{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YCEAW47ZHSGFDFIIDB2JBVNYDB","short_pith_number":"pith:YCEAW47Z","canonical_record":{"source":{"id":"1408.2361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-11T10:06:42Z","cross_cats_sorted":[],"title_canon_sha256":"45bfe921ba329a090249726451fa8836b5e1d2547a56cfdc76a13e14ca20487b","abstract_canon_sha256":"56c63893091975d6f92fee6952753d353c1f07a5c3a563640077ddb57d6d9af1"},"schema_version":"1.0"},"canonical_sha256":"c0880b73f93c8c519508187490d5b818797eb510afd106981735302c8a9cea61","source":{"kind":"arxiv","id":"1408.2361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2361","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2361v1","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2361","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"pith_short_12","alias_value":"YCEAW47ZHSGF","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YCEAW47ZHSGFDFII","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YCEAW47Z","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YCEAW47ZHSGFDFIIDB2JBVNYDB","target":"record","payload":{"canonical_record":{"source":{"id":"1408.2361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-11T10:06:42Z","cross_cats_sorted":[],"title_canon_sha256":"45bfe921ba329a090249726451fa8836b5e1d2547a56cfdc76a13e14ca20487b","abstract_canon_sha256":"56c63893091975d6f92fee6952753d353c1f07a5c3a563640077ddb57d6d9af1"},"schema_version":"1.0"},"canonical_sha256":"c0880b73f93c8c519508187490d5b818797eb510afd106981735302c8a9cea61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:29.646382Z","signature_b64":"fuN/1uvyFiSMZbuGOfgQ3nhAKbbFO5pzYMb/0g9DeJjg3f6JJbqIkUwt91JOdukrcqe7ahI15D1WfeXx2ub9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0880b73f93c8c519508187490d5b818797eb510afd106981735302c8a9cea61","last_reissued_at":"2026-05-18T02:45:29.645714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:29.645714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.2361","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":"2026-05-18T02:45:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Sh/qSBnmRWBxG90CkdJzsvrsaH1W3uY0cW4fRgBH4nwIkIKTH43nqRZzuXEK0/qZHEvZIAoQYOypRLn2VmtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:02:58.354057Z"},"content_sha256":"04b6b950de9d1a87f3b0e58967fee265f8db914fcdded486abadaef595328b34","schema_version":"1.0","event_id":"sha256:04b6b950de9d1a87f3b0e58967fee265f8db914fcdded486abadaef595328b34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YCEAW47ZHSGFDFIIDB2JBVNYDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral and scattering theory of self-adjoint Hankel operators with piecewise continuous symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Dmitri Yafaev","submitted_at":"2014-08-11T10:06:42Z","abstract_excerpt":"We develop the spectral and scattering theory for self-adjoint Hankel operators $H$ with piecewise continuous symbols. In this case every jump of the symbol gives rise to a band of the absolutely continuous spectrum of $H$. We construct wave operators relating simple \"model\" (that is, explicitly diagonalizable) Hankel operators for each jump and the given Hankel operator $H$. We show that the set of all these wave operators is asymptotically complete. This determines the absolutely continuous part of $H$. We also prove that the singular continuous spectrum of $H$ is empty and that its eigenval"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2361","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":"2026-05-18T02:45:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M+wd+HVSYVPreMbtXuZcV+yNpqXhHFLZAzwS4gZiNG9bHciSsDI03etVMPUt4VsuIdG2Xcw8zRa/LTGFldr5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:02:58.354415Z"},"content_sha256":"4bdaff055a351c91b64dab40574a9d9c5c6bd83041a4022ba79972a83614b201","schema_version":"1.0","event_id":"sha256:4bdaff055a351c91b64dab40574a9d9c5c6bd83041a4022ba79972a83614b201"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCEAW47ZHSGFDFIIDB2JBVNYDB/bundle.json","state_url":"https://pith.science/pith/YCEAW47ZHSGFDFIIDB2JBVNYDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCEAW47ZHSGFDFIIDB2JBVNYDB/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":"2026-06-01T12:02:58Z","links":{"resolver":"https://pith.science/pith/YCEAW47ZHSGFDFIIDB2JBVNYDB","bundle":"https://pith.science/pith/YCEAW47ZHSGFDFIIDB2JBVNYDB/bundle.json","state":"https://pith.science/pith/YCEAW47ZHSGFDFIIDB2JBVNYDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCEAW47ZHSGFDFIIDB2JBVNYDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YCEAW47ZHSGFDFIIDB2JBVNYDB","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":"56c63893091975d6f92fee6952753d353c1f07a5c3a563640077ddb57d6d9af1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-11T10:06:42Z","title_canon_sha256":"45bfe921ba329a090249726451fa8836b5e1d2547a56cfdc76a13e14ca20487b"},"schema_version":"1.0","source":{"id":"1408.2361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2361","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2361v1","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2361","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"pith_short_12","alias_value":"YCEAW47ZHSGF","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YCEAW47ZHSGFDFII","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YCEAW47Z","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:4bdaff055a351c91b64dab40574a9d9c5c6bd83041a4022ba79972a83614b201","target":"graph","created_at":"2026-05-18T02:45:29Z","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 develop the spectral and scattering theory for self-adjoint Hankel operators $H$ with piecewise continuous symbols. In this case every jump of the symbol gives rise to a band of the absolutely continuous spectrum of $H$. We construct wave operators relating simple \"model\" (that is, explicitly diagonalizable) Hankel operators for each jump and the given Hankel operator $H$. We show that the set of all these wave operators is asymptotically complete. This determines the absolutely continuous part of $H$. We also prove that the singular continuous spectrum of $H$ is empty and that its eigenval","authors_text":"Alexander Pushnitski, Dmitri Yafaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-11T10:06:42Z","title":"Spectral and scattering theory of self-adjoint Hankel operators with piecewise continuous symbols"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2361","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":"sha256:04b6b950de9d1a87f3b0e58967fee265f8db914fcdded486abadaef595328b34","target":"record","created_at":"2026-05-18T02:45:29Z","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":"56c63893091975d6f92fee6952753d353c1f07a5c3a563640077ddb57d6d9af1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-11T10:06:42Z","title_canon_sha256":"45bfe921ba329a090249726451fa8836b5e1d2547a56cfdc76a13e14ca20487b"},"schema_version":"1.0","source":{"id":"1408.2361","kind":"arxiv","version":1}},"canonical_sha256":"c0880b73f93c8c519508187490d5b818797eb510afd106981735302c8a9cea61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0880b73f93c8c519508187490d5b818797eb510afd106981735302c8a9cea61","first_computed_at":"2026-05-18T02:45:29.645714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:29.645714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fuN/1uvyFiSMZbuGOfgQ3nhAKbbFO5pzYMb/0g9DeJjg3f6JJbqIkUwt91JOdukrcqe7ahI15D1WfeXx2ub9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:29.646382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04b6b950de9d1a87f3b0e58967fee265f8db914fcdded486abadaef595328b34","sha256:4bdaff055a351c91b64dab40574a9d9c5c6bd83041a4022ba79972a83614b201"],"state_sha256":"48d2c386bf23f7da0a19249f0921cdcf265d8da60b5dd68ab4177fb875009686"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LLBvDkZgjCxFIzp4CX5Pt/DVZSEJOhfV6wV4oeJlUKbOJ0nrT96UJoO0ADQSuGqKEh3FEwGHq8hq0fqGhfdWAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:02:58.356371Z","bundle_sha256":"5b2c458b7133a6fdcac70af174ff32236f2315426c58499ca0ea6695f1f6a6c3"}}