{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:M3SXOEKNDQ7JZC6FENJYQEEF73","short_pith_number":"pith:M3SXOEKN","schema_version":"1.0","canonical_sha256":"66e577114d1c3e9c8bc52353881085fee7b090bcf29ef0bfd15e834168e7cd97","source":{"kind":"arxiv","id":"1708.00287","version":3},"attestation_state":"computed","paper":{"title":"Existence of Hartree-Fock excited states for atoms and molecules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Mathieu Lewin (CEREMADE)","submitted_at":"2017-08-01T12:43:04Z","abstract_excerpt":"For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the $N$-particle linear Schr{\\\"o}dinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with"},"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":"1708.00287","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-01T12:43:04Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"c9e6f7193efef099757f14df1c4c6191d9855803b2ccaa1c04e5b3327fce88d8","abstract_canon_sha256":"c12fd54f7595ea0e24e6ff236c89880a8649b24e298c0e2c99116bb67ccb1bd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:00.932253Z","signature_b64":"8/LVeOG4wa2IrnV+HSvYN2VT6u+Se01r+IzmZPD/ob3+NWwy2rzTGu8AkrPgt839DdKRDx05n2NRvKFR2icRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66e577114d1c3e9c8bc52353881085fee7b090bcf29ef0bfd15e834168e7cd97","last_reissued_at":"2026-05-18T00:30:00.931454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:00.931454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of Hartree-Fock excited states for atoms and molecules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Mathieu Lewin (CEREMADE)","submitted_at":"2017-08-01T12:43:04Z","abstract_excerpt":"For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the $N$-particle linear Schr{\\\"o}dinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00287","kind":"arxiv","version":3},"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":"1708.00287","created_at":"2026-05-18T00:30:00.931586+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.00287v3","created_at":"2026-05-18T00:30:00.931586+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00287","created_at":"2026-05-18T00:30:00.931586+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3SXOEKNDQ7J","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3SXOEKNDQ7JZC6F","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3SXOEKN","created_at":"2026-05-18T12:31:28.150371+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/M3SXOEKNDQ7JZC6FENJYQEEF73","json":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73.json","graph_json":"https://pith.science/api/pith-number/M3SXOEKNDQ7JZC6FENJYQEEF73/graph.json","events_json":"https://pith.science/api/pith-number/M3SXOEKNDQ7JZC6FENJYQEEF73/events.json","paper":"https://pith.science/paper/M3SXOEKN"},"agent_actions":{"view_html":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73","download_json":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73.json","view_paper":"https://pith.science/paper/M3SXOEKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.00287&json=true","fetch_graph":"https://pith.science/api/pith-number/M3SXOEKNDQ7JZC6FENJYQEEF73/graph.json","fetch_events":"https://pith.science/api/pith-number/M3SXOEKNDQ7JZC6FENJYQEEF73/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73/action/storage_attestation","attest_author":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73/action/author_attestation","sign_citation":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73/action/citation_signature","submit_replication":"https://pith.science/pith/M3SXOEKNDQ7JZC6FENJYQEEF73/action/replication_record"}},"created_at":"2026-05-18T00:30:00.931586+00:00","updated_at":"2026-05-18T00:30:00.931586+00:00"}