{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:APJJ6YNXVZIUVS3UXVRLWLGQYM","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":"4ca2927616eaa577d7ce766792763ad8dc0870c54cfd63a85de3525aa61d3a27","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.DG","submitted_at":"2004-11-15T13:22:10Z","title_canon_sha256":"e2106adaa5354e883d47658c74f5a6cab690cdf0643d92534a9d9288a21883f0"},"schema_version":"1.0","source":{"id":"math/0411327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411327","created_at":"2026-07-04T14:39:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411327v1","created_at":"2026-07-04T14:39:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411327","created_at":"2026-07-04T14:39:22Z"},{"alias_kind":"pith_short_12","alias_value":"APJJ6YNXVZIU","created_at":"2026-07-04T14:39:22Z"},{"alias_kind":"pith_short_16","alias_value":"APJJ6YNXVZIUVS3U","created_at":"2026-07-04T14:39:22Z"},{"alias_kind":"pith_short_8","alias_value":"APJJ6YNX","created_at":"2026-07-04T14:39:22Z"}],"graph_snapshots":[{"event_id":"sha256:cd9ee66056e5b49597162b06a5a56ad32c03734e979ccf13431a560363b95260","target":"graph","created_at":"2026-07-04T14:39:22Z","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/math/0411327/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a new set of coupled field equations motivated by the non-linear supersymmetric sigma model of quantum field theory. These equations couple a map into a Riemannian manifold controlled by a harmonic map like action with a spinor field along that map. We study the solutions which we call Dirac-harmonic maps from a Riemann surface to a sphere $\\S^n$. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.","authors_text":"Guofang Wang, Jiayu Li, Juergen Jost, Qun Chen","cross_cats":["math.AP"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2004-11-15T13:22:10Z","title":"Regularity Theorems and Energy Identities for Dirac-Harmonic Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411327","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":"sha256:7abdc617f811a2fa4e5bf7b0c454a53e1052cfac99e4f07f988098a88aa90590","target":"record","created_at":"2026-07-04T14:39:22Z","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":"4ca2927616eaa577d7ce766792763ad8dc0870c54cfd63a85de3525aa61d3a27","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.DG","submitted_at":"2004-11-15T13:22:10Z","title_canon_sha256":"e2106adaa5354e883d47658c74f5a6cab690cdf0643d92534a9d9288a21883f0"},"schema_version":"1.0","source":{"id":"math/0411327","kind":"arxiv","version":1}},"canonical_sha256":"03d29f61b7ae514acb74bd62bb2cd0c3061a7d4cc60c6497fd69705dd6e5b0d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03d29f61b7ae514acb74bd62bb2cd0c3061a7d4cc60c6497fd69705dd6e5b0d2","first_computed_at":"2026-07-04T14:39:22.544548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:22.544548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+qKcdQXVHtR5H6obiT4iRDwvSxHxbYIEJR9M9oMXPrhKy0lkodTqyPWSIC9bSxtpjPwli+Nf1p1A3Q4c1QWBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:22.544940Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0411327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7abdc617f811a2fa4e5bf7b0c454a53e1052cfac99e4f07f988098a88aa90590","sha256:cd9ee66056e5b49597162b06a5a56ad32c03734e979ccf13431a560363b95260"],"state_sha256":"c201fe055c01245342827564ba162cc99965a0107e94e9099e94484189b84102"}