{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:J6INMPIOE542PGEJQNWQ2BVQXE","short_pith_number":"pith:J6INMPIO","canonical_record":{"source":{"id":"1307.3133","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T14:59:03Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e569e63b9c2205af7a0a7c0065a4963a51779962541a72bb2160e2bac757a957","abstract_canon_sha256":"b8c77da7a3c57657eca04174ce0ebb48190ed77e7efa082b056c36b39d6c63e4"},"schema_version":"1.0"},"canonical_sha256":"4f90d63d0e2779a79889836d0d06b0b913db82ba18d6b415e882551f40432029","source":{"kind":"arxiv","id":"1307.3133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3133","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3133v1","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3133","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"J6INMPIOE542","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J6INMPIOE542PGEJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J6INMPIO","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:J6INMPIOE542PGEJQNWQ2BVQXE","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3133","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T14:59:03Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e569e63b9c2205af7a0a7c0065a4963a51779962541a72bb2160e2bac757a957","abstract_canon_sha256":"b8c77da7a3c57657eca04174ce0ebb48190ed77e7efa082b056c36b39d6c63e4"},"schema_version":"1.0"},"canonical_sha256":"4f90d63d0e2779a79889836d0d06b0b913db82ba18d6b415e882551f40432029","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:15.739522Z","signature_b64":"8uAYjv0+xaT5yh7nzJZUkjI2euPLq/lFy1S12eYSfEApX2jr8DUYokQwAdsfF/JeAhf+4ZwvCB+rvVYaYT/jCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f90d63d0e2779a79889836d0d06b0b913db82ba18d6b415e882551f40432029","last_reissued_at":"2026-05-18T01:30:15.739006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:15.739006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3133","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8lKqDMegeRhK4gcOrZMg76yCuD/eZ6UcDxpBUbymVRb9Q2y8bPSxzkwPISNwJ0x79YWlOYi9YC+N7D3x4vlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:30:07.072631Z"},"content_sha256":"054908dacfa8dabaf75020643913aaee8eed5d8cbe147f2d4c815ba3216431fe","schema_version":"1.0","event_id":"sha256:054908dacfa8dabaf75020643913aaee8eed5d8cbe147f2d4c815ba3216431fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:J6INMPIOE542PGEJQNWQ2BVQXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Magnetic Dirac-harmonic maps","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Volker Branding","submitted_at":"2013-07-11T14:59:03Z","abstract_excerpt":"We study a functional, whose critical points couple Dirac-harmonic maps from surfaces with a two form. The critical points can be interpreted as coupling the prescribed mean curvature equation to spinor fields. On the other hand, this functional also arises as part of the supersymmetric sigma model in theoretical physics. In two dimensions it is conformally invariant. We call critical points of this functional magnetic Dirac-harmonic maps. We study geometric and analytic properties of magnetic Dirac-harmonic maps including their regularity and the removal of isolated singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3133","kind":"arxiv","version":1},"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":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPhG51KfcctwKuY/NcQwqE9zHA2GgLIhP4+mIeok+2cidBus8snqrcaUt/SZ911Dx5W7maj/SZJpyrTcLsZCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:30:07.072982Z"},"content_sha256":"a1feab26c97d220284db1a0b024d36ecaf96e9d38d5507b85f51b7163773b455","schema_version":"1.0","event_id":"sha256:a1feab26c97d220284db1a0b024d36ecaf96e9d38d5507b85f51b7163773b455"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6INMPIOE542PGEJQNWQ2BVQXE/bundle.json","state_url":"https://pith.science/pith/J6INMPIOE542PGEJQNWQ2BVQXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6INMPIOE542PGEJQNWQ2BVQXE/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":"2026-06-23T12:30:07Z","links":{"resolver":"https://pith.science/pith/J6INMPIOE542PGEJQNWQ2BVQXE","bundle":"https://pith.science/pith/J6INMPIOE542PGEJQNWQ2BVQXE/bundle.json","state":"https://pith.science/pith/J6INMPIOE542PGEJQNWQ2BVQXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6INMPIOE542PGEJQNWQ2BVQXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J6INMPIOE542PGEJQNWQ2BVQXE","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":"b8c77da7a3c57657eca04174ce0ebb48190ed77e7efa082b056c36b39d6c63e4","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T14:59:03Z","title_canon_sha256":"e569e63b9c2205af7a0a7c0065a4963a51779962541a72bb2160e2bac757a957"},"schema_version":"1.0","source":{"id":"1307.3133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3133","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3133v1","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3133","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"J6INMPIOE542","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J6INMPIOE542PGEJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J6INMPIO","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:a1feab26c97d220284db1a0b024d36ecaf96e9d38d5507b85f51b7163773b455","target":"graph","created_at":"2026-05-18T01:30:15Z","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 study a functional, whose critical points couple Dirac-harmonic maps from surfaces with a two form. The critical points can be interpreted as coupling the prescribed mean curvature equation to spinor fields. On the other hand, this functional also arises as part of the supersymmetric sigma model in theoretical physics. In two dimensions it is conformally invariant. We call critical points of this functional magnetic Dirac-harmonic maps. We study geometric and analytic properties of magnetic Dirac-harmonic maps including their regularity and the removal of isolated singularities.","authors_text":"Volker Branding","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T14:59:03Z","title":"Magnetic Dirac-harmonic maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3133","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":"sha256:054908dacfa8dabaf75020643913aaee8eed5d8cbe147f2d4c815ba3216431fe","target":"record","created_at":"2026-05-18T01:30:15Z","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":"b8c77da7a3c57657eca04174ce0ebb48190ed77e7efa082b056c36b39d6c63e4","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T14:59:03Z","title_canon_sha256":"e569e63b9c2205af7a0a7c0065a4963a51779962541a72bb2160e2bac757a957"},"schema_version":"1.0","source":{"id":"1307.3133","kind":"arxiv","version":1}},"canonical_sha256":"4f90d63d0e2779a79889836d0d06b0b913db82ba18d6b415e882551f40432029","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f90d63d0e2779a79889836d0d06b0b913db82ba18d6b415e882551f40432029","first_computed_at":"2026-05-18T01:30:15.739006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:15.739006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8uAYjv0+xaT5yh7nzJZUkjI2euPLq/lFy1S12eYSfEApX2jr8DUYokQwAdsfF/JeAhf+4ZwvCB+rvVYaYT/jCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:15.739522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:054908dacfa8dabaf75020643913aaee8eed5d8cbe147f2d4c815ba3216431fe","sha256:a1feab26c97d220284db1a0b024d36ecaf96e9d38d5507b85f51b7163773b455"],"state_sha256":"c5891ef3618bb30fb6f92e3a6acdf63a0f9adbf6a4d743e4edca20458900a004"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MjlkwQhAAPSydJRXKOBHwVb8MokK6Aq7OgTVGmXOIH2gO6SCFNw7Eq3ORa3WMHAGr8EYBlPTjTsS6Z7EAnpiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:30:07.074921Z","bundle_sha256":"f30191a285e03ecc0adee6396412f1140a018dc346d96f035622be9ce648fa5d"}}