{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JB6K7UUFUW2TWD2QPTTLWRCCEG","short_pith_number":"pith:JB6K7UUF","canonical_record":{"source":{"id":"1209.1460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:28:15Z","cross_cats_sorted":[],"title_canon_sha256":"48a9e3ea0f842434ee191b9ca2f5416eb76e00c10374461003cf4ba231d4da42","abstract_canon_sha256":"2e1860f73951014770f5941ebee78ac3ac9620dd0ad091886c327e10af1cd915"},"schema_version":"1.0"},"canonical_sha256":"487cafd285a5b53b0f507ce6bb444221a0bd695cde9cde6318edaa0f2f0b6d06","source":{"kind":"arxiv","id":"1209.1460","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1460","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1460v1","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1460","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"JB6K7UUFUW2T","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JB6K7UUFUW2TWD2Q","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JB6K7UUF","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JB6K7UUFUW2TWD2QPTTLWRCCEG","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:28:15Z","cross_cats_sorted":[],"title_canon_sha256":"48a9e3ea0f842434ee191b9ca2f5416eb76e00c10374461003cf4ba231d4da42","abstract_canon_sha256":"2e1860f73951014770f5941ebee78ac3ac9620dd0ad091886c327e10af1cd915"},"schema_version":"1.0"},"canonical_sha256":"487cafd285a5b53b0f507ce6bb444221a0bd695cde9cde6318edaa0f2f0b6d06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:04.718582Z","signature_b64":"XVlccjixtFBz0ryvQiqCNf5rWsaMmgIrmT/i9jUhiI5ros8xReXOkswkfol1VAjQX+Ff6+WH2eP+BjNirjAkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"487cafd285a5b53b0f507ce6bb444221a0bd695cde9cde6318edaa0f2f0b6d06","last_reissued_at":"2026-05-18T03:46:04.717937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:04.717937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1460","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":"2026-05-18T03:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4lmRFs45nrvOdZO/OMpwjhrapuAsZYOswzcyclhGNa5jmEoz0BSOH1mZz/0ziw9q8LLYZSvi6jDJpAfEax2fBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T00:04:13.384089Z"},"content_sha256":"1f079a86895c073e90af92c80af947d01bf574f62ba4aac2af0463632021b0b0","schema_version":"1.0","event_id":"sha256:1f079a86895c073e90af92c80af947d01bf574f62ba4aac2af0463632021b0b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JB6K7UUFUW2TWD2QPTTLWRCCEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact operators without extended eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2012-09-07T08:28:15Z","abstract_excerpt":"A complex number $\\lambda$ is called an extended eigenvalue of a bounded linear operator $T$ on a Banach space $\\B$ if there exists a non-zero bounded linear operator $X$ acting on $\\B$ such that $XT=\\lambda TX$. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set ${1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1460","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":"2026-05-18T03:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Y8cKeNzItj2i0rciUTbYDxgWfA87a3fRombavcXoqaztOk/lwL47tJPjl1QBzDR2N4q/4YPx2jNzUb0PomQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T00:04:13.384457Z"},"content_sha256":"facf0d424cb4574516a0d7480c6f96ac7e04a689681026bd78a76015ab9d59e0","schema_version":"1.0","event_id":"sha256:facf0d424cb4574516a0d7480c6f96ac7e04a689681026bd78a76015ab9d59e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JB6K7UUFUW2TWD2QPTTLWRCCEG/bundle.json","state_url":"https://pith.science/pith/JB6K7UUFUW2TWD2QPTTLWRCCEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JB6K7UUFUW2TWD2QPTTLWRCCEG/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":"2026-06-24T00:04:13Z","links":{"resolver":"https://pith.science/pith/JB6K7UUFUW2TWD2QPTTLWRCCEG","bundle":"https://pith.science/pith/JB6K7UUFUW2TWD2QPTTLWRCCEG/bundle.json","state":"https://pith.science/pith/JB6K7UUFUW2TWD2QPTTLWRCCEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JB6K7UUFUW2TWD2QPTTLWRCCEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JB6K7UUFUW2TWD2QPTTLWRCCEG","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":"2e1860f73951014770f5941ebee78ac3ac9620dd0ad091886c327e10af1cd915","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:28:15Z","title_canon_sha256":"48a9e3ea0f842434ee191b9ca2f5416eb76e00c10374461003cf4ba231d4da42"},"schema_version":"1.0","source":{"id":"1209.1460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1460","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1460v1","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1460","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"JB6K7UUFUW2T","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JB6K7UUFUW2TWD2Q","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JB6K7UUF","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:facf0d424cb4574516a0d7480c6f96ac7e04a689681026bd78a76015ab9d59e0","target":"graph","created_at":"2026-05-18T03:46:04Z","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":"A complex number $\\lambda$ is called an extended eigenvalue of a bounded linear operator $T$ on a Banach space $\\B$ if there exists a non-zero bounded linear operator $X$ acting on $\\B$ such that $XT=\\lambda TX$. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set ${1}$.","authors_text":"Stanislav Shkarin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:28:15Z","title":"Compact operators without extended eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1460","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":"sha256:1f079a86895c073e90af92c80af947d01bf574f62ba4aac2af0463632021b0b0","target":"record","created_at":"2026-05-18T03:46:04Z","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":"2e1860f73951014770f5941ebee78ac3ac9620dd0ad091886c327e10af1cd915","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:28:15Z","title_canon_sha256":"48a9e3ea0f842434ee191b9ca2f5416eb76e00c10374461003cf4ba231d4da42"},"schema_version":"1.0","source":{"id":"1209.1460","kind":"arxiv","version":1}},"canonical_sha256":"487cafd285a5b53b0f507ce6bb444221a0bd695cde9cde6318edaa0f2f0b6d06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"487cafd285a5b53b0f507ce6bb444221a0bd695cde9cde6318edaa0f2f0b6d06","first_computed_at":"2026-05-18T03:46:04.717937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:04.717937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XVlccjixtFBz0ryvQiqCNf5rWsaMmgIrmT/i9jUhiI5ros8xReXOkswkfol1VAjQX+Ff6+WH2eP+BjNirjAkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:04.718582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f079a86895c073e90af92c80af947d01bf574f62ba4aac2af0463632021b0b0","sha256:facf0d424cb4574516a0d7480c6f96ac7e04a689681026bd78a76015ab9d59e0"],"state_sha256":"06db8cf67ae59ceeb448c86102af1d2d97fcad0c85f668d0faf556baa7060387"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSvzMoDCJcR9/64sSXb98Buv43SRs7MFgFqQ3eyKZiaMG1amogyH7H+SY/ypRmSfytPxUM1GQZFOvW9QGiaWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T00:04:13.386818Z","bundle_sha256":"d865b13d2679ecf136d038c81e28dbbfbb4d880d239cdc332903a9b320bb8007"}}