{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XPPSCMKF4WEWPX355UDTMHQM3Z","short_pith_number":"pith:XPPSCMKF","canonical_record":{"source":{"id":"1103.3901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-20T23:06:41Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"aa73a5a52eed172c0b22539de3558bb50185e0d56ca636f552211c87d58f6d81","abstract_canon_sha256":"87caf207c0caa0e69564dfe39c878962f739ef253ca1ee44e50d7561694e6171"},"schema_version":"1.0"},"canonical_sha256":"bbdf213145e58967df7ded07361e0cde4a2f0b74d1cac8ec430310281c4daf13","source":{"kind":"arxiv","id":"1103.3901","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3901","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3901v1","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3901","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"XPPSCMKF4WEW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XPPSCMKF4WEWPX35","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XPPSCMKF","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XPPSCMKF4WEWPX355UDTMHQM3Z","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-20T23:06:41Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"aa73a5a52eed172c0b22539de3558bb50185e0d56ca636f552211c87d58f6d81","abstract_canon_sha256":"87caf207c0caa0e69564dfe39c878962f739ef253ca1ee44e50d7561694e6171"},"schema_version":"1.0"},"canonical_sha256":"bbdf213145e58967df7ded07361e0cde4a2f0b74d1cac8ec430310281c4daf13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:22.147449Z","signature_b64":"VteHdmHEvf5Y+MHwhSaf0DN+7Hpz/loeU+Icm+9MVDpcOSb/17zUY+tlK7StoJc13WZyMdlT5p2y2rI+yUQIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbdf213145e58967df7ded07361e0cde4a2f0b74d1cac8ec430310281c4daf13","last_reissued_at":"2026-05-18T04:26:22.146961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:22.146961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3901","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":"2026-05-18T04:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rV4aIRq1lfkZ0uzK6o+T1SZzGT8FHWkrdxoxDEz+Z1wZoccsidsxpND4K0nK+Js+sMdwA592hW+SQykaR/V7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:30:16.917354Z"},"content_sha256":"7c1eb6dfb3b0127f013303441de84a37585a51b71829c529436bc3a35a95e517","schema_version":"1.0","event_id":"sha256:7c1eb6dfb3b0127f013303441de84a37585a51b71829c529436bc3a35a95e517"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XPPSCMKF4WEWPX355UDTMHQM3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time delay for an abstract quantum scattering process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"S. Richard","submitted_at":"2011-03-20T23:06:41Z","abstract_excerpt":"In this short review paper, we discuss the concept of time delay for an abstract quantum scattering system. Its definition in terms of sojourn times is explained as well as its identity with the so-called Eisenbud-Wigner time delay. Necessary and natural conditions for such a construction are introduced and thoroughly discussed. Assumptions and statements are precisely formulated but proofs are contained in two companion papers written in collaboration with R. Tiedra de Aldecoa."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3901","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":"2026-05-18T04:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6a1ZZhG0qX+EFctUz6sPK4QddWOl6Ngy9RtAaxXhHLm4RVwwlgQ40TJDTzgTtlTFt7CCpMOyQZYIWRzR6dXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:30:16.918032Z"},"content_sha256":"ed5c21962a3ce6db6ea207e45b0b90c717d6340f2d802f23635a7a626604409e","schema_version":"1.0","event_id":"sha256:ed5c21962a3ce6db6ea207e45b0b90c717d6340f2d802f23635a7a626604409e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPPSCMKF4WEWPX355UDTMHQM3Z/bundle.json","state_url":"https://pith.science/pith/XPPSCMKF4WEWPX355UDTMHQM3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPPSCMKF4WEWPX355UDTMHQM3Z/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":"2026-05-26T00:30:16Z","links":{"resolver":"https://pith.science/pith/XPPSCMKF4WEWPX355UDTMHQM3Z","bundle":"https://pith.science/pith/XPPSCMKF4WEWPX355UDTMHQM3Z/bundle.json","state":"https://pith.science/pith/XPPSCMKF4WEWPX355UDTMHQM3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPPSCMKF4WEWPX355UDTMHQM3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XPPSCMKF4WEWPX355UDTMHQM3Z","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":"87caf207c0caa0e69564dfe39c878962f739ef253ca1ee44e50d7561694e6171","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-20T23:06:41Z","title_canon_sha256":"aa73a5a52eed172c0b22539de3558bb50185e0d56ca636f552211c87d58f6d81"},"schema_version":"1.0","source":{"id":"1103.3901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3901","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3901v1","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3901","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"XPPSCMKF4WEW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XPPSCMKF4WEWPX35","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XPPSCMKF","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:ed5c21962a3ce6db6ea207e45b0b90c717d6340f2d802f23635a7a626604409e","target":"graph","created_at":"2026-05-18T04:26:22Z","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":"In this short review paper, we discuss the concept of time delay for an abstract quantum scattering system. Its definition in terms of sojourn times is explained as well as its identity with the so-called Eisenbud-Wigner time delay. Necessary and natural conditions for such a construction are introduced and thoroughly discussed. Assumptions and statements are precisely formulated but proofs are contained in two companion papers written in collaboration with R. Tiedra de Aldecoa.","authors_text":"S. Richard","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-20T23:06:41Z","title":"Time delay for an abstract quantum scattering process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3901","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":"sha256:7c1eb6dfb3b0127f013303441de84a37585a51b71829c529436bc3a35a95e517","target":"record","created_at":"2026-05-18T04:26:22Z","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":"87caf207c0caa0e69564dfe39c878962f739ef253ca1ee44e50d7561694e6171","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-20T23:06:41Z","title_canon_sha256":"aa73a5a52eed172c0b22539de3558bb50185e0d56ca636f552211c87d58f6d81"},"schema_version":"1.0","source":{"id":"1103.3901","kind":"arxiv","version":1}},"canonical_sha256":"bbdf213145e58967df7ded07361e0cde4a2f0b74d1cac8ec430310281c4daf13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbdf213145e58967df7ded07361e0cde4a2f0b74d1cac8ec430310281c4daf13","first_computed_at":"2026-05-18T04:26:22.146961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:22.146961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VteHdmHEvf5Y+MHwhSaf0DN+7Hpz/loeU+Icm+9MVDpcOSb/17zUY+tlK7StoJc13WZyMdlT5p2y2rI+yUQIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:22.147449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c1eb6dfb3b0127f013303441de84a37585a51b71829c529436bc3a35a95e517","sha256:ed5c21962a3ce6db6ea207e45b0b90c717d6340f2d802f23635a7a626604409e"],"state_sha256":"fe5eb9bc48c88ca4187c23c5d627051b2c1f612f2d30a972d48c4f715adb6ceb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Auu7mO/AOV46F/4ZiFATjOrPDjOcpxNKcckIPJYWJaVVEXJ5nibgNBUa+i35p6a/16IreaWxWD/DxLasY3zRCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:30:16.921566Z","bundle_sha256":"786f60cf221363b8951b91f55c742f1db078a60423dc91a2acfc1beb23624262"}}