{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:DBHFWGAVPZ277Y634LSDV6PRSN","short_pith_number":"pith:DBHFWGAV","canonical_record":{"source":{"id":"2105.06542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-13T20:25:54Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"0a2e2b61a9ce2dfdf6ec23c79984d5b6bc63217eb4bd13526c29d2bf69680dd8","abstract_canon_sha256":"0a80d39a5295b0755b5867f36ebbc33cc014a0861d32c432a49cdf1db6d687f0"},"schema_version":"1.0"},"canonical_sha256":"184e5b18157e75ffe3dbe2e43af9f19346a0e397f705b56eb9586e455ee43f94","source":{"kind":"arxiv","id":"2105.06542","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:DBHFWGAVPZ277Y634LSDV6PRSN","target":"record","payload":{"canonical_record":{"source":{"id":"2105.06542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-13T20:25:54Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"0a2e2b61a9ce2dfdf6ec23c79984d5b6bc63217eb4bd13526c29d2bf69680dd8","abstract_canon_sha256":"0a80d39a5295b0755b5867f36ebbc33cc014a0861d32c432a49cdf1db6d687f0"},"schema_version":"1.0"},"canonical_sha256":"184e5b18157e75ffe3dbe2e43af9f19346a0e397f705b56eb9586e455ee43f94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:52:57.736696Z","signature_b64":"gO+d9pcarKw+wvXCBenihJrhh40uDxN/p/ojE6rV4fFkivTJrSN+UODNXd3SCMwISIdGJGdOSc1vOl+nFAZnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"184e5b18157e75ffe3dbe2e43af9f19346a0e397f705b56eb9586e455ee43f94","last_reissued_at":"2026-07-05T03:52:57.736199Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:52:57.736199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.06542","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":"2026-07-05T03:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3eYoyuZtErToAnzIfq/vARepc3NDuD+Ma4j3sxPOxl4D9p61cmeIOjSp8mVxlBQjbbL5QBbn6uCvP9/npF1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:55:39.588642Z"},"content_sha256":"cebac13b94e3074d159f7fa4e784b930f20ac8c6d5359e22c831321366d6a6f6","schema_version":"1.0","event_id":"sha256:cebac13b94e3074d159f7fa4e784b930f20ac8c6d5359e22c831321366d6a6f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:DBHFWGAVPZ277Y634LSDV6PRSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Mengxuan Yang","submitted_at":"2021-05-13T20:25:54Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.06542","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.06542/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcmkNhbIsZN5TH9KTx1vvIaxY3Awz7W+IYbef2/d/M5ccmuypUy/gn7p7v9gH4zQmm8N6geCMknavD+GAlV5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:55:39.589020Z"},"content_sha256":"424b5d69780e6a62465476bbecc04ad9615bcd71fa8f3b6afc8dc4674c05379d","schema_version":"1.0","event_id":"sha256:424b5d69780e6a62465476bbecc04ad9615bcd71fa8f3b6afc8dc4674c05379d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DBHFWGAVPZ277Y634LSDV6PRSN/bundle.json","state_url":"https://pith.science/pith/DBHFWGAVPZ277Y634LSDV6PRSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DBHFWGAVPZ277Y634LSDV6PRSN/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":"2026-07-06T16:55:39Z","links":{"resolver":"https://pith.science/pith/DBHFWGAVPZ277Y634LSDV6PRSN","bundle":"https://pith.science/pith/DBHFWGAVPZ277Y634LSDV6PRSN/bundle.json","state":"https://pith.science/pith/DBHFWGAVPZ277Y634LSDV6PRSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DBHFWGAVPZ277Y634LSDV6PRSN/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMSa1cyzySoR3EMlg0yPSGv/BOF3OPqoopgXfjV2VdxKmrrLZrE/PnDaqdSqv40EYMvd54lbfT6/tuy/upslBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T16:55:39.590993Z","bundle_sha256":"657db5b8696796e327a4c96b537cf133067b3dff6a62ac0eda8ed948c73b1e33"}}