{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:ZNX74ZG5TVANR7DHYAS45TGKUE","short_pith_number":"pith:ZNX74ZG5","schema_version":"1.0","canonical_sha256":"cb6ffe64dd9d40d8fc67c025cecccaa116eccb3802de70d5b51fc261a02bf16c","source":{"kind":"arxiv","id":"0906.3589","version":1},"attestation_state":"computed","paper":{"title":"The Hubbard model extended by nearest-neighbor Coulomb and exchange interaction on a cubic cluster - rigorous and exact results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas"],"primary_cat":"cond-mat.str-el","authors_text":"David Zwicker, Rolf Schumann","submitted_at":"2009-06-19T15:56:39Z","abstract_excerpt":"The Hubbard model on a cube was revisited and extended by both nearest-neighbor (nn) Coulomb correlation and {nearest-neighbor} Heisenberg exchange. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on-site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossi"},"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":"0906.3589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-06-19T15:56:39Z","cross_cats_sorted":["cond-mat.quant-gas"],"title_canon_sha256":"da50187f78d0a2fc57f5ac6fb5ab75af09514ecef7ae0d8fec82d4acb2e82ead","abstract_canon_sha256":"2656082509db93fd1c46e8dd64b900f242cc772a574b3ec6ff885b596d7ab627"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:18.860586Z","signature_b64":"lM/UszGc2bwadUVqdlnDCES2LLZUXKzYDlraO2mSjls/EhlVCUZzoV2bSIKU3xyDKMogot8yl/Lq5uJ9SkseDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb6ffe64dd9d40d8fc67c025cecccaa116eccb3802de70d5b51fc261a02bf16c","last_reissued_at":"2026-05-18T02:13:18.859976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:18.859976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Hubbard model extended by nearest-neighbor Coulomb and exchange interaction on a cubic cluster - rigorous and exact results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas"],"primary_cat":"cond-mat.str-el","authors_text":"David Zwicker, Rolf Schumann","submitted_at":"2009-06-19T15:56:39Z","abstract_excerpt":"The Hubbard model on a cube was revisited and extended by both nearest-neighbor (nn) Coulomb correlation and {nearest-neighbor} Heisenberg exchange. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on-site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3589","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":"0906.3589","created_at":"2026-05-18T02:13:18.860058+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.3589v1","created_at":"2026-05-18T02:13:18.860058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3589","created_at":"2026-05-18T02:13:18.860058+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZNX74ZG5TVAN","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZNX74ZG5TVANR7DH","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZNX74ZG5","created_at":"2026-05-18T12:26:03.138858+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/ZNX74ZG5TVANR7DHYAS45TGKUE","json":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE.json","graph_json":"https://pith.science/api/pith-number/ZNX74ZG5TVANR7DHYAS45TGKUE/graph.json","events_json":"https://pith.science/api/pith-number/ZNX74ZG5TVANR7DHYAS45TGKUE/events.json","paper":"https://pith.science/paper/ZNX74ZG5"},"agent_actions":{"view_html":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE","download_json":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE.json","view_paper":"https://pith.science/paper/ZNX74ZG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.3589&json=true","fetch_graph":"https://pith.science/api/pith-number/ZNX74ZG5TVANR7DHYAS45TGKUE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZNX74ZG5TVANR7DHYAS45TGKUE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE/action/storage_attestation","attest_author":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE/action/author_attestation","sign_citation":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE/action/citation_signature","submit_replication":"https://pith.science/pith/ZNX74ZG5TVANR7DHYAS45TGKUE/action/replication_record"}},"created_at":"2026-05-18T02:13:18.860058+00:00","updated_at":"2026-05-18T02:13:18.860058+00:00"}