{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VXBVJVCPBNLKOIYPHGQW5D7J52","short_pith_number":"pith:VXBVJVCP","canonical_record":{"source":{"id":"1705.09632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-26T16:03:57Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"ac802a48d0603578a07d848a0933ed544ee3f3e5ecd788b04bd4d0a5c22d879d","abstract_canon_sha256":"423f7b6a4f6ebb9ce5e940591f64d73a0e1ee50cd83c62740ab2acf27c68ff28"},"schema_version":"1.0"},"canonical_sha256":"adc354d44f0b56a7230f39a16e8fe9eeaea84e4843790870cefcecf27b269b77","source":{"kind":"arxiv","id":"1705.09632","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09632","created_at":"2026-05-18T00:30:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09632v2","created_at":"2026-05-18T00:30:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09632","created_at":"2026-05-18T00:30:44Z"},{"alias_kind":"pith_short_12","alias_value":"VXBVJVCPBNLK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VXBVJVCPBNLKOIYP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VXBVJVCP","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VXBVJVCPBNLKOIYPHGQW5D7J52","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-26T16:03:57Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"ac802a48d0603578a07d848a0933ed544ee3f3e5ecd788b04bd4d0a5c22d879d","abstract_canon_sha256":"423f7b6a4f6ebb9ce5e940591f64d73a0e1ee50cd83c62740ab2acf27c68ff28"},"schema_version":"1.0"},"canonical_sha256":"adc354d44f0b56a7230f39a16e8fe9eeaea84e4843790870cefcecf27b269b77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:44.616926Z","signature_b64":"7Uil/yK7VuO1SegCOaggI7f0l/qX0n3J3QLZvxlUxa+qI7sYtyUyyTcV1mzKIyMY1EUkfd2sPNKJR9Pyc7nmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adc354d44f0b56a7230f39a16e8fe9eeaea84e4843790870cefcecf27b269b77","last_reissued_at":"2026-05-18T00:30:44.616472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:44.616472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09632","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":"2026-05-18T00:30:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQlXF9hShTbxqwaI3TQfWQqCLGwjDGN822oJFjUKoIKQlaWrByeLT0iFP6xLviWMCDllfU+SzPWeU3d1naMpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:58:38.909708Z"},"content_sha256":"063994a3439f303f141f4d3a34a8d046abc4f09185d7c7ebb7bfbce3eff5e52d","schema_version":"1.0","event_id":"sha256:063994a3439f303f141f4d3a34a8d046abc4f09185d7c7ebb7bfbce3eff5e52d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VXBVJVCPBNLKOIYPHGQW5D7J52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Magnetic Zero-Modes, Vortices and Cartan Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Bernd Schroers, Calum Ross","submitted_at":"2017-05-26T16:03:57Z","abstract_excerpt":"We show that magnetic zero-modes of the Dirac operator on $\\mathbb{R}^3$ which obey an additional non-linear equation are closely related to vortex configurations on the 2-sphere, and that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09632","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":"2026-05-18T00:30:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzQ4FLDAVIeXQRxLXRSOFl/wHleL2kYdiDi7HYIcx8w16pi3y6rbSfqD8XXaUOycFKXOE0Aw9dPisg0LFHvMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:58:38.910220Z"},"content_sha256":"a373c2b026c2cdcdd89ecd0932968896fac24d3c77b2f18cf5895a65c894398e","schema_version":"1.0","event_id":"sha256:a373c2b026c2cdcdd89ecd0932968896fac24d3c77b2f18cf5895a65c894398e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXBVJVCPBNLKOIYPHGQW5D7J52/bundle.json","state_url":"https://pith.science/pith/VXBVJVCPBNLKOIYPHGQW5D7J52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXBVJVCPBNLKOIYPHGQW5D7J52/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":"2026-05-30T16:58:38Z","links":{"resolver":"https://pith.science/pith/VXBVJVCPBNLKOIYPHGQW5D7J52","bundle":"https://pith.science/pith/VXBVJVCPBNLKOIYPHGQW5D7J52/bundle.json","state":"https://pith.science/pith/VXBVJVCPBNLKOIYPHGQW5D7J52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXBVJVCPBNLKOIYPHGQW5D7J52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VXBVJVCPBNLKOIYPHGQW5D7J52","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":"423f7b6a4f6ebb9ce5e940591f64d73a0e1ee50cd83c62740ab2acf27c68ff28","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-26T16:03:57Z","title_canon_sha256":"ac802a48d0603578a07d848a0933ed544ee3f3e5ecd788b04bd4d0a5c22d879d"},"schema_version":"1.0","source":{"id":"1705.09632","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09632","created_at":"2026-05-18T00:30:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09632v2","created_at":"2026-05-18T00:30:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09632","created_at":"2026-05-18T00:30:44Z"},{"alias_kind":"pith_short_12","alias_value":"VXBVJVCPBNLK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VXBVJVCPBNLKOIYP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VXBVJVCP","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:a373c2b026c2cdcdd89ecd0932968896fac24d3c77b2f18cf5895a65c894398e","target":"graph","created_at":"2026-05-18T00:30:44Z","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 show that magnetic zero-modes of the Dirac operator on $\\mathbb{R}^3$ which obey an additional non-linear equation are closely related to vortex configurations on the 2-sphere, and that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables.","authors_text":"Bernd Schroers, Calum Ross","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-26T16:03:57Z","title":"Magnetic Zero-Modes, Vortices and Cartan Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09632","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":"sha256:063994a3439f303f141f4d3a34a8d046abc4f09185d7c7ebb7bfbce3eff5e52d","target":"record","created_at":"2026-05-18T00:30:44Z","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":"423f7b6a4f6ebb9ce5e940591f64d73a0e1ee50cd83c62740ab2acf27c68ff28","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-26T16:03:57Z","title_canon_sha256":"ac802a48d0603578a07d848a0933ed544ee3f3e5ecd788b04bd4d0a5c22d879d"},"schema_version":"1.0","source":{"id":"1705.09632","kind":"arxiv","version":2}},"canonical_sha256":"adc354d44f0b56a7230f39a16e8fe9eeaea84e4843790870cefcecf27b269b77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adc354d44f0b56a7230f39a16e8fe9eeaea84e4843790870cefcecf27b269b77","first_computed_at":"2026-05-18T00:30:44.616472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:44.616472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Uil/yK7VuO1SegCOaggI7f0l/qX0n3J3QLZvxlUxa+qI7sYtyUyyTcV1mzKIyMY1EUkfd2sPNKJR9Pyc7nmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:44.616926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09632","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:063994a3439f303f141f4d3a34a8d046abc4f09185d7c7ebb7bfbce3eff5e52d","sha256:a373c2b026c2cdcdd89ecd0932968896fac24d3c77b2f18cf5895a65c894398e"],"state_sha256":"263ad9fa0e1d4884fc91f1d084735c6ebec9b552507090203b441d6b8f06dac2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AMFKi9Jh5cN6UzSKxMOXqy0g6w9BHpXNreV3E/xC98Oy68/GcnbzEMd8PaxBKlS9TOPE0j5x1iBCDchqMd0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:58:38.914132Z","bundle_sha256":"2597f7e74ded2977fcdbc8aa9dee24f6448a1e141d680efc0ec4a30c13798e14"}}