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For the one-electron case, a Hohenberg-Kohn theorem exists formulated with the total current density. Here we show that the generalized Hohenberg-Kohn energy functional $\\mathord{\\cal E}_{V_0,\\mathbf{A}_0}(\\rho,\\mathbf{j}) = \\langle \\psi(\\rho,\\mathbf{j}),H(V_0,\\mathbf{A}_0)\\psi(\\rho,\\mathbf{j})\\rangle$ can be minimal for densi"},"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":false},"canonical_record":{"source":{"id":"1404.3297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-12T15:30:52Z","cross_cats_sorted":["cond-mat.mtrl-sci","physics.chem-ph"],"title_canon_sha256":"2e5da7bd1cd9eee9226f46e15a9cff0a13aa69da501cbcaf2d47186ce8aa1ee1","abstract_canon_sha256":"c2aace79a685dcf9e153050c16945fe1a42f1c2e4b96d90bf4c26bcb0e2f85cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:00.105521Z","signature_b64":"YeKdsBqAQWHenexPz4dbr9L28twePCFxyTWO56Mq0BNTQnYvEqr9Df7I0OJCSwk0+ID8lQLFBAiGbcrWZ+mKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c7fe00c3b7d982591d54e00671f5a88f99c31bd712913277e81be92fe160ffe","last_reissued_at":"2026-05-18T02:20:00.104829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:00.104829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-existence of a Hohenberg-Kohn Variational Principle in Total Current Density Functional Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Andre Laestadius, Michael Benedicks","submitted_at":"2014-04-12T15:30:52Z","abstract_excerpt":"For a many-electron system, whether the particle density $\\rho(\\mathbf{r})$ and the total current density $\\mathbf{j}(\\mathbf{r})$ are sufficient to determine the one-body potential $V(\\mathbf{r})$ and vector potential $\\mathbf{A}(\\mathbf{r})$, is still an open question. For the one-electron case, a Hohenberg-Kohn theorem exists formulated with the total current density. Here we show that the generalized Hohenberg-Kohn energy functional $\\mathord{\\cal E}_{V_0,\\mathbf{A}_0}(\\rho,\\mathbf{j}) = \\langle \\psi(\\rho,\\mathbf{j}),H(V_0,\\mathbf{A}_0)\\psi(\\rho,\\mathbf{j})\\rangle$ can be minimal for densi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3297","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"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":"1404.3297","created_at":"2026-05-18T02:20:00.104937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.3297v1","created_at":"2026-05-18T02:20:00.104937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3297","created_at":"2026-05-18T02:20:00.104937+00:00"},{"alias_kind":"pith_short_12","alias_value":"RR76ADB3PWMC","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RR76ADB3PWMCLEOV","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RR76ADB3","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD","json":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD.json","graph_json":"https://pith.science/api/pith-number/RR76ADB3PWMCLEOVJYAGOH22RD/graph.json","events_json":"https://pith.science/api/pith-number/RR76ADB3PWMCLEOVJYAGOH22RD/events.json","paper":"https://pith.science/paper/RR76ADB3"},"agent_actions":{"view_html":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD","download_json":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD.json","view_paper":"https://pith.science/paper/RR76ADB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.3297&json=true","fetch_graph":"https://pith.science/api/pith-number/RR76ADB3PWMCLEOVJYAGOH22RD/graph.json","fetch_events":"https://pith.science/api/pith-number/RR76ADB3PWMCLEOVJYAGOH22RD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD/action/storage_attestation","attest_author":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD/action/author_attestation","sign_citation":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD/action/citation_signature","submit_replication":"https://pith.science/pith/RR76ADB3PWMCLEOVJYAGOH22RD/action/replication_record"}},"created_at":"2026-05-18T02:20:00.104937+00:00","updated_at":"2026-05-18T02:20:00.104937+00:00"}