{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M5AYMRR2ORX65YYI56FWUFI26R","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":"29144a80ba04f5eec3e62cdda8fd8136e696d8e520261a67c8e2106182054530","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-15T20:28:19Z","title_canon_sha256":"a6fae12e555825fba8bbe4e626d0f959abf5d134b1f8de998b84c89bbdcf0553"},"schema_version":"1.0","source":{"id":"1503.04470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04470","created_at":"2026-05-18T01:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04470v1","created_at":"2026-05-18T01:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04470","created_at":"2026-05-18T01:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"M5AYMRR2ORX6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M5AYMRR2ORX65YYI","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M5AYMRR2","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:d75aba20c32a21284b127edfb10d388ef3005add2f71dbf44b870a0458172ad8","target":"graph","created_at":"2026-05-18T01:55:01Z","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 consider the Pauli operator in $\\mathbb R^3$ for magnetic fields in $L^{3/2}$ that decay at infinity as $|x|^{-2-\\beta}$ with $\\beta > 0$. In this case we are able to prove that the existence of a zero mode for this operator is equivalent to a quantity $\\delta(\\mathbf B)$, defined below, being equal to zero. Complementing a result from [Balinsky, Evans, Lewis (2001)], this implies that for the class of magnetic fields considered, Sobolev, Hardy and CLR inequalities hold whenever the magnetic field has no zero mode.","authors_text":"Hanne Van Den Bosch, Rafael D. Benguria","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-15T20:28:19Z","title":"A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04470","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":"sha256:0725910f66587887c837d6ef2daf15db57250dc2ae6199aa8c42326591d15166","target":"record","created_at":"2026-05-18T01:55:01Z","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":"29144a80ba04f5eec3e62cdda8fd8136e696d8e520261a67c8e2106182054530","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-15T20:28:19Z","title_canon_sha256":"a6fae12e555825fba8bbe4e626d0f959abf5d134b1f8de998b84c89bbdcf0553"},"schema_version":"1.0","source":{"id":"1503.04470","kind":"arxiv","version":1}},"canonical_sha256":"674186463a746feee308ef8b6a151af4775d412bd0a335d8437bb1c64928cf8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"674186463a746feee308ef8b6a151af4775d412bd0a335d8437bb1c64928cf8f","first_computed_at":"2026-05-18T01:55:01.225521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:01.225521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Vy8pqSfnHfdV0nG7wSeotD/fBlPRMyrLZlUpSxNJlyCnzMrjQhGp+vp3RirzjT2Xh8OnwEOz02kofF2xx05Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:01.226079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0725910f66587887c837d6ef2daf15db57250dc2ae6199aa8c42326591d15166","sha256:d75aba20c32a21284b127edfb10d388ef3005add2f71dbf44b870a0458172ad8"],"state_sha256":"24ef207a4512820c4c0e5d37e31848d1fed391f2c84f6adbb8ac33c1e18c31a9"}