{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DBHFWGAVPZ277Y634LSDV6PRSN","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":"0a80d39a5295b0755b5867f36ebbc33cc014a0861d32c432a49cdf1db6d687f0","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-13T20:25:54Z","title_canon_sha256":"0a2e2b61a9ce2dfdf6ec23c79984d5b6bc63217eb4bd13526c29d2bf69680dd8"},"schema_version":"1.0","source":{"id":"2105.06542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.06542","created_at":"2026-07-05T03:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"2105.06542v2","created_at":"2026-07-05T03:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.06542","created_at":"2026-07-05T03:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"DBHFWGAVPZ27","created_at":"2026-07-05T03:52:57Z"},{"alias_kind":"pith_short_16","alias_value":"DBHFWGAVPZ277Y63","created_at":"2026-07-05T03:52:57Z"},{"alias_kind":"pith_short_8","alias_value":"DBHFWGAV","created_at":"2026-07-05T03:52:57Z"}],"graph_snapshots":[{"event_id":"sha256:424b5d69780e6a62465476bbecc04ad9615bcd71fa8f3b6afc8dc4674c05379d","target":"graph","created_at":"2026-07-05T03:52:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.06542/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study leading order singularities of the wave trace of the Aharonov--Bohm Hamiltonian on $\\mathbf{R}^2$ with multiple solenoids under a generic assumption that no three solenoids are collinear. Then we apply our formula to get a lower bound of scattering resonances in a logarithmic neighborhood near the real axis.","authors_text":"Mengxuan Yang","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-13T20:25:54Z","title":"The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.06542","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:cebac13b94e3074d159f7fa4e784b930f20ac8c6d5359e22c831321366d6a6f6","target":"record","created_at":"2026-07-05T03:52:57Z","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":"0a80d39a5295b0755b5867f36ebbc33cc014a0861d32c432a49cdf1db6d687f0","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-13T20:25:54Z","title_canon_sha256":"0a2e2b61a9ce2dfdf6ec23c79984d5b6bc63217eb4bd13526c29d2bf69680dd8"},"schema_version":"1.0","source":{"id":"2105.06542","kind":"arxiv","version":2}},"canonical_sha256":"184e5b18157e75ffe3dbe2e43af9f19346a0e397f705b56eb9586e455ee43f94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"184e5b18157e75ffe3dbe2e43af9f19346a0e397f705b56eb9586e455ee43f94","first_computed_at":"2026-07-05T03:52:57.736199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:52:57.736199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gO+d9pcarKw+wvXCBenihJrhh40uDxN/p/ojE6rV4fFkivTJrSN+UODNXd3SCMwISIdGJGdOSc1vOl+nFAZnAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:52:57.736696Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.06542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cebac13b94e3074d159f7fa4e784b930f20ac8c6d5359e22c831321366d6a6f6","sha256:424b5d69780e6a62465476bbecc04ad9615bcd71fa8f3b6afc8dc4674c05379d"],"state_sha256":"5ac494a56a51f6a8938e736b94b11905e064ed7a5dfb8a41ebd331d5f076a7eb"}