{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PSAYW57XVLLDAUZ2FWGPPIQD3H","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":"8232c8dfc0902131b7567556e5bcfa04962169fab4e6874d9cc932ef36288fd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-01-13T22:01:58Z","title_canon_sha256":"0aaa122c89df835c75fc229a5751ef057f1453843e6690800a426de6f187d55b"},"schema_version":"1.0","source":{"id":"1601.03423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03423","created_at":"2026-05-18T00:44:25Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03423v1","created_at":"2026-05-18T00:44:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03423","created_at":"2026-05-18T00:44:25Z"},{"alias_kind":"pith_short_12","alias_value":"PSAYW57XVLLD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PSAYW57XVLLDAUZ2","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PSAYW57X","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:0a1059a336245ccd38216e28ab8fe4a416032082ddf83c54cc883672e88aee3a","target":"graph","created_at":"2026-05-18T00:44:25Z","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":"A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit algebras which are isomorphic to tensor algebras, we give a very concrete description for their defining C*-correspondence and we show that it forms a complete invariant for isometric isomorphisms between such algebras. A related class of operator algebras is also classified using a variant of the Aho-Hopcroft-Ullman algorithm from computer aided graph theory.","authors_text":"Chris Ramsey, Elias Katsoulis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-01-13T22:01:58Z","title":"Limit algebras and integer-valued cocycles, revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03423","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:d9b1a6545e215d1823078aaa3d26e30e2548d1d2aa4bc9c0a2139e4d51ca4c1b","target":"record","created_at":"2026-05-18T00:44:25Z","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":"8232c8dfc0902131b7567556e5bcfa04962169fab4e6874d9cc932ef36288fd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-01-13T22:01:58Z","title_canon_sha256":"0aaa122c89df835c75fc229a5751ef057f1453843e6690800a426de6f187d55b"},"schema_version":"1.0","source":{"id":"1601.03423","kind":"arxiv","version":1}},"canonical_sha256":"7c818b77f7aad630533a2d8cf7a203d9c7848a7b0cbeb4cfcf92cc0964290cd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c818b77f7aad630533a2d8cf7a203d9c7848a7b0cbeb4cfcf92cc0964290cd5","first_computed_at":"2026-05-18T00:44:25.015473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:25.015473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/pjzZ3nQfFnDrKaL2JsOYVWrytgrHNgHqDHhuOmdNP8B+jYSOks6Outk0mRsU5f3o56CZUItRevAPI8gs3JtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:25.016102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9b1a6545e215d1823078aaa3d26e30e2548d1d2aa4bc9c0a2139e4d51ca4c1b","sha256:0a1059a336245ccd38216e28ab8fe4a416032082ddf83c54cc883672e88aee3a"],"state_sha256":"d4668b4db79475cc1c097137496ee3bad2bc3066efc8c4fe89822400ed64cce4"}