{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2B27JHSBIA5VXCXHMACOYKA54B","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":"57a8e0616763510cb705fdda04b0900afbb5d97ce2105e91b63496dad553b270","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T06:29:53Z","title_canon_sha256":"9a1052e65aa1238ad65d072e5c126627b5f82557c347c95604cecb037ec34420"},"schema_version":"1.0","source":{"id":"1505.04524","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04524","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04524v2","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04524","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"2B27JHSBIA5V","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2B27JHSBIA5VXCXH","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2B27JHSB","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:0abc81d7bb3174417632949148df56556603f27b770d84546f4c8fe83a9b11bf","target":"graph","created_at":"2026-05-18T01:34:45Z","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":"This paper is devoted to semiclassical tunneling estimates induced on the circle by a double well electric potential in the case when a magnetic field is added. When the two electric wells are connected by two geodesics for the Agmon distance, we highlight an oscillating factor (related to the circulation of the magnetic field) in the splitting estimate of the first two eigenvalues.","authors_text":"Fr\\'ed\\'eric H\\'erau (LMJL), Nicolas Raymond (IRMAR), Virginie Bonnaillie-No\\\"el (DMA)","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T06:29:53Z","title":"Semiclassical tunneling and magnetic flux effects on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04524","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:c0182979462d8ad769de7e84c679e04ab8aa77195e7019289be37330c2fc804c","target":"record","created_at":"2026-05-18T01:34:45Z","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":"57a8e0616763510cb705fdda04b0900afbb5d97ce2105e91b63496dad553b270","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T06:29:53Z","title_canon_sha256":"9a1052e65aa1238ad65d072e5c126627b5f82557c347c95604cecb037ec34420"},"schema_version":"1.0","source":{"id":"1505.04524","kind":"arxiv","version":2}},"canonical_sha256":"d075f49e41403b5b8ae76004ec281de04964111b3a35671cad30b02d3fd37614","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d075f49e41403b5b8ae76004ec281de04964111b3a35671cad30b02d3fd37614","first_computed_at":"2026-05-18T01:34:45.092153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:45.092153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FudvnAq7f6k2nWI8MWBN0vsx75LwuUdW4Oqfapca0gOklJJLDTzuwdatf3tmOZxb5S/7U847gHRKMCawC94sCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:45.092703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04524","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0182979462d8ad769de7e84c679e04ab8aa77195e7019289be37330c2fc804c","sha256:0abc81d7bb3174417632949148df56556603f27b770d84546f4c8fe83a9b11bf"],"state_sha256":"3085e82f28a1202de181d2dbf1f94f6792a8bc84a972273f8292bac3d29eda16"}