{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IGBPD5R4HU73MLX5SQFZBKGWFR","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":"d8cace7d61bfcc5c3f00157b36be25d3cfe43613811d7f264e68a453a8c8b159","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-01T09:41:44Z","title_canon_sha256":"2a2a2843e654940d4defc21f6b8939901afef8b198d1b7a7d2694d986b1b1f27"},"schema_version":"1.0","source":{"id":"1310.0210","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0210","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0210v2","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0210","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"pith_short_12","alias_value":"IGBPD5R4HU73","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IGBPD5R4HU73MLX5","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IGBPD5R4","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:da055c89e817ed76ad1973dc1822dd92d2fe673e6b7698292b60acad2490b658","target":"graph","created_at":"2026-05-18T00:49:05Z","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":"Let M be an even dimensional compact Riemannian manifold with boundary and let D be a Dirac operator acting on the sections of the Clifford module E over M. We impose certain local elliptic boundary conditions for D obtaining a selfadjoint extension D_F of D. For a smooth U(n)--valued function g:M -> U(n) we establish a formula for the spectral flow along the straight line between D_F and g^{-1} D_F g. This spectral flow is motivated by index theory: in odd dimensions it gives the natural pairing between the K--homology class of the operator and the K--theory class of g.\n  In our situation, wi","authors_text":"Alexander Gorokhovsky, Matthias Lesch","cross_cats":["math.DG","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-01T09:41:44Z","title":"On the spectral flow for Dirac operators with local boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0210","kind":"arxiv","version":2},"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:d2c21fd266909aaf02589cddf820e727ed55f553888e031fbd798aab04102804","target":"record","created_at":"2026-05-18T00:49:05Z","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":"d8cace7d61bfcc5c3f00157b36be25d3cfe43613811d7f264e68a453a8c8b159","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-01T09:41:44Z","title_canon_sha256":"2a2a2843e654940d4defc21f6b8939901afef8b198d1b7a7d2694d986b1b1f27"},"schema_version":"1.0","source":{"id":"1310.0210","kind":"arxiv","version":2}},"canonical_sha256":"4182f1f63c3d3fb62efd940b90a8d62c663eda978301c646eedf48cc03b7f35c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4182f1f63c3d3fb62efd940b90a8d62c663eda978301c646eedf48cc03b7f35c","first_computed_at":"2026-05-18T00:49:05.003471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:05.003471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6chSIyxJDsSy8HLZD0dQhau0wKlZnYIsjha73bo6xwpnnofBDC8UJr5ite/60jf13/BBwzKqc8FiThFltuwXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:05.003946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0210","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2c21fd266909aaf02589cddf820e727ed55f553888e031fbd798aab04102804","sha256:da055c89e817ed76ad1973dc1822dd92d2fe673e6b7698292b60acad2490b658"],"state_sha256":"01718e8368fdb03957e34b85edf8682c18d1197e6a52addea4fb5c8b70d2c1f4"}