{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HNKPVLS6W5625TBRFKBP7C3SPR","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":"858eca80e8772504c2e4c7aff772cac4a7d930f888f666eae028de114373884f","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-24T20:44:22Z","title_canon_sha256":"038506072412e034aaa005a88d6996914293be6c438b45dd069c31b2568eeb2d"},"schema_version":"1.0","source":{"id":"1811.09894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09894","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09894v1","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09894","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"HNKPVLS6W562","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HNKPVLS6W5625TBR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HNKPVLS6","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:fba40c561b7032727b502d231e561e79a8e081a6a9cee572af5acbe68d8490c1","target":"graph","created_at":"2026-05-17T23:59:59Z","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":"The paper is devoted to counterexamples involving the triviality of domains of products and/or adjoints of densely defined operators.","authors_text":"Mohammed Hichem Mortad","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-24T20:44:22Z","title":"On the triviality of domains of powers and adjoints of closed operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09894","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:dba2e3d93cd529345f02d37b93bc8735570d9adde929aa05a950e2b931331537","target":"record","created_at":"2026-05-17T23:59:59Z","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":"858eca80e8772504c2e4c7aff772cac4a7d930f888f666eae028de114373884f","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-24T20:44:22Z","title_canon_sha256":"038506072412e034aaa005a88d6996914293be6c438b45dd069c31b2568eeb2d"},"schema_version":"1.0","source":{"id":"1811.09894","kind":"arxiv","version":1}},"canonical_sha256":"3b54faae5eb77daecc312a82ff8b727c5fcf957cbab457239b44f5943b1d0c46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b54faae5eb77daecc312a82ff8b727c5fcf957cbab457239b44f5943b1d0c46","first_computed_at":"2026-05-17T23:59:59.189420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:59.189420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XTKtKSeBSnmGlw+EzA9e+E+RSHk8TQK3iwL7BfC0ilcW7feJ4aPVa5e+d7UQlMjTJJlQRa9sG32+Al6QIJ7xAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:59.189927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dba2e3d93cd529345f02d37b93bc8735570d9adde929aa05a950e2b931331537","sha256:fba40c561b7032727b502d231e561e79a8e081a6a9cee572af5acbe68d8490c1"],"state_sha256":"1f35c547e9f9b54aaeb6257ce9dcae5be75a540bcb50c4a215c6638beb6a6942"}