{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CTDV5IVXCZUOIWKIHCUUTEQ7UY","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":"c08b113c1ba92adb805cedfdc6069dd1973518a9b8994645a685247603e9c527","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-25T07:45:51Z","title_canon_sha256":"225f32fd16f4ae54d2eb2368edc58a4394a8cb371d7b9e4f2fa63be888308966"},"schema_version":"1.0","source":{"id":"1603.07836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07836","created_at":"2026-05-18T01:18:17Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07836v1","created_at":"2026-05-18T01:18:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07836","created_at":"2026-05-18T01:18:17Z"},{"alias_kind":"pith_short_12","alias_value":"CTDV5IVXCZUO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CTDV5IVXCZUOIWKI","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CTDV5IVX","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:8580652c690ff33c67f5353942f62ede0ddd00da9ec878fe7bb1ee63ba23bac2","target":"graph","created_at":"2026-05-18T01:18:17Z","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 unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory of Hilbert representations of quivers is a generalization of the theory of unbounded operators. A non-zero Hilbert representation of a quiver is said to be transitive if the endomorphism algebra is trivial. If a Hilbert representation of a quiver is transitive, then it is indecomposable. But the converse is not true. Let $\\Gamma$ be a quiver whose underlyin","authors_text":"Masatoshi Enomoto, Yasuo Watatani","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-25T07:45:51Z","title":"Unbounded strongly irreducible operators and transitive representations of quivers on infinite-dimensional Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07836","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:f4b50ba0305f2cf0860e145551e7601c051254e4975dbd8412f95f2727719bfa","target":"record","created_at":"2026-05-18T01:18:17Z","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":"c08b113c1ba92adb805cedfdc6069dd1973518a9b8994645a685247603e9c527","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-25T07:45:51Z","title_canon_sha256":"225f32fd16f4ae54d2eb2368edc58a4394a8cb371d7b9e4f2fa63be888308966"},"schema_version":"1.0","source":{"id":"1603.07836","kind":"arxiv","version":1}},"canonical_sha256":"14c75ea2b71668e4594838a949921fa6048a04e7888d671ae09c427757e494c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14c75ea2b71668e4594838a949921fa6048a04e7888d671ae09c427757e494c7","first_computed_at":"2026-05-18T01:18:17.702962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:17.702962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nzCz9h6nrPpcOl64QnZOl9XW15W0bu8nUbEivJ+Tqm2RP6iFG9HL8QFR+ijaWR8paOpkk0PH0bLqF3MEQze1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:17.703600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4b50ba0305f2cf0860e145551e7601c051254e4975dbd8412f95f2727719bfa","sha256:8580652c690ff33c67f5353942f62ede0ddd00da9ec878fe7bb1ee63ba23bac2"],"state_sha256":"544c0966bcff08eb1e7caaddc4d7a6f5deb1e40133919d4a2556f39d72a447ea"}