{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YXLZTMHZ3I63CPHKZSJYHZPWIR","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":"c3232130e4e2727ba672778a1ac40334ac0ba48e4ff7bf1eb40eeb9a9ba9a201","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-24T20:42:14Z","title_canon_sha256":"dd29f75e6883a835c90438dddcb0392a6554bce9486696b9776370fac792db25"},"schema_version":"1.0","source":{"id":"1811.09893","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09893","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09893v1","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09893","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"YXLZTMHZ3I63","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YXLZTMHZ3I63CPHK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YXLZTMHZ","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:712307800ddb0211f5fed77159d8d87db90295c08fc23aae9f2886e7f3f5ac4f","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 present paper is exclusively devoted to counterexamples about commutators and self commutators of unbounded operators on a Hilbert space. As a bonus, we provide a simpler counterexample than McIntosh's famous example obtained some while ago.","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":"2018-11-24T20:42:14Z","title":"Counterexamples Related to Commutators of Unbounded Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09893","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:b70e426e9a4c969292c8332bacc718d2b54ecb909e0f5f575d30c409205eae60","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":"c3232130e4e2727ba672778a1ac40334ac0ba48e4ff7bf1eb40eeb9a9ba9a201","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-24T20:42:14Z","title_canon_sha256":"dd29f75e6883a835c90438dddcb0392a6554bce9486696b9776370fac792db25"},"schema_version":"1.0","source":{"id":"1811.09893","kind":"arxiv","version":1}},"canonical_sha256":"c5d799b0f9da3db13ceacc9383e5f64478e4afaf0697f15b858a14f86a1a96bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5d799b0f9da3db13ceacc9383e5f64478e4afaf0697f15b858a14f86a1a96bf","first_computed_at":"2026-05-17T23:59:59.196685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:59.196685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iypKpyqWzpluknRp5/YKbxEzXfrbFzdfJzw66SXOIJk7VgGUxRDsUU5ikMJBxqfqVsTW7mXFkT5XxntbbTtQCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:59.197182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09893","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b70e426e9a4c969292c8332bacc718d2b54ecb909e0f5f575d30c409205eae60","sha256:712307800ddb0211f5fed77159d8d87db90295c08fc23aae9f2886e7f3f5ac4f"],"state_sha256":"993baa8fee07ea720787a34b63a979a5c6313f98d9f3dad0e17464395c134408"}