{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:F6SE34YPYA4UHQLHELDDTQP6J4","short_pith_number":"pith:F6SE34YP","canonical_record":{"source":{"id":"1103.1507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-08T12:40:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"142caca3a21386d33b6d7e4e1360c29bda2a608c307608b15af468aeae9fd413","abstract_canon_sha256":"6d5a7143fa3853e1f75a3e9dc3861bf26be20180b4a1329c9eb78e6c524a199e"},"schema_version":"1.0"},"canonical_sha256":"2fa44df30fc03943c16722c639c1fe4f185dd90b0983d4171af326c76f0ccb7f","source":{"kind":"arxiv","id":"1103.1507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1507","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1507v1","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1507","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"F6SE34YPYA4U","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F6SE34YPYA4UHQLH","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F6SE34YP","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:F6SE34YPYA4UHQLHELDDTQP6J4","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-08T12:40:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"142caca3a21386d33b6d7e4e1360c29bda2a608c307608b15af468aeae9fd413","abstract_canon_sha256":"6d5a7143fa3853e1f75a3e9dc3861bf26be20180b4a1329c9eb78e6c524a199e"},"schema_version":"1.0"},"canonical_sha256":"2fa44df30fc03943c16722c639c1fe4f185dd90b0983d4171af326c76f0ccb7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:15.712509Z","signature_b64":"8eiMMKTQQNNvmndydjz8p+ByYWkZXmsTQk1Ry5SjfWDJxfXq3xRhUAHB0qNgeM44yxrwP3sCWYZi1Jsy2W+rDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fa44df30fc03943c16722c639c1fe4f185dd90b0983d4171af326c76f0ccb7f","last_reissued_at":"2026-05-18T04:27:15.711893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:15.711893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1507","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":"2026-05-18T04:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Frk0lBRl6fNzYj4Q1vNUvDKNueIjmNfsqS9FoMyuh+PLoflvQz92pKto8AzLzf6AW3ULxk0Cxyb/MIATbEt1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:36:44.875882Z"},"content_sha256":"992c848f5f1f99baba1631385039838682275c67069cc5e2aba6b1819351fe7c","schema_version":"1.0","event_id":"sha256:992c848f5f1f99baba1631385039838682275c67069cc5e2aba6b1819351fe7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:F6SE34YPYA4UHQLHELDDTQP6J4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bohr-Sommerfeld phases for avoided crossings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Yves Colin De Verdi\\`ere (IF)","submitted_at":"2011-03-08T12:40:37Z","abstract_excerpt":"We consider the adiabatic limit in quantum mechanics with several avoided crossings. We compute the interferences effects uniformly w.r. to the gaps and the adiabatic parameter. This way we get the asymoptotic expansion of the global scattering matrix. We use the technics of normal forms introduced in the paper written with B. Parisse (Commun. Math. Phys. 205 pp. 459--500 (1999))."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1507","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":"2026-05-18T04:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ls831yGYbz0bxLH4HSgrfNqoeEYm+PP57nmA1mLnJuJf+9RaAt68pTfMugYrqSFkK3nvIsss8hMJW/WwIDcWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:36:44.876236Z"},"content_sha256":"2ac6bbfa11b51d27832589594a04e25bc99e5444406dc1d474cd14833073f61d","schema_version":"1.0","event_id":"sha256:2ac6bbfa11b51d27832589594a04e25bc99e5444406dc1d474cd14833073f61d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6SE34YPYA4UHQLHELDDTQP6J4/bundle.json","state_url":"https://pith.science/pith/F6SE34YPYA4UHQLHELDDTQP6J4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6SE34YPYA4UHQLHELDDTQP6J4/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":"2026-06-02T21:36:44Z","links":{"resolver":"https://pith.science/pith/F6SE34YPYA4UHQLHELDDTQP6J4","bundle":"https://pith.science/pith/F6SE34YPYA4UHQLHELDDTQP6J4/bundle.json","state":"https://pith.science/pith/F6SE34YPYA4UHQLHELDDTQP6J4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6SE34YPYA4UHQLHELDDTQP6J4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F6SE34YPYA4UHQLHELDDTQP6J4","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":"6d5a7143fa3853e1f75a3e9dc3861bf26be20180b4a1329c9eb78e6c524a199e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-08T12:40:37Z","title_canon_sha256":"142caca3a21386d33b6d7e4e1360c29bda2a608c307608b15af468aeae9fd413"},"schema_version":"1.0","source":{"id":"1103.1507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1507","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1507v1","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1507","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"F6SE34YPYA4U","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F6SE34YPYA4UHQLH","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F6SE34YP","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:2ac6bbfa11b51d27832589594a04e25bc99e5444406dc1d474cd14833073f61d","target":"graph","created_at":"2026-05-18T04:27:15Z","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 consider the adiabatic limit in quantum mechanics with several avoided crossings. We compute the interferences effects uniformly w.r. to the gaps and the adiabatic parameter. This way we get the asymoptotic expansion of the global scattering matrix. We use the technics of normal forms introduced in the paper written with B. Parisse (Commun. Math. Phys. 205 pp. 459--500 (1999)).","authors_text":"Yves Colin De Verdi\\`ere (IF)","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-08T12:40:37Z","title":"Bohr-Sommerfeld phases for avoided crossings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1507","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":"sha256:992c848f5f1f99baba1631385039838682275c67069cc5e2aba6b1819351fe7c","target":"record","created_at":"2026-05-18T04:27:15Z","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":"6d5a7143fa3853e1f75a3e9dc3861bf26be20180b4a1329c9eb78e6c524a199e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-08T12:40:37Z","title_canon_sha256":"142caca3a21386d33b6d7e4e1360c29bda2a608c307608b15af468aeae9fd413"},"schema_version":"1.0","source":{"id":"1103.1507","kind":"arxiv","version":1}},"canonical_sha256":"2fa44df30fc03943c16722c639c1fe4f185dd90b0983d4171af326c76f0ccb7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fa44df30fc03943c16722c639c1fe4f185dd90b0983d4171af326c76f0ccb7f","first_computed_at":"2026-05-18T04:27:15.711893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:15.711893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8eiMMKTQQNNvmndydjz8p+ByYWkZXmsTQk1Ry5SjfWDJxfXq3xRhUAHB0qNgeM44yxrwP3sCWYZi1Jsy2W+rDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:15.712509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:992c848f5f1f99baba1631385039838682275c67069cc5e2aba6b1819351fe7c","sha256:2ac6bbfa11b51d27832589594a04e25bc99e5444406dc1d474cd14833073f61d"],"state_sha256":"106ff198ce79d62a653c948e113948dc859a480d7b29985680beedfeb8102c88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ao1m3Orw5YuSKxDSw9qqRYxnhCaodwJKGLTUPCL/fWsiF9UASxk2zQkKWVEwN7Be0hU92yZ1y77Zd+a5RZvfCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:36:44.878253Z","bundle_sha256":"417c4dbf0ac24edeffbcdc7e8aa44e98ca5d0bda8fd075eb56cf80445dc1c638"}}