{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ACIWVKG2BGVLFTNRHDHQPGB3YY","short_pith_number":"pith:ACIWVKG2","canonical_record":{"source":{"id":"1004.3361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-20T07:02:20Z","cross_cats_sorted":["cs.LG","math-ph","math.DS","math.MP","nlin.CD"],"title_canon_sha256":"a9d8f972faf78fc154a9c1ee54b271eacc488b617cc34dd22df7f00c5ed1a3b1","abstract_canon_sha256":"76e2a37871cad0e0678299a17a3a309a8b587af6361194b1d9d7fd9b6a304aa2"},"schema_version":"1.0"},"canonical_sha256":"00916aa8da09aab2cdb138cf07983bc6061604abbf170b6cbeac80c5f345501f","source":{"kind":"arxiv","id":"1004.3361","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3361","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3361v3","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3361","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"ACIWVKG2BGVL","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ACIWVKG2BGVLFTNR","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ACIWVKG2","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ACIWVKG2BGVLFTNRHDHQPGB3YY","target":"record","payload":{"canonical_record":{"source":{"id":"1004.3361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-20T07:02:20Z","cross_cats_sorted":["cs.LG","math-ph","math.DS","math.MP","nlin.CD"],"title_canon_sha256":"a9d8f972faf78fc154a9c1ee54b271eacc488b617cc34dd22df7f00c5ed1a3b1","abstract_canon_sha256":"76e2a37871cad0e0678299a17a3a309a8b587af6361194b1d9d7fd9b6a304aa2"},"schema_version":"1.0"},"canonical_sha256":"00916aa8da09aab2cdb138cf07983bc6061604abbf170b6cbeac80c5f345501f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:56.413547Z","signature_b64":"qedhMo/ajG5FOdvXuG+b3LfIXO8cOrJcpXPcOy6fNCu1w5uvbi36fVStYLz6z6h7m76b+IbRVvt8Vwix6BV9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00916aa8da09aab2cdb138cf07983bc6061604abbf170b6cbeac80c5f345501f","last_reissued_at":"2026-05-18T02:07:56.412796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:56.412796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.3361","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6Hc9aaXGlGEgN6Ylx2a9Tnq5icu7XSF701Zw49ACSx5lo31I0AELkoneksZPrFV07QouOGy8AjqoGAK5TaDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:46:10.162966Z"},"content_sha256":"071b20c0d06d8ddd6ce187806e25938e656933101a1873f0b3628b377668c338","schema_version":"1.0","event_id":"sha256:071b20c0d06d8ddd6ce187806e25938e656933101a1873f0b3628b377668c338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ACIWVKG2BGVLFTNRHDHQPGB3YY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From open quantum systems to open quantum maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math-ph","math.DS","math.MP","nlin.CD"],"primary_cat":"math.AP","authors_text":"Johannes Sjoestrand (IMB), Maciej Zworski (UC BERKELEY MATHS), St\\'ephane Nonnenmacher (IPHT)","submitted_at":"2010-04-20T07:02:20Z","abstract_excerpt":"For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincar\\'e map associated with the flow near the set of trapped trajectories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3361","kind":"arxiv","version":3},"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":"2026-05-18T02:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K99MSYK/nt43VwfBB5yzzEhQfelMcTHLzvQ8t2ZBh2DXxg1ksNee6PvTCWN/UB7N4hH8hTUYxyzQFWWaHz+HCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:46:10.163330Z"},"content_sha256":"6c5f9ea2a9753cf6dc97607f14100db62c6a1e847a46af6dc4a155899a91a4ad","schema_version":"1.0","event_id":"sha256:6c5f9ea2a9753cf6dc97607f14100db62c6a1e847a46af6dc4a155899a91a4ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACIWVKG2BGVLFTNRHDHQPGB3YY/bundle.json","state_url":"https://pith.science/pith/ACIWVKG2BGVLFTNRHDHQPGB3YY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACIWVKG2BGVLFTNRHDHQPGB3YY/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":"2026-06-23T07:46:10Z","links":{"resolver":"https://pith.science/pith/ACIWVKG2BGVLFTNRHDHQPGB3YY","bundle":"https://pith.science/pith/ACIWVKG2BGVLFTNRHDHQPGB3YY/bundle.json","state":"https://pith.science/pith/ACIWVKG2BGVLFTNRHDHQPGB3YY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACIWVKG2BGVLFTNRHDHQPGB3YY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ACIWVKG2BGVLFTNRHDHQPGB3YY","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":"76e2a37871cad0e0678299a17a3a309a8b587af6361194b1d9d7fd9b6a304aa2","cross_cats_sorted":["cs.LG","math-ph","math.DS","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-20T07:02:20Z","title_canon_sha256":"a9d8f972faf78fc154a9c1ee54b271eacc488b617cc34dd22df7f00c5ed1a3b1"},"schema_version":"1.0","source":{"id":"1004.3361","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3361","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3361v3","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3361","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"ACIWVKG2BGVL","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ACIWVKG2BGVLFTNR","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ACIWVKG2","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:6c5f9ea2a9753cf6dc97607f14100db62c6a1e847a46af6dc4a155899a91a4ad","target":"graph","created_at":"2026-05-18T02:07:56Z","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":"For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincar\\'e map associated with the flow near the set of trapped trajectories.","authors_text":"Johannes Sjoestrand (IMB), Maciej Zworski (UC BERKELEY MATHS), St\\'ephane Nonnenmacher (IPHT)","cross_cats":["cs.LG","math-ph","math.DS","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-20T07:02:20Z","title":"From open quantum systems to open quantum maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3361","kind":"arxiv","version":3},"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":"sha256:071b20c0d06d8ddd6ce187806e25938e656933101a1873f0b3628b377668c338","target":"record","created_at":"2026-05-18T02:07:56Z","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":"76e2a37871cad0e0678299a17a3a309a8b587af6361194b1d9d7fd9b6a304aa2","cross_cats_sorted":["cs.LG","math-ph","math.DS","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-20T07:02:20Z","title_canon_sha256":"a9d8f972faf78fc154a9c1ee54b271eacc488b617cc34dd22df7f00c5ed1a3b1"},"schema_version":"1.0","source":{"id":"1004.3361","kind":"arxiv","version":3}},"canonical_sha256":"00916aa8da09aab2cdb138cf07983bc6061604abbf170b6cbeac80c5f345501f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00916aa8da09aab2cdb138cf07983bc6061604abbf170b6cbeac80c5f345501f","first_computed_at":"2026-05-18T02:07:56.412796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:56.412796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qedhMo/ajG5FOdvXuG+b3LfIXO8cOrJcpXPcOy6fNCu1w5uvbi36fVStYLz6z6h7m76b+IbRVvt8Vwix6BV9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:56.413547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3361","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:071b20c0d06d8ddd6ce187806e25938e656933101a1873f0b3628b377668c338","sha256:6c5f9ea2a9753cf6dc97607f14100db62c6a1e847a46af6dc4a155899a91a4ad"],"state_sha256":"af7311a6fe4a2551e7d03feaae4ffea7b74251aa0504dc3932778a1eda2dc814"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YkJdduiUpU9bEF9yLVAl3jOrZaUZpGedcohb9q3yTkGYPloVKrAiKo6vKbijhmEcZ1rTQ3e3+jdIEILjFNSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:46:10.165312Z","bundle_sha256":"0618d315c9a52a2ccf843fec46febd2611e36ea81db83efd7f5614c5a1197332"}}