{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ANGXK3DIAKQBFJKIH3XM5BBGXK","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":"9392cfb0ce0734c720f04d8c89677a03bf9a1705a2f890f3c04819015a2499f5","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-11-04T23:19:57Z","title_canon_sha256":"c393fd0a89e60e29646a94ce73a095c32e21365b18d0fb3d1fbc030b37e92a3f"},"schema_version":"1.0","source":{"id":"2411.11883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.11883","created_at":"2026-07-05T09:37:13Z"},{"alias_kind":"arxiv_version","alias_value":"2411.11883v1","created_at":"2026-07-05T09:37:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.11883","created_at":"2026-07-05T09:37:13Z"},{"alias_kind":"pith_short_12","alias_value":"ANGXK3DIAKQB","created_at":"2026-07-05T09:37:13Z"},{"alias_kind":"pith_short_16","alias_value":"ANGXK3DIAKQBFJKI","created_at":"2026-07-05T09:37:13Z"},{"alias_kind":"pith_short_8","alias_value":"ANGXK3DI","created_at":"2026-07-05T09:37:13Z"}],"graph_snapshots":[{"event_id":"sha256:9d1d217df84ccddd1652dea4ac68c8eb33574b19e33fc9f1aba3b77dfe27b0a1","target":"graph","created_at":"2026-07-05T09:37:13Z","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/2411.11883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper explores operators with countable, continuous, and hybrid spectra, focusing on both finite dimensional and infinite dimensional cases, particularly in non-Hermitian systems. For finite dimensional operators, a novel concept of analogous matrices is introduced. Here, matrices are considered analogous if they share the same projector and nilpotent structures, indicating structural equivalences beyond simple spectral similarities. A graph-based model represents these projector and nilpotent structures, offering insights for classifying analogous matrices. Additionally, the paper calcul","authors_text":"Shih-Yu Chang","cross_cats":["math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-11-04T23:19:57Z","title":"Operator Characterization via Projectors and Nilpotents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11883","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":"sha256:87da6587655412b1feb28390339557c7cac5b35adc19d74d77aca96bb22d1d4b","target":"record","created_at":"2026-07-05T09:37:13Z","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":"9392cfb0ce0734c720f04d8c89677a03bf9a1705a2f890f3c04819015a2499f5","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-11-04T23:19:57Z","title_canon_sha256":"c393fd0a89e60e29646a94ce73a095c32e21365b18d0fb3d1fbc030b37e92a3f"},"schema_version":"1.0","source":{"id":"2411.11883","kind":"arxiv","version":1}},"canonical_sha256":"034d756c6802a012a5483eeece8426ba9f033efb2b5d4ddbac4a31daf97fc292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"034d756c6802a012a5483eeece8426ba9f033efb2b5d4ddbac4a31daf97fc292","first_computed_at":"2026-07-05T09:37:13.376874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:37:13.376874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ofUuYURVX8o0cWG7GgmG4HwdZ58/F/cV19DL4FE2hEcWStCNPS9RgzZ/ls0yX9Nn1E5fdZoHmlbnqECLaq0zBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:37:13.377287Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.11883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87da6587655412b1feb28390339557c7cac5b35adc19d74d77aca96bb22d1d4b","sha256:9d1d217df84ccddd1652dea4ac68c8eb33574b19e33fc9f1aba3b77dfe27b0a1"],"state_sha256":"63d81c89145aa9c44459670e547cc69178e84f7cc4ddbade97ed105fc913ebc2"}