{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NGWNRMB3TUUITZ7QFGCWLRBK4W","short_pith_number":"pith:NGWNRMB3","canonical_record":{"source":{"id":"1601.07816","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-01-28T16:23:38Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"5d16edce99a44662f623ac207edaab31d3e416eba1a4624acb508c89a96d002a","abstract_canon_sha256":"23580d90087166373b46262e59920d06f5904bf33aaf735afe903c6fd897040f"},"schema_version":"1.0"},"canonical_sha256":"69acd8b03b9d2889e7f0298565c42ae5942d1f41d3b34f27ec6b4fa2391d1802","source":{"kind":"arxiv","id":"1601.07816","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NGWNRMB3TUUITZ7QFGCWLRBK4W","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07816","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-01-28T16:23:38Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"5d16edce99a44662f623ac207edaab31d3e416eba1a4624acb508c89a96d002a","abstract_canon_sha256":"23580d90087166373b46262e59920d06f5904bf33aaf735afe903c6fd897040f"},"schema_version":"1.0"},"canonical_sha256":"69acd8b03b9d2889e7f0298565c42ae5942d1f41d3b34f27ec6b4fa2391d1802","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:23.186168Z","signature_b64":"lqP3Yrw2pWeg7kJgBd0F0uks0iZvo6bnVvbyQH3sMi6XAXPZXcMCURxOqljF3kifXOM92iq25Z0rIExKrKcjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69acd8b03b9d2889e7f0298565c42ae5942d1f41d3b34f27ec6b4fa2391d1802","last_reissued_at":"2026-05-18T00:14:23.185672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:23.185672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07816","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOwtG4/BFnIi0dyDWS8vKL1rjc/fmSW1Ws+HWZCgu0qbT9zFFxsIMtNkmKsd32MsAyrIdmy7IJiP6dF4/K2UBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:04:14.378728Z"},"content_sha256":"5c484a88de4b3fb944b48dfd93c950f8f1313fe8ab5b18e8e0575a3b98a7acae","schema_version":"1.0","event_id":"sha256:5c484a88de4b3fb944b48dfd93c950f8f1313fe8ab5b18e8e0575a3b98a7acae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NGWNRMB3TUUITZ7QFGCWLRBK4W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on twisted Dirac operators on closed surfaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Volker Branding","submitted_at":"2016-01-28T16:23:38Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07816","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+SXyeZrvfEWaVVwNyYVn1bMQ4CilzBwwOXf2X6SiU/B6QYSxAmOLl05P4qBgcUnbr+W8xZeU2oc7ehEUhQdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:04:14.379073Z"},"content_sha256":"69e11f6aca33978a56461c8a0cfd0db1a97c2405ff18e6afee6bb87983559ec1","schema_version":"1.0","event_id":"sha256:69e11f6aca33978a56461c8a0cfd0db1a97c2405ff18e6afee6bb87983559ec1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGWNRMB3TUUITZ7QFGCWLRBK4W/bundle.json","state_url":"https://pith.science/pith/NGWNRMB3TUUITZ7QFGCWLRBK4W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGWNRMB3TUUITZ7QFGCWLRBK4W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T14:04:14Z","links":{"resolver":"https://pith.science/pith/NGWNRMB3TUUITZ7QFGCWLRBK4W","bundle":"https://pith.science/pith/NGWNRMB3TUUITZ7QFGCWLRBK4W/bundle.json","state":"https://pith.science/pith/NGWNRMB3TUUITZ7QFGCWLRBK4W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGWNRMB3TUUITZ7QFGCWLRBK4W/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bN9WThWxOWtpP9IWG9ORZwFw2jljG6VkfxChtrh4CzU05qNIEZaDlMB/0nt/cwOGpPzigG4e+bFC1YwB/QBjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:04:14.380973Z","bundle_sha256":"d08a0617ff0b24fef55c8904f1acdf29c0ae1349989cc7a814add6116926ba46"}}