{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ML2447V34DAGQQIYRGRRCCDPDV","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":"8b1b0f2f12b7b45ad4e77bc6340f79a06bd14faf43b09cbf1019a6e958db46fc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-10-11T05:27:18Z","title_canon_sha256":"309f36fac903bf8e5eff92438694630e4a43336aad8193fd0dfa784c7394d012"},"schema_version":"1.0","source":{"id":"1210.3127","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3127","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3127v4","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3127","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"ML2447V34DAG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"ML2447V34DAGQQIY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"ML2447V3","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:98685d34dbc44a59b28bb8e03aa4c31ca9059ebcc10ede4b00d4ae1c2709e85a","target":"graph","created_at":"2026-05-18T02:52:48Z","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":"Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs.","authors_text":"E. Pardo, P. Ara","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-10-11T05:27:18Z","title":"Towards a K-theoretic characterization of graded isomorphisms between Leavitt path algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3127","kind":"arxiv","version":4},"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":"sha256:80b9d5fed7634090350742247c1c980ed7df1896918d2e8e3ca66d9544fed8dc","target":"record","created_at":"2026-05-18T02:52:48Z","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":"8b1b0f2f12b7b45ad4e77bc6340f79a06bd14faf43b09cbf1019a6e958db46fc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-10-11T05:27:18Z","title_canon_sha256":"309f36fac903bf8e5eff92438694630e4a43336aad8193fd0dfa784c7394d012"},"schema_version":"1.0","source":{"id":"1210.3127","kind":"arxiv","version":4}},"canonical_sha256":"62f5ce7ebbe0c068411889a311086f1d7299d6ec210e1ee90876fb84a98dc8c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62f5ce7ebbe0c068411889a311086f1d7299d6ec210e1ee90876fb84a98dc8c6","first_computed_at":"2026-05-18T02:52:48.616367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:48.616367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QUxFuu49mxt+9aHdh5zCFcqjwAOtgyYqWYx7L4M+Bc/FLcdNerlqJ7RD0OBzsRsOKcHhhvJZVniJgSxEt5c8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:48.616828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3127","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80b9d5fed7634090350742247c1c980ed7df1896918d2e8e3ca66d9544fed8dc","sha256:98685d34dbc44a59b28bb8e03aa4c31ca9059ebcc10ede4b00d4ae1c2709e85a"],"state_sha256":"8757fc33193e56d375d4d6bbf86ca37843461f5e338c21e2c1d71fa339d3241c"}