{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:LMFZ44HLG5HCYOVXQHJYR5OREP","short_pith_number":"pith:LMFZ44HL","canonical_record":{"source":{"id":"2007.08841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-07-17T09:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"29f97a5c96adaadfad8d24ac19c750b33059954cc4749e9a487a162d111be7db","abstract_canon_sha256":"216ea95c5edd16355e2053a8e750d8f2d7ce9b534d46f2cfb7cc6a1e54402168"},"schema_version":"1.0"},"canonical_sha256":"5b0b9e70eb374e2c3ab781d388f5d123c6ec002fe0fc25287be12c0959325dba","source":{"kind":"arxiv","id":"2007.08841","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.08841","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"2007.08841v1","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.08841","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"LMFZ44HLG5HC","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"pith_short_16","alias_value":"LMFZ44HLG5HCYOVX","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"pith_short_8","alias_value":"LMFZ44HL","created_at":"2026-07-05T01:19:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:LMFZ44HLG5HCYOVXQHJYR5OREP","target":"record","payload":{"canonical_record":{"source":{"id":"2007.08841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-07-17T09:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"29f97a5c96adaadfad8d24ac19c750b33059954cc4749e9a487a162d111be7db","abstract_canon_sha256":"216ea95c5edd16355e2053a8e750d8f2d7ce9b534d46f2cfb7cc6a1e54402168"},"schema_version":"1.0"},"canonical_sha256":"5b0b9e70eb374e2c3ab781d388f5d123c6ec002fe0fc25287be12c0959325dba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:19:57.864060Z","signature_b64":"QMp82xOQLuo8D+BpWe2O/PUk/3aGwstbWP3iN6+J/Wn/EbzRfEKMUu+zUS0vXmKskLNieUMgRNMbHRdmUzhbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b0b9e70eb374e2c3ab781d388f5d123c6ec002fe0fc25287be12c0959325dba","last_reissued_at":"2026-07-05T01:19:57.863644Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:19:57.863644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.08841","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":"2026-07-05T01:19:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7s1oQpqyoLv+N7nqNnMlp6PDnwhTMnZhVgtXliOupt6VT6bO6ktdhkio4e/EOuPi05atnSrRDg/v7qCU0u8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T18:46:47.602041Z"},"content_sha256":"293cffc0d2ce227722deeb1a181b04fccd3c557fb637959ae479aae822f2d11d","schema_version":"1.0","event_id":"sha256:293cffc0d2ce227722deeb1a181b04fccd3c557fb637959ae479aae822f2d11d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:LMFZ44HLG5HCYOVXQHJYR5OREP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Oles Dobosevych, Rostyslav Hryniv","submitted_at":"2020-07-17T09:10:29Z","abstract_excerpt":"For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.08841","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.08841/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:19:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cOs2F2yYtgFEIvMoWu3M0NyMrWh3GDr7XIsPFH7rS5QKumhXGs73b0w+2HVfQKNfS5Q5unpOB4FDwpdqecmbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T18:46:47.602553Z"},"content_sha256":"36d89a085962e8e46422e048ce05b2723588913ea9dfc24dd31e6a62349cd084","schema_version":"1.0","event_id":"sha256:36d89a085962e8e46422e048ce05b2723588913ea9dfc24dd31e6a62349cd084"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMFZ44HLG5HCYOVXQHJYR5OREP/bundle.json","state_url":"https://pith.science/pith/LMFZ44HLG5HCYOVXQHJYR5OREP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMFZ44HLG5HCYOVXQHJYR5OREP/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":"2026-08-22T18:46:47Z","links":{"resolver":"https://pith.science/pith/LMFZ44HLG5HCYOVXQHJYR5OREP","bundle":"https://pith.science/pith/LMFZ44HLG5HCYOVXQHJYR5OREP/bundle.json","state":"https://pith.science/pith/LMFZ44HLG5HCYOVXQHJYR5OREP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMFZ44HLG5HCYOVXQHJYR5OREP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LMFZ44HLG5HCYOVXQHJYR5OREP","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":"216ea95c5edd16355e2053a8e750d8f2d7ce9b534d46f2cfb7cc6a1e54402168","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-07-17T09:10:29Z","title_canon_sha256":"29f97a5c96adaadfad8d24ac19c750b33059954cc4749e9a487a162d111be7db"},"schema_version":"1.0","source":{"id":"2007.08841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.08841","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"2007.08841v1","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.08841","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"LMFZ44HLG5HC","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"pith_short_16","alias_value":"LMFZ44HLG5HCYOVX","created_at":"2026-07-05T01:19:57Z"},{"alias_kind":"pith_short_8","alias_value":"LMFZ44HL","created_at":"2026-07-05T01:19:57Z"}],"graph_snapshots":[{"event_id":"sha256:36d89a085962e8e46422e048ce05b2723588913ea9dfc24dd31e6a62349cd084","target":"graph","created_at":"2026-07-05T01:19:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.08841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.","authors_text":"Oles Dobosevych, Rostyslav Hryniv","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-07-17T09:10:29Z","title":"Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.08841","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":"sha256:293cffc0d2ce227722deeb1a181b04fccd3c557fb637959ae479aae822f2d11d","target":"record","created_at":"2026-07-05T01:19:57Z","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":"216ea95c5edd16355e2053a8e750d8f2d7ce9b534d46f2cfb7cc6a1e54402168","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-07-17T09:10:29Z","title_canon_sha256":"29f97a5c96adaadfad8d24ac19c750b33059954cc4749e9a487a162d111be7db"},"schema_version":"1.0","source":{"id":"2007.08841","kind":"arxiv","version":1}},"canonical_sha256":"5b0b9e70eb374e2c3ab781d388f5d123c6ec002fe0fc25287be12c0959325dba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b0b9e70eb374e2c3ab781d388f5d123c6ec002fe0fc25287be12c0959325dba","first_computed_at":"2026-07-05T01:19:57.863644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:19:57.863644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QMp82xOQLuo8D+BpWe2O/PUk/3aGwstbWP3iN6+J/Wn/EbzRfEKMUu+zUS0vXmKskLNieUMgRNMbHRdmUzhbAw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:19:57.864060Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.08841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:293cffc0d2ce227722deeb1a181b04fccd3c557fb637959ae479aae822f2d11d","sha256:36d89a085962e8e46422e048ce05b2723588913ea9dfc24dd31e6a62349cd084"],"state_sha256":"a8b708d9c95dd26fd996d05ba842d791d4b7d45c64b2f7e5413d216bfdad4ca8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRQjYXP9rklSpvacng7YOQrt+9R+3vmeiMesMWzv9668sMWB0XSnFSLw56MEDP1uBvEkPeI3xmAbg/iZ7ElPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T18:46:47.607704Z","bundle_sha256":"f82220b276a47ca3b2fc045dab435ac3bdea79808a3a1a0cef5d448b29279c49"}}