{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YBNHHPJKDS45XMATPKEA3QAPKS","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":"09b227d21809ed71fba79e6ce77b989362196a5e60fb39049bc3b483da1fdb40","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-09T12:58:23Z","title_canon_sha256":"077d71c80aaed4526a7d9e7e41311deffe7fc19da28351ade992f07c81e6eefc"},"schema_version":"1.0","source":{"id":"1105.1661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1661","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1661v1","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1661","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"YBNHHPJKDS45","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YBNHHPJKDS45XMAT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YBNHHPJK","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:7c06fc8fa59aec648648d0ccc24f73b4ad16dea94fb49882b3f726ab34ca2109","target":"graph","created_at":"2026-05-18T02:02:02Z","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":"We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slater type variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove that they are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.","authors_text":"Eduardo Chiumiento, Michael Melgaard","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-09T12:58:23Z","title":"Stiefel and Grassmann manifolds in Quantum Chemistry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1661","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:dd00aa77e3f5fa6aa7dce9543e1dd306bf1f34d968d27d52b6e403f58a1d70ee","target":"record","created_at":"2026-05-18T02:02:02Z","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":"09b227d21809ed71fba79e6ce77b989362196a5e60fb39049bc3b483da1fdb40","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-09T12:58:23Z","title_canon_sha256":"077d71c80aaed4526a7d9e7e41311deffe7fc19da28351ade992f07c81e6eefc"},"schema_version":"1.0","source":{"id":"1105.1661","kind":"arxiv","version":1}},"canonical_sha256":"c05a73bd2a1cb9dbb0137a880dc00f54bc14bea5f262ec1b080ef1aaa3c6909a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c05a73bd2a1cb9dbb0137a880dc00f54bc14bea5f262ec1b080ef1aaa3c6909a","first_computed_at":"2026-05-18T02:02:02.577107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:02.577107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u9zWQXcUCF0Ke+nxS+0jxHwg/uL1L/jP1/kPfO6K0dRiKRo9SQvTF3NBOo5etqiYTDyvZ5fs4D3rjJKNmnoxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:02.577906Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd00aa77e3f5fa6aa7dce9543e1dd306bf1f34d968d27d52b6e403f58a1d70ee","sha256:7c06fc8fa59aec648648d0ccc24f73b4ad16dea94fb49882b3f726ab34ca2109"],"state_sha256":"c5aa3dd53a5accc741412d668e634922b42e703a8ba4f3f21932a392dae60974"}