{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NGWNRMB3TUUITZ7QFGCWLRBK4W","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":"23580d90087166373b46262e59920d06f5904bf33aaf735afe903c6fd897040f","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-01-28T16:23:38Z","title_canon_sha256":"5d16edce99a44662f623ac207edaab31d3e416eba1a4624acb508c89a96d002a"},"schema_version":"1.0","source":{"id":"1601.07816","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07816","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07816v2","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07816","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"pith_short_12","alias_value":"NGWNRMB3TUUI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGWNRMB3TUUITZ7Q","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGWNRMB3","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:69e11f6aca33978a56461c8a0cfd0db1a97c2405ff18e6afee6bb87983559ec1","target":"graph","created_at":"2026-05-18T00:14:23Z","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 derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the $\\rm Spin^c$ Dirac operator. This allows us to obtain eigenvalue estimates for the twisted Dirac operator appearing in the context of Dirac-harmonic maps and their extensions, from which we also obtain several Liouville type results.","authors_text":"Volker Branding","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-01-28T16:23:38Z","title":"A note on twisted Dirac operators on closed surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07816","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":"sha256:5c484a88de4b3fb944b48dfd93c950f8f1313fe8ab5b18e8e0575a3b98a7acae","target":"record","created_at":"2026-05-18T00:14:23Z","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":"23580d90087166373b46262e59920d06f5904bf33aaf735afe903c6fd897040f","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-01-28T16:23:38Z","title_canon_sha256":"5d16edce99a44662f623ac207edaab31d3e416eba1a4624acb508c89a96d002a"},"schema_version":"1.0","source":{"id":"1601.07816","kind":"arxiv","version":2}},"canonical_sha256":"69acd8b03b9d2889e7f0298565c42ae5942d1f41d3b34f27ec6b4fa2391d1802","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69acd8b03b9d2889e7f0298565c42ae5942d1f41d3b34f27ec6b4fa2391d1802","first_computed_at":"2026-05-18T00:14:23.185672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:23.185672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lqP3Yrw2pWeg7kJgBd0F0uks0iZvo6bnVvbyQH3sMi6XAXPZXcMCURxOqljF3kifXOM92iq25Z0rIExKrKcjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:23.186168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07816","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c484a88de4b3fb944b48dfd93c950f8f1313fe8ab5b18e8e0575a3b98a7acae","sha256:69e11f6aca33978a56461c8a0cfd0db1a97c2405ff18e6afee6bb87983559ec1"],"state_sha256":"26bef14ff1fd4a06bbab8f8eeffcf2d686f61e5327f5a6e82927942373b02df2"}