{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SKAIREOYVB4URNS5HR6OUQ6COX","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":"ca07efe6b931322dc6701e28250a1ebf9d279e9919232c4efc9cc4bffa9c6df5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-17T20:28:42Z","title_canon_sha256":"7873d418e60664e626e559369b8cb808da2c60b272fe4e310cc61d17af5c124f"},"schema_version":"1.0","source":{"id":"1309.4475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4475","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4475v1","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4475","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"SKAIREOYVB4U","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SKAIREOYVB4URNS5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SKAIREOY","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:a6c04e4e2d640af7422b1594c17e7f53eb1b425eb97f5937c8d5afd659741b1a","target":"graph","created_at":"2026-05-18T03:12:59Z","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 describe essential (in particular Fredholm and semi-Fredholm) spectra of operators on Banach lattices of the form $T=wU$, where $w$ is a central operator and $U$ is a disjointness preserving operator such that its spectrum $\\sigma(U)$ is a subset of the unit circle.","authors_text":"Arkady Kitover","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-17T20:28:42Z","title":"Spectrum of Weighted Composition Operators. Part III. Essential spectra of some disjointness preserving operators on Banach lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4475","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:f9e1f6c73c74e9dcc9cd45898b7d53ab8ed529fc11ba24941b931336398e1474","target":"record","created_at":"2026-05-18T03:12:59Z","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":"ca07efe6b931322dc6701e28250a1ebf9d279e9919232c4efc9cc4bffa9c6df5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-17T20:28:42Z","title_canon_sha256":"7873d418e60664e626e559369b8cb808da2c60b272fe4e310cc61d17af5c124f"},"schema_version":"1.0","source":{"id":"1309.4475","kind":"arxiv","version":1}},"canonical_sha256":"92808891d8a87948b65d3c7cea43c275c9f6999d6ca21904c0c210785eb25931","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92808891d8a87948b65d3c7cea43c275c9f6999d6ca21904c0c210785eb25931","first_computed_at":"2026-05-18T03:12:59.380367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:59.380367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HvUPwjPYJCyrSSjgngr+tcEkeyTt5QJMEMWzTQ3aGdKci9H9Au7+QVnsvPV+hHUYB1ZpES4fZpuXwlhb4n0PCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:59.381127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9e1f6c73c74e9dcc9cd45898b7d53ab8ed529fc11ba24941b931336398e1474","sha256:a6c04e4e2d640af7422b1594c17e7f53eb1b425eb97f5937c8d5afd659741b1a"],"state_sha256":"8049bee2375cfa1b3b8f0f9c202f2f8b7123587980c952217d750539c74150e1"}