strongest_claim":"Exact density-functional theory is reconstructed here from its convex variational structure as two parallel exact ensemble hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in the exact noninteracting ensemble theory. The Kohn-Sham construction links the two on a common admissible density class.","one_line_summary":"Exact DFT is reorganized as parallel interacting and noninteracting ensemble variational hierarchies whose geometry produces fractional particle numbers, piecewise linearity, and the derivative discontinuity as direct consequences.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the convex variational structure of the energy functional admits exact parallel ensemble hierarchies for both interacting and noninteracting systems whose densities coincide under the Kohn-Sham mapping without additional constraints that would invalidate the claimed consequences for fractional occupations and derivative discontinuities.","pith_extraction_headline":"Exact density-functional theory emerges as two parallel ensemble variational hierarchies linked by the Kohn-Sham mapping on a shared density class."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.23399/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"b752e23dd858d0168064896984597bc85ac891e81fddf58f701094a08dfc88d4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}