{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3TZ3Z7JGDGTD6G27INVUN2G5YK","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":"108d032b36ce9a05c7e4acb78f5151bba158b971e1bc94716b3f919ce9daf053","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-18T09:03:47Z","title_canon_sha256":"b06474d70bf26ce20ce7ef6d4ef40194d08c86bd98281a7b535295ce000daa9d"},"schema_version":"1.0","source":{"id":"1701.04987","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04987","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04987v3","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04987","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"pith_short_12","alias_value":"3TZ3Z7JGDGTD","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3TZ3Z7JGDGTD6G27","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3TZ3Z7JG","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:edb4fba5ce47746b8fa2233cd13a987438b06269a9eb87b4dd3b795acf8ae0e2","target":"graph","created_at":"2026-05-18T00:23:01Z","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 define Dirac operators on $\\mathbb{S}^3$ (and $\\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum. Certain examples, such as circles in $\\mathbb{S}^3$, are investigated in detail and we compute the dimension of the zero-energy eigenspace.","authors_text":"Fabian Portmann, Jan Philip Solovej, J\\'er\\'emy Sok","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-18T09:03:47Z","title":"Self-adjointness and spectral properties of Dirac operators with magnetic links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04987","kind":"arxiv","version":3},"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":"sha256:05ff10442b1d32e79fe9e8a571ee4cb84092a7fe5557f5d774550c16239913e6","target":"record","created_at":"2026-05-18T00:23:01Z","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":"108d032b36ce9a05c7e4acb78f5151bba158b971e1bc94716b3f919ce9daf053","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-18T09:03:47Z","title_canon_sha256":"b06474d70bf26ce20ce7ef6d4ef40194d08c86bd98281a7b535295ce000daa9d"},"schema_version":"1.0","source":{"id":"1701.04987","kind":"arxiv","version":3}},"canonical_sha256":"dcf3bcfd2619a63f1b5f436b46e8ddc296346c84ff0213f1359ac1678ebf5235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcf3bcfd2619a63f1b5f436b46e8ddc296346c84ff0213f1359ac1678ebf5235","first_computed_at":"2026-05-18T00:23:01.441493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:01.441493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3UarCTg3XI/2Qkc+E3KUPDb/ywxYTOfu1orURVWtkCkpcsu+Vp6SZ0+e0T6hyU2S7BZCS4Ehj8NvRpGEGxjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:01.442148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04987","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05ff10442b1d32e79fe9e8a571ee4cb84092a7fe5557f5d774550c16239913e6","sha256:edb4fba5ce47746b8fa2233cd13a987438b06269a9eb87b4dd3b795acf8ae0e2"],"state_sha256":"843e2f82732b22fd609d0445af49b961536864ebe1338312455362f81decaca1"}