{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XOJXOIN4RTH5NWIA5LJLR3PHAS","short_pith_number":"pith:XOJXOIN4","schema_version":"1.0","canonical_sha256":"bb937721bc8ccfd6d900ead2b8ede704a847b1dcde655931f587992de679e032","source":{"kind":"arxiv","id":"1604.06994","version":3},"attestation_state":"computed","paper":{"title":"Spectral flow for real skew-adjoint Fredholm operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Alan L. Carey, Hermann Schulz-Baldes, John Phillips","submitted_at":"2016-04-24T08:20:12Z","abstract_excerpt":"An analytic definition of a $\\mathbb{Z}_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings through $0$ along the path. The $\\mathbb{Z}_2$-valued spectral flow is shown to satisfy a concatenation property and homotopy invariance, and it provides an isomorphism on the fundamental group of the real skew-adjoint Fredholm operators. Moreover, it is connected to a $\\mathbb{Z}_2$-index pairing for suitable paths. Applications concern the zero energy bound sta"},"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":"1604.06994","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-24T08:20:12Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"279bb5d81be743dfe497125590cd234d1f53387067241b070e794753078e6aa6","abstract_canon_sha256":"1bb332a07b9cac3a03ebdfa31396770c7f31f5cefecffff381554ad8f75ce645"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:57.428771Z","signature_b64":"WS1WblYp+4WGo7QWuE8Rd7oT8fOuaUYVLtvHFyNqLp51qZK0FdZ1Va2vgSeYsAG706dJlzAmveMhtmDv6sU6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb937721bc8ccfd6d900ead2b8ede704a847b1dcde655931f587992de679e032","last_reissued_at":"2026-05-18T00:14:57.428078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:57.428078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral flow for real skew-adjoint Fredholm operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Alan L. Carey, Hermann Schulz-Baldes, John Phillips","submitted_at":"2016-04-24T08:20:12Z","abstract_excerpt":"An analytic definition of a $\\mathbb{Z}_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings through $0$ along the path. The $\\mathbb{Z}_2$-valued spectral flow is shown to satisfy a concatenation property and homotopy invariance, and it provides an isomorphism on the fundamental group of the real skew-adjoint Fredholm operators. Moreover, it is connected to a $\\mathbb{Z}_2$-index pairing for suitable paths. Applications concern the zero energy bound sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06994","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":"1604.06994","created_at":"2026-05-18T00:14:57.428167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06994v3","created_at":"2026-05-18T00:14:57.428167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06994","created_at":"2026-05-18T00:14:57.428167+00:00"},{"alias_kind":"pith_short_12","alias_value":"XOJXOIN4RTH5","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XOJXOIN4RTH5NWIA","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XOJXOIN4","created_at":"2026-05-18T12:30:51.357362+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/XOJXOIN4RTH5NWIA5LJLR3PHAS","json":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS.json","graph_json":"https://pith.science/api/pith-number/XOJXOIN4RTH5NWIA5LJLR3PHAS/graph.json","events_json":"https://pith.science/api/pith-number/XOJXOIN4RTH5NWIA5LJLR3PHAS/events.json","paper":"https://pith.science/paper/XOJXOIN4"},"agent_actions":{"view_html":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS","download_json":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS.json","view_paper":"https://pith.science/paper/XOJXOIN4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06994&json=true","fetch_graph":"https://pith.science/api/pith-number/XOJXOIN4RTH5NWIA5LJLR3PHAS/graph.json","fetch_events":"https://pith.science/api/pith-number/XOJXOIN4RTH5NWIA5LJLR3PHAS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS/action/storage_attestation","attest_author":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS/action/author_attestation","sign_citation":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS/action/citation_signature","submit_replication":"https://pith.science/pith/XOJXOIN4RTH5NWIA5LJLR3PHAS/action/replication_record"}},"created_at":"2026-05-18T00:14:57.428167+00:00","updated_at":"2026-05-18T00:14:57.428167+00:00"}