{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WTZCTPJWRDTE4M7F7L6I2FFGUW","short_pith_number":"pith:WTZCTPJW","schema_version":"1.0","canonical_sha256":"b4f229bd3688e64e33e5fafc8d14a6a5a09dc3545feca4ebc9857e6a2fb3c4b6","source":{"kind":"arxiv","id":"2603.23399","version":4},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2603.23399","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-03-24T16:35:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"454ca0623ee85b374e00c4a82944996d9619271eb3b1eb13d7d1f5cb791fe794","abstract_canon_sha256":"5ee67b21bfa5bd2a8b536e6c772286defc359acad7e68caa833121ae55a202b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:24.684631Z","signature_b64":"A41H9Gjp20BPNXv/gKAJv9VkZU0pLrUGRKCEAfKIbweQQx6YWE8tefdFCY6wt0DEppkAuRgMJAPysn9s1jRaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4f229bd3688e64e33e5fafc8d14a6a5a09dc3545feca4ebc9857e6a2fb3c4b6","last_reissued_at":"2026-06-09T02:07:24.683724Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:24.683724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.23399","created_at":"2026-06-09T02:07:24.683835+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.23399v4","created_at":"2026-06-09T02:07:24.683835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.23399","created_at":"2026-06-09T02:07:24.683835+00:00"},{"alias_kind":"pith_short_12","alias_value":"WTZCTPJWRDTE","created_at":"2026-06-09T02:07:24.683835+00:00"},{"alias_kind":"pith_short_16","alias_value":"WTZCTPJWRDTE4M7F","created_at":"2026-06-09T02:07:24.683835+00:00"},{"alias_kind":"pith_short_8","alias_value":"WTZCTPJW","created_at":"2026-06-09T02:07:24.683835+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.25215","citing_title":"A density-functional perspective on force fields","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW","json":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW.json","graph_json":"https://pith.science/api/pith-number/WTZCTPJWRDTE4M7F7L6I2FFGUW/graph.json","events_json":"https://pith.science/api/pith-number/WTZCTPJWRDTE4M7F7L6I2FFGUW/events.json","paper":"https://pith.science/paper/WTZCTPJW"},"agent_actions":{"view_html":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW","download_json":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW.json","view_paper":"https://pith.science/paper/WTZCTPJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.23399&json=true","fetch_graph":"https://pith.science/api/pith-number/WTZCTPJWRDTE4M7F7L6I2FFGUW/graph.json","fetch_events":"https://pith.science/api/pith-number/WTZCTPJWRDTE4M7F7L6I2FFGUW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW/action/storage_attestation","attest_author":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW/action/author_attestation","sign_citation":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW/action/citation_signature","submit_replication":"https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW/action/replication_record"}},"created_at":"2026-06-09T02:07:24.683835+00:00","updated_at":"2026-06-09T02:07:24.683835+00:00"}