{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:AM5SON4H5SIXCUKHKVASK3VVXH","short_pith_number":"pith:AM5SON4H","canonical_record":{"source":{"id":"0810.1032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-06T18:21:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c0482f199d2e7a97352784327b737218978ec833b71af2b79f387c0618fa485e","abstract_canon_sha256":"59ff6afd5f69d310e20853548c4c07bddeb7fd9b4c0c0d3d8a847857fede4f45"},"schema_version":"1.0"},"canonical_sha256":"033b273787ec917151475541256eb5b9da7fe01212573e10ae636da4ba611306","source":{"kind":"arxiv","id":"0810.1032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1032","created_at":"2026-05-18T02:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1032v1","created_at":"2026-05-18T02:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1032","created_at":"2026-05-18T02:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"AM5SON4H5SIX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AM5SON4H5SIXCUKH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AM5SON4H","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:AM5SON4H5SIXCUKHKVASK3VVXH","target":"record","payload":{"canonical_record":{"source":{"id":"0810.1032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-06T18:21:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c0482f199d2e7a97352784327b737218978ec833b71af2b79f387c0618fa485e","abstract_canon_sha256":"59ff6afd5f69d310e20853548c4c07bddeb7fd9b4c0c0d3d8a847857fede4f45"},"schema_version":"1.0"},"canonical_sha256":"033b273787ec917151475541256eb5b9da7fe01212573e10ae636da4ba611306","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:32.739990Z","signature_b64":"6u+K12lVMbJBwlCwWK5DBhT/Yu63qe8b5nHy0/cG3NG+lThn2uSSqbQn7zrhjf3f8jN0CUVohollp6DJ3hSHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"033b273787ec917151475541256eb5b9da7fe01212573e10ae636da4ba611306","last_reissued_at":"2026-05-18T02:15:32.739050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:32.739050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.1032","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":"2026-05-18T02:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJSUUF8vvYNOTIlos4rJ+NBWjk9MJ31LH6SLR1ElP04nnP+wbh+2gTDa+K5Ztpr3cx4OmmVfVZyOvWf8x6yZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:09:18.247764Z"},"content_sha256":"aeefec01f44828fe5bdd2c655ddad67e122dffd7214ab6cf9ee7299406a421ac","schema_version":"1.0","event_id":"sha256:aeefec01f44828fe5bdd2c655ddad67e122dffd7214ab6cf9ee7299406a421ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:AM5SON4H5SIXCUKHKVASK3VVXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time delay for dispersive systems in quantum scattering theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Rafael Tiedra de Aldecoa","submitted_at":"2008-10-06T18:21:08Z","abstract_excerpt":"We consider time delay and symmetrised time delay (defined in terms of sojourn times) for quantum scattering pairs $\\{H_0=h(P),H\\}$, where $h(P)$ a dispersive operator of hypoelliptic-type. For instance $h(P)$ can be one of the usual elliptic operators such as the Schr\\\"odinger operator $h(P)=P^2$ or the square-root Klein-Gordon operator $h(P)=\\sqrt{1+P^2}$. We show under general conditions that the symmetrised time delay exists for all smooth even localization functions. It is equal to the Eisenbud-Wigner time delay plus a contribution due to the non-radial component of the localization funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1032","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":"2026-05-18T02:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u83gH8flAfJ8IM3qVkMAlMQnBUDLBjn+w9PsE0KhEFH16kkMYeuLA2zfFUjD/EuYk7iOEdsiX/tWaUQsLXPVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:09:18.248123Z"},"content_sha256":"638518c373f8ee61c061d5ea165f9ffa74b4e5af76e0cc7d23578928e10693ef","schema_version":"1.0","event_id":"sha256:638518c373f8ee61c061d5ea165f9ffa74b4e5af76e0cc7d23578928e10693ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AM5SON4H5SIXCUKHKVASK3VVXH/bundle.json","state_url":"https://pith.science