{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WCV26V6W6XL5FKDNKYJUZASK6E","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":"c7b7a2edd2f89d63e6f06c9445f98a1975bd4a193f24b02c3b1ead321186969d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-12T06:11:53Z","title_canon_sha256":"797bbacf5c64efbd1d199facd11c76bcf50adf61add65f027741f4e32cd88788"},"schema_version":"1.0","source":{"id":"1302.2708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2708","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2708v2","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2708","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"WCV26V6W6XL5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WCV26V6W6XL5FKDN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WCV26V6W","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:57019bf580f40901cc8f8ce122fb85712e5df5c486ad2e289d38eb05f5fec17f","target":"graph","created_at":"2026-05-18T03:15:57Z","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"},"paper":{"abstract_excerpt":"In this paper, some ?-classes of weighted conditional expectation type operators, such as A-class, ?-A-class and quasi-?-A classes on L2(?) are investigated. Also, the spectrum, point spectrum and spectral radius of these operators are computed.","authors_text":"Yousef Estaremi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-12T06:11:53Z","title":"Some classes of weighted conditional type operators and their spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2708","kind":"arxiv","version":2},"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":"sha256:560f92b6057af321eec909e4215fd1db54d03c719eeff4d66947e067fff8fdd6","target":"record","created_at":"2026-05-18T03:15:57Z","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":"c7b7a2edd2f89d63e6f06c9445f98a1975bd4a193f24b02c3b1ead321186969d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-12T06:11:53Z","title_canon_sha256":"797bbacf5c64efbd1d199facd11c76bcf50adf61add65f027741f4e32cd88788"},"schema_version":"1.0","source":{"id":"1302.2708","kind":"arxiv","version":2}},"canonical_sha256":"b0abaf57d6f5d7d2a86d56134c824af1390362f511a3c64d604f909c66728bfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0abaf57d6f5d7d2a86d56134c824af1390362f511a3c64d604f909c66728bfe","first_computed_at":"2026-05-18T03:15:57.561587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:57.561587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ytP36JVz0D37G66DD9QPhAWuB2NhlnoPUzhk1I5MEvMbbhBUKO1qp47cl9uDONc6Wu7IuZxnGtV/nIeC1xRwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:57.562203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:560f92b6057af321eec909e4215fd1db54d03c719eeff4d66947e067fff8fdd6","sha256:57019bf580f40901cc8f8ce122fb85712e5df5c486ad2e289d38eb05f5fec17f"],"state_sha256":"e64d4a045a1d6664b2af98eb7fb4d7caba3a3a7964e23e6a0a8aeac32b0e48b4"}