{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UP4AUKEGVFPOGD3YLDE7OUXTDW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"65544d7d381028a24495391d63a23c995dbc305c9a703ad0cda1b788acbbb739","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-23T07:53:01Z","title_canon_sha256":"7e7d31631d43fd66012f5a4b1a06ba80b37d9f57f84fffa180c097aa33241df1"},"schema_version":"1.0","source":{"id":"1108.4517","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4517","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4517v1","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4517","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"UP4AUKEGVFPO","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UP4AUKEGVFPOGD3Y","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UP4AUKEG","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:667f57afbe937d9a13d5c093d6d46ad45eecb233b4777c3a7fafa6cceaf7eb25","target":"graph","created_at":"2026-05-18T04:14:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Density functional theory (DFT) has become a basic tool for the study of electronic structure of matter, in which the Hohenberg-Kohn theorem plays a fundamental role in the development of DFT. Unfortunately, the existing proofs are incomplete even incorrect; besides, the statement of the Hohenberg-Kohn theorem for many-electron Coulomb systems is not perfect. In this paper, we shall restate the Hohenberg-Kohn theorem for Coulomb type systems and present a rigorous proof by using the Fundamental Theorem of Algebra.","authors_text":"Aihui Zhou","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-23T07:53:01Z","title":"Hohenberg-Kohn Theorem for Coulomb Type Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4517","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b2ccc93d1a23aa5f813966bfdb6ccffc7cf065102df9cea7414b046eaa1f0ddc","target":"record","created_at":"2026-05-18T04:14:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"65544d7d381028a24495391d63a23c995dbc305c9a703ad0cda1b788acbbb739","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-23T07:53:01Z","title_canon_sha256":"7e7d31631d43fd66012f5a4b1a06ba80b37d9f57f84fffa180c097aa33241df1"},"schema_version":"1.0","source":{"id":"1108.4517","kind":"arxiv","version":1}},"canonical_sha256":"a3f80a2886a95ee30f7858c9f752f31d9364671931ace7d26712837fec9a7182","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3f80a2886a95ee30f7858c9f752f31d9364671931ace7d26712837fec9a7182","first_computed_at":"2026-05-18T04:14:54.352138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:54.352138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BNbqkpfP/NvxmdhXSIFyaWtJZUYpqtdwT66YXBc9ABzWpt3VpfJzPkCXvb4ybEmosLY24eENT2pnyVE66HgUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:54.352746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4517","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2ccc93d1a23aa5f813966bfdb6ccffc7cf065102df9cea7414b046eaa1f0ddc","sha256:667f57afbe937d9a13d5c093d6d46ad45eecb233b4777c3a7fafa6cceaf7eb25"],"state_sha256":"cd45017ba53437489dc94deefcd321c022a83bff7409a75768c1eeb4b1c21343"}