{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:63I6FDT7LYIWXQBEUMCCOURZ45","short_pith_number":"pith:63I6FDT7","canonical_record":{"source":{"id":"1603.02856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-09T11:47:40Z","cross_cats_sorted":[],"title_canon_sha256":"897c7378e9bc485322cbc26e840df8b546bc218d7f9c5fc9f7fc7080d36567ed","abstract_canon_sha256":"a66b8e25f1d52f7d4a0cf168cf4812e5d9955e89784f38dbc90f5d993b5c657b"},"schema_version":"1.0"},"canonical_sha256":"f6d1e28e7f5e116bc024a304275239e74a26add0b969c62dc1d658ec783c3491","source":{"kind":"arxiv","id":"1603.02856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02856","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02856v1","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02856","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"63I6FDT7LYIW","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"63I6FDT7LYIWXQBE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"63I6FDT7","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:63I6FDT7LYIWXQBEUMCCOURZ45","target":"record","payload":{"canonical_record":{"source":{"id":"1603.02856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-09T11:47:40Z","cross_cats_sorted":[],"title_canon_sha256":"897c7378e9bc485322cbc26e840df8b546bc218d7f9c5fc9f7fc7080d36567ed","abstract_canon_sha256":"a66b8e25f1d52f7d4a0cf168cf4812e5d9955e89784f38dbc90f5d993b5c657b"},"schema_version":"1.0"},"canonical_sha256":"f6d1e28e7f5e116bc024a304275239e74a26add0b969c62dc1d658ec783c3491","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:19.710662Z","signature_b64":"QbZ3d0BFp21Cc30zeAS4De7WHpBwWgL4sUb1xFUFeHu7O416LbiH+JJloOyHVPg+8E/BVgZhn0KwkwxmryRACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6d1e28e7f5e116bc024a304275239e74a26add0b969c62dc1d658ec783c3491","last_reissued_at":"2026-05-18T01:19:19.710192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:19.710192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.02856","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":"2026-05-18T01:19:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+383T/s8zSrRnA8QdPlIuHYP04h7EunoKq53skwPpnxtVdHJIHWyKI8PHziPHN5QFtFlUwmWMXC+Qbdq3DoqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:55:27.646300Z"},"content_sha256":"e0a9e790efaa7fb9c27a6d4ec2e5a416fa8c54a0ebb8be78f6adc6cf6a3151c4","schema_version":"1.0","event_id":"sha256:e0a9e790efaa7fb9c27a6d4ec2e5a416fa8c54a0ebb8be78f6adc6cf6a3151c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:63I6FDT7LYIWXQBEUMCCOURZ45","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the joint spectra of the two dimensional Lie algebra of operators in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrico Boasso","submitted_at":"2016-03-09T11:47:40Z","abstract_excerpt":"We consider the complex solvable non-commutative two dimensional Lie algebra $L$, $L=<y>\\oplus <x>$, with Lie bracket $[x,y]=y$, as linear bounded operators acting on a complex Hilbert space $H$. Under the assumption $R(y)$ closed, we reduce the computation of the joint spectra $Sp(L,E)$, $\\sigma_{\\delta ,k}(L,E)$ and $\\sigma_{\\pi ,k}(L,E)$, $k= 0,1,2$, to the computation of the spectrum, the approximate point spectrum, and the approximate compression spectrum of a single operator. Besides, we also study the case $y^2=0$, and we apply our results to the case $H$ finite dimensional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02856","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":"2026-05-18T01:19:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1dfG64FF44OPwZufmtRc92ub4kvzt6Np/k+AuBftjFFQW3t8DMksGxUZdZxoLfRLTdn3XZjx8d18rm5b9txzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:55:27.646663Z"},"content_sha256":"92cda9e4c92cfdf8e94d345c7a740cdf428e53068284747bbee969ea86fc776d","schema_version":"1.0","event_id":"sha256:92cda9e4c92cfdf8e94d345c7a740cdf428e53068284747bbee969ea86fc776d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63I6FDT7LYIWXQBEUMCCOURZ45/bundle.json","state_url":