{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NEYD2Y3MM27TO52AWPEQLIWAQB","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":"9fa4cafea52f2bc574042a73761f21cc40bb01982bbf477fe8059b92695a1ca8","cross_cats_sorted":["math.OA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-17T04:12:57Z","title_canon_sha256":"0af3726739c20a8ae0160004aa4805eefc16179c73024902474bf44f95480886"},"schema_version":"1.0","source":{"id":"1807.06215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06215","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06215v1","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06215","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"NEYD2Y3MM27T","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NEYD2Y3MM27TO52A","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NEYD2Y3M","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:3a6d7d536236cf6351daf9e94b463e8549e0363ef5d0ebbbac31a1d5afb6e1c4","target":"graph","created_at":"2026-05-18T00:10:33Z","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 the Pythagorean C*-algebras and use the category/functor method to construct unitary representations of Thompson's groups from representations of them. We calculate several examples.","authors_text":"Arnaud Brothier, Vaughan F. R. Jones","cross_cats":["math.OA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-17T04:12:57Z","title":"Pythagorean representations of Thompson's groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06215","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":"sha256:910b467e5384b0f3976ab79ec1297878889d76acf5ae2fa051d60e7a7f7f05be","target":"record","created_at":"2026-05-18T00:10:33Z","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":"9fa4cafea52f2bc574042a73761f21cc40bb01982bbf477fe8059b92695a1ca8","cross_cats_sorted":["math.OA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-17T04:12:57Z","title_canon_sha256":"0af3726739c20a8ae0160004aa4805eefc16179c73024902474bf44f95480886"},"schema_version":"1.0","source":{"id":"1807.06215","kind":"arxiv","version":1}},"canonical_sha256":"69303d636c66bf377740b3c905a2c0805cfd921ac2b92a331e186a8fbfe8cf64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69303d636c66bf377740b3c905a2c0805cfd921ac2b92a331e186a8fbfe8cf64","first_computed_at":"2026-05-18T00:10:33.700098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:33.700098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"58Tpg6PKop8ciT4NXy6/Ubs8avdzRTcAjmp47AjyVC5J8OEPx8jWleZmcYZ0YsmbP2n2jMhYLKVkpymkDea3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:33.700758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:910b467e5384b0f3976ab79ec1297878889d76acf5ae2fa051d60e7a7f7f05be","sha256:3a6d7d536236cf6351daf9e94b463e8549e0363ef5d0ebbbac31a1d5afb6e1c4"],"state_sha256":"b84bfe9f71745a56b030fa258b5145477581cd8a69bed7cd491c1476bdce4597"}