{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZGE4LI5I7AYYBCDSHQQI6T4IFT","short_pith_number":"pith:ZGE4LI5I","canonical_record":{"source":{"id":"1309.4548","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-18T06:47:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"192eb4a699d2045031f0679168e95ef7b22df42af6b2e9744215c690385ccf99","abstract_canon_sha256":"bde097a018627897c7361d275743b61ef2054f4762c9fa964a46dc1431f9049a"},"schema_version":"1.0"},"canonical_sha256":"c989c5a3a8f8318088723c208f4f882cd670cfdfd0c6821fea59260e0078f1c0","source":{"kind":"arxiv","id":"1309.4548","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4548","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4548v3","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4548","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZGE4LI5I7AYY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZGE4LI5I7AYYBCDS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZGE4LI5I","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZGE4LI5I7AYYBCDSHQQI6T4IFT","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4548","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-18T06:47:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"192eb4a699d2045031f0679168e95ef7b22df42af6b2e9744215c690385ccf99","abstract_canon_sha256":"bde097a018627897c7361d275743b61ef2054f4762c9fa964a46dc1431f9049a"},"schema_version":"1.0"},"canonical_sha256":"c989c5a3a8f8318088723c208f4f882cd670cfdfd0c6821fea59260e0078f1c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:54.335131Z","signature_b64":"9WnKEesOec/nEn88g7H/GeX7Ky03e78JjZlFuJ0PPDF6kSdBZhIAe2bNES9WfKyCVYlsCMsi+dcORO4evQokBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c989c5a3a8f8318088723c208f4f882cd670cfdfd0c6821fea59260e0078f1c0","last_reissued_at":"2026-05-18T03:06:54.334440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:54.334440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4548","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rx7upVFe3hTxHB316N2YhC7cGvMpF+p7XpZuGfQqAGEBfgIBZiFnKk0qqWX6goAd63ZbNmAXysWEheT/mvPmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:02:12.954823Z"},"content_sha256":"9ade438c2fb676939579f88e47c96d0a9ba944bd9c5ad7187765f1bcb9fc2eb4","schema_version":"1.0","event_id":"sha256:9ade438c2fb676939579f88e47c96d0a9ba944bd9c5ad7187765f1bcb9fc2eb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZGE4LI5I7AYYBCDSHQQI6T4IFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edge currents and eigenvalue estimates for magnetic barrier Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eric Soccorsi (CPT), Nicolas Dombrowski, Peter D. Hislop","submitted_at":"2013-09-18T06:47:56Z","abstract_excerpt":"We study two-dimensional magnetic Schr\\\"odinger operators with a magnetic field that is equal to b>0 for x > 0 and (-b) for x < 0. This magnetic Schr\\\"odinger operator exhibits a magnetic barrier at x=0. The unperturbed system is invariant with respect to translations in the y-direction. As a result, the Schr\\\"odinger operator admits a direct integral decomposition. We analyze the band functions of the fiber operators as functions of the wave number and establish their asymptotic behavior. Because the fiber operators are reflection symmetric, the band functions may be classified as odd or even"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4548","kind":"arxiv","version":3},"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":"2026-05-18T03:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxrc+0xg7sf/n18vmDglZBgZ+JccGOQKHbYaTck1xpC+dUGIYY8NK0Lco0WFLRAnRaoLR/Pyftq09Zj0C8tSDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:02:12.955196Z"},"content_sha256":"4c5d4cf1f625f6b059f65e15d68d2f919be6404dc614d8040e0176bff0ea44a0","schema_version":"1.0","event_id":"sha256:4c5d4cf1f625f6b059f65e15d68d2f919be6404dc614d8040e0176bff0ea44a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGE4LI5I7AYYBCDSHQQI6T4IFT/bundle.json","state_url":"https://pith.science/pith/ZGE4LI5I7AYYBCDSHQQI6T4IFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGE4LI5I7AYYBCDSHQQI6T4IFT/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":"2026-05-28T02:02:12Z","links":{"resolver":"https://pith.science/pith/ZGE4LI5I7AYYBCDSHQQI6T4IFT","bundle":"https://pith.science/pith/ZGE4LI5I7AYYBCDSHQQI6T4IFT/bundle.json","state":"https://pith.science/pith/ZGE4LI5I7AYYBCDSHQQI6T4IFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGE4LI5I7AYYBCDSHQQI6T4IFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZGE4LI5I7AYYBCDSHQQI6T4IFT","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":"bde097a018627897c7361d275743b61ef2054f4762c9fa964a46dc1431f9049a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-18T06:47:56Z","title_canon_sha256":"192eb4a699d2045031f0679168e95ef7b22df42af6b2e9744215c690385ccf99"},"schema_version":"1.0","source":{"id":"1309.4548","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4548","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4548v3","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4548","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZGE4LI5I7AYY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZGE4LI5I7AYYBCDS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZGE4LI5I","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:4c5d4cf1f625f6b059f65e15d68d2f919be6404dc614d8040e0176bff0ea44a0","target":"graph","created_at":"2026-05-18T03:06:54Z","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 two-dimensional magnetic Schr\\\"odinger operators with a magnetic field that is equal to b>0 for x > 0 and (-b) for x < 0. This magnetic Schr\\\"odinger operator exhibits a magnetic barrier at x=0. The unperturbed system is invariant with respect to translations in the y-direction. As a result, the Schr\\\"odinger operator admits a direct integral decomposition. We analyze the band functions of the fiber operators as functions of the wave number and establish their asymptotic behavior. Because the fiber operators are reflection symmetric, the band functions may be classified as odd or even","authors_text":"Eric Soccorsi (CPT), Nicolas Dombrowski, Peter D. Hislop","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-18T06:47:56Z","title":"Edge currents and eigenvalue estimates for magnetic barrier Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4548","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":"sha256:9ade438c2fb676939579f88e47c96d0a9ba944bd9c5ad7187765f1bcb9fc2eb4","target":"record","created_at":"2026-05-18T03:06:54Z","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":"bde097a018627897c7361d275743b61ef2054f4762c9fa964a46dc1431f9049a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-18T06:47:56Z","title_canon_sha256":"192eb4a699d2045031f0679168e95ef7b22df42af6b2e9744215c690385ccf99"},"schema_version":"1.0","source":{"id":"1309.4548","kind":"arxiv","version":3}},"canonical_sha256":"c989c5a3a8f8318088723c208f4f882cd670cfdfd0c6821fea59260e0078f1c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c989c5a3a8f8318088723c208f4f882cd670cfdfd0c6821fea59260e0078f1c0","first_computed_at":"2026-05-18T03:06:54.334440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.334440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9WnKEesOec/nEn88g7H/GeX7Ky03e78JjZlFuJ0PPDF6kSdBZhIAe2bNES9WfKyCVYlsCMsi+dcORO4evQokBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.335131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4548","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ade438c2fb676939579f88e47c96d0a9ba944bd9c5ad7187765f1bcb9fc2eb4","sha256:4c5d4cf1f625f6b059f65e15d68d2f919be6404dc614d8040e0176bff0ea44a0"],"state_sha256":"adbc31682a04d7448767997fa432d7c7c63594c7aa161d129509769025332608"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYtNLIRZ27XWYTRcM3wY6WOriGNZgy4ok8QFntAZQzdNi7kocLHAmf0ZBwya0VxrzgsLcXddP+0uqNjD1zOuBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:02:12.957168Z","bundle_sha256":"c6a68464a5e52d18cbab9fdd3004241c0de12f27738febf054d65a6a4f670b8b"}}