{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:UUMBQIOHSKHSK5JCW5U646SBPD","short_pith_number":"pith:UUMBQIOH","canonical_record":{"source":{"id":"0806.4513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-27T10:09:26Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"0689d25b50461f1479470f137950147fe34c264f13bbb9644f23a55d9a46a0d0","abstract_canon_sha256":"20841bb610667483db475e05cb665fa3ddf8f1a3a30889bf5266c6746c520f74"},"schema_version":"1.0"},"canonical_sha256":"a5181821c7928f257522b769ee7a4178e81cd370138597881fef0795afbe74e8","source":{"kind":"arxiv","id":"0806.4513","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4513","created_at":"2026-05-18T02:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4513v1","created_at":"2026-05-18T02:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4513","created_at":"2026-05-18T02:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"UUMBQIOHSKHS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UUMBQIOHSKHSK5JC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UUMBQIOH","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:UUMBQIOHSKHSK5JCW5U646SBPD","target":"record","payload":{"canonical_record":{"source":{"id":"0806.4513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-27T10:09:26Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"0689d25b50461f1479470f137950147fe34c264f13bbb9644f23a55d9a46a0d0","abstract_canon_sha256":"20841bb610667483db475e05cb665fa3ddf8f1a3a30889bf5266c6746c520f74"},"schema_version":"1.0"},"canonical_sha256":"a5181821c7928f257522b769ee7a4178e81cd370138597881fef0795afbe74e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:45.912730Z","signature_b64":"TY8uIdTjEVRX/7WAR5sDuwPVDVc2pVlW2rvd8UjqJcFd+BZ3LPMRPsnAXnSt+IdRSnmm/UQVHEOUAGL6HOR3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5181821c7928f257522b769ee7a4178e81cd370138597881fef0795afbe74e8","last_reissued_at":"2026-05-18T02:15:45.911971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:45.911971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.4513","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":"2026-05-18T02:15:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGjRUoCIXEgsZevAHIdmk9PZoJqAEAGcEmGtMKisikGKJNSYUnaqGGQu1fCvpExuoK9ck/kWRIGaTvtNVTgZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:35:36.534160Z"},"content_sha256":"23807153da8c63d659dd4f48abbe9dc5fe866e5d9a03a7b30d5a9620b17e04cf","schema_version":"1.0","event_id":"sha256:23807153da8c63d659dd4f48abbe9dc5fe866e5d9a03a7b30d5a9620b17e04cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:UUMBQIOHSKHSK5JCW5U646SBPD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Mikael Persson","submitted_at":"2008-06-27T10:09:26Z","abstract_excerpt":"We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\\mathbb{R}^{2d}$, $d\\geq 1$. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give asymptotic formulas for the rate of accumulation of eigenvalues in these clusters. When the compact is a Reinhart domain we are able to show a more precise asymptotic formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4513","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":"2026-05-18T02:15:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOuQ7qcn8pbRrlF3ZMB8UV6s0q9NbBfwdH22s35Jil3t7cMtKg6L+vws9G7k+p+HBoJy22sE6OD3jv1KYoTpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:35:36.534706Z"},"content_sha256":"4a23bac5a32032b6aba59ada6ce7be2e6ce3d8cbf0837a4291a1476a1f028abd","schema_version":"1.0","event_id":"sha256:4a23bac5a32032b6aba59ada6ce7be2e6ce3d8cbf0837a4291a1476a1f028abd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUMBQIOHSKHSK5JCW5U646SBPD/bundle.json","state_url":"https://pith.science/pith/UUMBQIOHSKHSK5JCW5U646SBPD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUMBQIOHSKHSK5JCW5U646SBPD/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":"2026-05-26T21:35:36Z","links":{"resolver":"https://pith.science/pith/UUMBQIOHSKHSK5JCW5U646SBPD","bundle":"https://pith.science/pith/UUMBQIOHSKHSK5JCW5U646SBPD/bundle.json","state":"https://pith.science/pith/UUMBQIOHSKHSK5JCW5U646SBPD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUMBQIOHSKHSK5JCW5U646SBPD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:UUMBQIOHSKHSK5JCW5U646SBPD","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":"20841bb610667483db475e05cb665fa3ddf8f1a3a30889bf5266c6746c520f74","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-27T10:09:26Z","title_canon_sha256":"0689d25b50461f1479470f137950147fe34c264f13bbb9644f23a55d9a46a0d0"},"schema_version":"1.0","source":{"id":"0806.4513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4513","created_at":"2026-05-18T02:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4513v1","created_at":"2026-05-18T02:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4513","created_at":"2026-05-18T02:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"UUMBQIOHSKHS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UUMBQIOHSKHSK5JC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UUMBQIOH","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:4a23bac5a32032b6aba59ada6ce7be2e6ce3d8cbf0837a4291a1476a1f028abd","target":"graph","created_at":"2026-05-18T02:15:45Z","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 the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\\mathbb{R}^{2d}$, $d\\geq 1$. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give asymptotic formulas for the rate of accumulation of eigenvalues in these clusters. When the compact is a Reinhart domain we are able to show a more precise asymptotic formula.","authors_text":"Mikael Persson","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-27T10:09:26Z","title":"Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4513","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":"sha256:23807153da8c63d659dd4f48abbe9dc5fe866e5d9a03a7b30d5a9620b17e04cf","target":"record","created_at":"2026-05-18T02:15:45Z","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":"20841bb610667483db475e05cb665fa3ddf8f1a3a30889bf5266c6746c520f74","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-27T10:09:26Z","title_canon_sha256":"0689d25b50461f1479470f137950147fe34c264f13bbb9644f23a55d9a46a0d0"},"schema_version":"1.0","source":{"id":"0806.4513","kind":"arxiv","version":1}},"canonical_sha256":"a5181821c7928f257522b769ee7a4178e81cd370138597881fef0795afbe74e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5181821c7928f257522b769ee7a4178e81cd370138597881fef0795afbe74e8","first_computed_at":"2026-05-18T02:15:45.911971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:45.911971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TY8uIdTjEVRX/7WAR5sDuwPVDVc2pVlW2rvd8UjqJcFd+BZ3LPMRPsnAXnSt+IdRSnmm/UQVHEOUAGL6HOR3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:45.912730Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.4513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23807153da8c63d659dd4f48abbe9dc5fe866e5d9a03a7b30d5a9620b17e04cf","sha256:4a23bac5a32032b6aba59ada6ce7be2e6ce3d8cbf0837a4291a1476a1f028abd"],"state_sha256":"c1ca0912694d6dcef0018082c8c083d53aae33964968feae442ae5101f0e0d25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ftjreeHSyqCfylO3U/Y5Ztqr0sunk3PbkuXmnXlgeB1EAptfDvHQ9QSpyxfr1nrjrw/LbOYS/xuvKQwoFtdDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:35:36.538294Z","bundle_sha256":"f4334b611079dba4a5d0f8f7f8e834e83950a1c7fa6d02c1936db33feea90122"}}