/pith/AM5SON4H5SIXCUKHKVASK3VVXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AM5SON4H5SIXCUKHKVASK3VVXH/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":"2026-06-23T15:09:18Z","links":{"resolver":"https://pith.science/pith/AM5SON4H5SIXCUKHKVASK3VVXH","bundle":"https://pith.science/pith/AM5SON4H5SIXCUKHKVASK3VVXH/bundle.json","state":"https://pith.science/pith/AM5SON4H5SIXCUKHKVASK3VVXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AM5SON4H5SIXCUKHKVASK3VVXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:AM5SON4H5SIXCUKHKVASK3VVXH","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":"59ff6afd5f69d310e20853548c4c07bddeb7fd9b4c0c0d3d8a847857fede4f45","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-06T18:21:08Z","title_canon_sha256":"c0482f199d2e7a97352784327b737218978ec833b71af2b79f387c0618fa485e"},"schema_version":"1.0","source":{"id":"0810.1032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1032","created_at":"2026-05-18T02:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1032v1","created_at":"2026-05-18T02:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1032","created_at":"2026-05-18T02:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"AM5SON4H5SIX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AM5SON4H5SIXCUKH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AM5SON4H","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:638518c373f8ee61c061d5ea165f9ffa74b4e5af76e0cc7d23578928e10693ef","target":"graph","created_at":"2026-05-18T02:15:32Z","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 time delay and symmetrised time delay (defined in terms of sojourn times) for quantum scattering pairs $\\{H_0=h(P),H\\}$, where $h(P)$ a dispersive operator of hypoelliptic-type. For instance $h(P)$ can be one of the usual elliptic operators such as the Schr\\\"odinger operator $h(P)=P^2$ or the square-root Klein-Gordon operator $h(P)=\\sqrt{1+P^2}$. We show under general conditions that the symmetrised time delay exists for all smooth even localization functions. It is equal to the Eisenbud-Wigner time delay plus a contribution due to the non-radial component of the localization funct","authors_text":"Rafael Tiedra de Aldecoa","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-06T18:21:08Z","title":"Time delay for dispersive systems in quantum scattering theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1032","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:aeefec01f44828fe5bdd2c655ddad67e122dffd7214ab6cf9ee7299406a421ac","target":"record","created_at":"2026-05-18T02:15:32Z","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":"59ff6afd5f69d310e20853548c4c07bddeb7fd9b4c0c0d3d8a847857fede4f45","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-06T18:21:08Z","title_canon_sha256":"c0482f199d2e7a97352784327b737218978ec833b71af2b79f387c0618fa485e"},"schema_version":"1.0","source":{"id":"0810.1032","kind":"arxiv","version":1}},"canonical_sha256":"033b273787ec917151475541256eb5b9da7fe01212573e10ae636da4ba611306","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"033b273787ec917151475541256eb5b9da7fe01212573e10ae636da4ba611306","first_computed_at":"2026-05-18T02:15:32.739050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:32.739050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6u+K12lVMbJBwlCwWK5DBhT/Yu63qe8b5nHy0/cG3NG+lThn2uSSqbQn7zrhjf3f8jN0CUVohollp6DJ3hSHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:32.739990Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.1032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeefec01f44828fe5bdd2c655ddad67e122dffd7214ab6cf9ee7299406a421ac","sha256:638518c373f8ee61c061d5ea165f9ffa74b4e5af76e0cc7d23578928e10693ef"],"state_sha256":"2fbbff524247f7dcb06db7d756f3b558a814de7f7930767ecf6df678ae758314"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2sRqO7RDBszn/nhoagFb7SFxLdszslcORmXFQXp2l82XeMukMlAkIF6pOy+xjeUVra7qd05vgN9kI9tUtzwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:09:18.250229Z","bundle_sha256":"a23f95e1d6ceb79b1fb1a2dd770d1189b74f187a8f3b9ee694cc8b706a3494fb"}}