{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:X62MD5ZFDPIMO6RBUVB2BGQ5NQ","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":"f744b72e8bc0f952df4db9cafbcda19265f081a89e851baa280c0205ec83b7f6","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2003-11-19T11:13:37Z","title_canon_sha256":"f4427853bdd655425a43560de2fe155fc362e1dc7ca74826d84b0f17c30ecfb2"},"schema_version":"1.0","source":{"id":"math/0311324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0311324","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0311324v1","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311324","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"X62MD5ZFDPIM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"X62MD5ZFDPIMO6RB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"X62MD5ZF","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:fef9782bd4f119e0617701f1a9a492e08046ae655905dd99625715ecbe9b988b","target":"graph","created_at":"2026-05-18T04:26:44Z","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 introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$ into a space with an unconditional basis belongs to this class.","authors_text":"Dirk Werner, Nigel Kalton, Vladimir Kadets","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2003-11-19T11:13:37Z","title":"Unconditionally convergent series of operators and narrow operators on $L_1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311324","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":"sha256:2365609833f7d0ed3c96e02144cf5b0b2b4185a94d731d753e3bf9355ecc7c83","target":"record","created_at":"2026-05-18T04:26:44Z","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":"f744b72e8bc0f952df4db9cafbcda19265f081a89e851baa280c0205ec83b7f6","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2003-11-19T11:13:37Z","title_canon_sha256":"f4427853bdd655425a43560de2fe155fc362e1dc7ca74826d84b0f17c30ecfb2"},"schema_version":"1.0","source":{"id":"math/0311324","kind":"arxiv","version":1}},"canonical_sha256":"bfb4c1f7251bd0c77a21a543a09a1d6c2702e36d97c6452d57d9ed797b95a781","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfb4c1f7251bd0c77a21a543a09a1d6c2702e36d97c6452d57d9ed797b95a781","first_computed_at":"2026-05-18T04:26:44.086046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:44.086046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"asg/lfgD92msnPHgADki8Sqs6sJSGpeLTO0FqGpLSiD4lEqDxIVfyqbPn4s6Gs/yv3mWQRTaHo6J6g8mzyqzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:44.086591Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0311324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2365609833f7d0ed3c96e02144cf5b0b2b4185a94d731d753e3bf9355ecc7c83","sha256:fef9782bd4f119e0617701f1a9a492e08046ae655905dd99625715ecbe9b988b"],"state_sha256":"499bab666a2d1a4c0a51e79bc75e2b2565c34f228a39aa91a2c37910b5373f84"}