{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2W5WYXGMUOP5RKZSROLLEHFOUQ","short_pith_number":"pith:2W5WYXGM","canonical_record":{"source":{"id":"1212.1727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-12-07T21:33:10Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"1abc773554a49c7de57b1b0a6434735a414f4b55f692fc5669401090fe21a5be","abstract_canon_sha256":"fa78d96e975594842019c3b948a01fed73f404d261b071dd46aec6315aa56e8e"},"schema_version":"1.0"},"canonical_sha256":"d5bb6c5ccca39fd8ab328b96b21caea421067252d5dd83cbb73105fd6a8e6271","source":{"kind":"arxiv","id":"1212.1727","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1727","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1727v1","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1727","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"pith_short_12","alias_value":"2W5WYXGMUOP5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2W5WYXGMUOP5RKZS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2W5WYXGM","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2W5WYXGMUOP5RKZSROLLEHFOUQ","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-12-07T21:33:10Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"1abc773554a49c7de57b1b0a6434735a414f4b55f692fc5669401090fe21a5be","abstract_canon_sha256":"fa78d96e975594842019c3b948a01fed73f404d261b071dd46aec6315aa56e8e"},"schema_version":"1.0"},"canonical_sha256":"d5bb6c5ccca39fd8ab328b96b21caea421067252d5dd83cbb73105fd6a8e6271","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:55.278139Z","signature_b64":"4/nGB3H2pb6VEA8n3lK9EFt96ZiJKCrk251tZsTFoltg/tVMAbIgCPNc4yQFVfgbLcPm2To5TBcSzDW+4YNRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5bb6c5ccca39fd8ab328b96b21caea421067252d5dd83cbb73105fd6a8e6271","last_reissued_at":"2026-05-18T03:38:55.277666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:55.277666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1727","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1zeT7tDhDDAo7fU11NrIB20YMh6m9imX82EUdw9Uq5pzHL4hgMh6x78v0sWgtOnM+ITup2Lp/59hudR5RkJUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:43:18.803966Z"},"content_sha256":"548fa55cbdc217fe7b6b484b5453f4f05d68f0533db6c01f91b98e889b467d97","schema_version":"1.0","event_id":"sha256:548fa55cbdc217fe7b6b484b5453f4f05d68f0533db6c01f91b98e889b467d97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2W5WYXGMUOP5RKZSROLLEHFOUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirichlet and Neumann Eigenvalues for Half-Plane Magnetic Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Raikov, Pablo Miranda, Vincent Bruneau","submitted_at":"2012-12-07T21:33:10Z","abstract_excerpt":"Let $H_{0, D}$ (resp., $H_{0,N}$) be the Schroedinger operator in constant magnetic field on the half-plane with Dirichlet (resp., Neumann) boundary conditions, and let $H_\\ell : = H_{0, \\ell} - V$, $\\ell =D,N$, where the scalar potential $V$ is non negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of $H_D$ and $H_N$ below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behaviour of the discrete spectrum of $H_\\ell$ near $\\inf \\sigma_{ess}(H_\\ell) = "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1727","kind":"arxiv","version":1},"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":"2026-05-18T03:38:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zrAuY9jKD3TFCjxoxFX+zrw/pPmIPF5dl7ZqqREm3Fw2SYbaZqdW34/cqVt7sJcHnTCZ72W5ZfDldOQA0U3WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:43:18.804293Z"},"content_sha256":"a052612d7bc8c424f9bce209bd94bed2064916e7e485b8954134f141a09bccb4","schema_version":"1.0","event_id":"sha256:a052612d7bc8c424f9bce209bd94bed2064916e7e485b8954134f141a09bccb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/bundle.json","state_url":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/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":"2026-06-23T20:43:18Z","links":{"resolver":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ","bundle":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/bundle.json","state":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2W5WYXGMUOP5RKZSROLLEHFOUQ","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":"fa78d96e975594842019c3b948a01fed73f404d261b071dd46aec6315aa56e8e","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-12-07T21:33:10Z","title_canon_sha256":"1abc773554a49c7de57b1b0a6434735a414f4b55f692fc5669401090fe21a5be"},"schema_version":"1.0","source":{"id":"1212.1727","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1727","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1727v1","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1727","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"pith_short_12","alias_value":"2W5WYXGMUOP5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2W5WYXGMUOP5RKZS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2W5WYXGM","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:a052612d7bc8c424f9bce209bd94bed2064916e7e485b8954134f141a09bccb4","target":"graph","created_at":"2026-05-18T03:38:55Z","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":"Let $H_{0, D}$ (resp., $H_{0,N}$) be the Schroedinger operator in constant magnetic field on the half-plane with Dirichlet (resp., Neumann) boundary conditions, and let $H_\\ell : = H_{0, \\ell} - V$, $\\ell =D,N$, where the scalar potential $V$ is non negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of $H_D$ and $H_N$ below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behaviour of the discrete spectrum of $H_\\ell$ near $\\inf \\sigma_{ess}(H_\\ell) = ","authors_text":"Georgi Raikov, Pablo Miranda, Vincent Bruneau","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-12-07T21:33:10Z","title":"Dirichlet and Neumann Eigenvalues for Half-Plane Magnetic Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1727","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":"sha256:548fa55cbdc217fe7b6b484b5453f4f05d68f0533db6c01f91b98e889b467d97","target":"record","created_at":"2026-05-18T03:38:55Z","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":"fa78d96e975594842019c3b948a01fed73f404d261b071dd46aec6315aa56e8e","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-12-07T21:33:10Z","title_canon_sha256":"1abc773554a49c7de57b1b0a6434735a414f4b55f692fc5669401090fe21a5be"},"schema_version":"1.0","source":{"id":"1212.1727","kind":"arxiv","version":1}},"canonical_sha256":"d5bb6c5ccca39fd8ab328b96b21caea421067252d5dd83cbb73105fd6a8e6271","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5bb6c5ccca39fd8ab328b96b21caea421067252d5dd83cbb73105fd6a8e6271","first_computed_at":"2026-05-18T03:38:55.277666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:55.277666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/nGB3H2pb6VEA8n3lK9EFt96ZiJKCrk251tZsTFoltg/tVMAbIgCPNc4yQFVfgbLcPm2To5TBcSzDW+4YNRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:55.278139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1727","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:548fa55cbdc217fe7b6b484b5453f4f05d68f0533db6c01f91b98e889b467d97","sha256:a052612d7bc8c424f9bce209bd94bed2064916e7e485b8954134f141a09bccb4"],"state_sha256":"895202a9666c322be7cc8d96baaa8209f0e4cbcc5132e03d4c536a06660cb9cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9y2oNuR7799+XMvwK5kvn251JUyE20mS1Sk4whV7S5LR0fpaqtxZYgjcXTVKvXHiFh+LMe9POWmLkL67jMiIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:43:18.808785Z","bundle_sha256":"49b2f04715a461564c3fb5a016f86954eb7152d9acfe5096e8e0cbee94bec3f2"}}