{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:77I5EAUCPPNQWGENWSYLERG6IK","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":"7ec72de63a1b6fc028d25ee06be65d4745dce1f0c9cfdf5f36d2cf953dca2642","cross_cats_sorted":["math-ph","math.AP","math.DG","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-12-20T20:42:23Z","title_canon_sha256":"8eb0bed0e13292ba54e6a2a679eb8f51d82522c3bfc531967ce61d9bf898965c"},"schema_version":"1.0","source":{"id":"2412.16332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16332","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16332v1","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16332","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"77I5EAUCPPNQ","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"pith_short_16","alias_value":"77I5EAUCPPNQWGEN","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"pith_short_8","alias_value":"77I5EAUC","created_at":"2026-07-05T09:52:44Z"}],"graph_snapshots":[{"event_id":"sha256:6988cdeced35128905266e13682fc05b83aed39453ae258286bdac76719aab28","target":"graph","created_at":"2026-07-05T09:52:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.16332/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we consider operators of the form $\\partial_s\\xi+A(s)\\xi$ where $s$ lies in an interval $[-T,T]$ and $s\\mapsto A(s)$ is continuous. Without boundary conditions these operators are not Fredholm. However, using interpolation theory one can define suitable boundary conditions for these operators so that they become Fredholm. We show that in this case the Fredholm index is given by the spectral flow of the operator path $A$.","authors_text":"Joa Weber, Urs Frauenfelder","cross_cats":["math-ph","math.AP","math.DG","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-12-20T20:42:23Z","title":"On the spectral flow theorem of Robbin-Salamon for finite intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16332","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:b434a17599f389258ebb32865e5aa1c88ce290a9d762e85d553bc29bf59ee631","target":"record","created_at":"2026-07-05T09:52:44Z","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":"7ec72de63a1b6fc028d25ee06be65d4745dce1f0c9cfdf5f36d2cf953dca2642","cross_cats_sorted":["math-ph","math.AP","math.DG","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-12-20T20:42:23Z","title_canon_sha256":"8eb0bed0e13292ba54e6a2a679eb8f51d82522c3bfc531967ce61d9bf898965c"},"schema_version":"1.0","source":{"id":"2412.16332","kind":"arxiv","version":1}},"canonical_sha256":"ffd1d202827bdb0b188db4b0b244de4299a25036fe0c76a37fc2496c43571065","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffd1d202827bdb0b188db4b0b244de4299a25036fe0c76a37fc2496c43571065","first_computed_at":"2026-07-05T09:52:44.717808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:44.717808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AUgBhWdyNHL1/XLHunkR3BvJNx/A5+qmdGG1DJ36ksyE/ubW99HnKl31ioJtIfcWGm0Cc5mrzrgL2mAxF/rWDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:44.718224Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.16332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b434a17599f389258ebb32865e5aa1c88ce290a9d762e85d553bc29bf59ee631","sha256:6988cdeced35128905266e13682fc05b83aed39453ae258286bdac76719aab28"],"state_sha256":"04ed7b7d96267d57551e0b73b48a8338dc4a43b80e721b4e48e82f4c187449ea"}