"https://pith.science/pith/63I6FDT7LYIWXQBEUMCCOURZ45/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63I6FDT7LYIWXQBEUMCCOURZ45/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":"2026-06-21T03:55:27Z","links":{"resolver":"https://pith.science/pith/63I6FDT7LYIWXQBEUMCCOURZ45","bundle":"https://pith.science/pith/63I6FDT7LYIWXQBEUMCCOURZ45/bundle.json","state":"https://pith.science/pith/63I6FDT7LYIWXQBEUMCCOURZ45/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63I6FDT7LYIWXQBEUMCCOURZ45/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:63I6FDT7LYIWXQBEUMCCOURZ45","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":"a66b8e25f1d52f7d4a0cf168cf4812e5d9955e89784f38dbc90f5d993b5c657b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-09T11:47:40Z","title_canon_sha256":"897c7378e9bc485322cbc26e840df8b546bc218d7f9c5fc9f7fc7080d36567ed"},"schema_version":"1.0","source":{"id":"1603.02856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02856","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02856v1","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02856","created_at":"2026-05-18T01:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"63I6FDT7LYIW","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"63I6FDT7LYIWXQBE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"63I6FDT7","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:92cda9e4c92cfdf8e94d345c7a740cdf428e53068284747bbee969ea86fc776d","target":"graph","created_at":"2026-05-18T01:19:19Z","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 the complex solvable non-commutative two dimensional Lie algebra $L$, $L=<y>\\oplus <x>$, with Lie bracket $[x,y]=y$, as linear bounded operators acting on a complex Hilbert space $H$. Under the assumption $R(y)$ closed, we reduce the computation of the joint spectra $Sp(L,E)$, $\\sigma_{\\delta ,k}(L,E)$ and $\\sigma_{\\pi ,k}(L,E)$, $k= 0,1,2$, to the computation of the spectrum, the approximate point spectrum, and the approximate compression spectrum of a single operator. Besides, we also study the case $y^2=0$, and we apply our results to the case $H$ finite dimensional.","authors_text":"Enrico Boasso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-09T11:47:40Z","title":"On the joint spectra of the two dimensional Lie algebra of operators in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02856","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:e0a9e790efaa7fb9c27a6d4ec2e5a416fa8c54a0ebb8be78f6adc6cf6a3151c4","target":"record","created_at":"2026-05-18T01:19:19Z","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":"a66b8e25f1d52f7d4a0cf168cf4812e5d9955e89784f38dbc90f5d993b5c657b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-09T11:47:40Z","title_canon_sha256":"897c7378e9bc485322cbc26e840df8b546bc218d7f9c5fc9f7fc7080d36567ed"},"schema_version":"1.0","source":{"id":"1603.02856","kind":"arxiv","version":1}},"canonical_sha256":"f6d1e28e7f5e116bc024a304275239e74a26add0b969c62dc1d658ec783c3491","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6d1e28e7f5e116bc024a304275239e74a26add0b969c62dc1d658ec783c3491","first_computed_at":"2026-05-18T01:19:19.710192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:19.710192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QbZ3d0BFp21Cc30zeAS4De7WHpBwWgL4sUb1xFUFeHu7O416LbiH+JJloOyHVPg+8E/BVgZhn0KwkwxmryRACw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:19.710662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0a9e790efaa7fb9c27a6d4ec2e5a416fa8c54a0ebb8be78f6adc6cf6a3151c4","sha256:92cda9e4c92cfdf8e94d345c7a740cdf428e53068284747bbee969ea86fc776d"],"state_sha256":"dba001ed572a18449930afdab5a5029dff7edca185b2bf840f64f2fb167b7b60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oUvKLEd87SMlKbXpk4ooleOUy5y2+52zA3onF7ow5DYBwnpOqVTgA9ooJiRFLnYNeQpCj/WeA8ZIoeX+TGaXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T03:55:27.648576Z","bundle_sha256":"eb9be34465e0b085d1aef492f44eafa19531399556abd882b098182e2a96658b"}}