{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MG4AAHTCLPPFGZYNBDYEBSF6K7","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":"f401474e260fb867ae15d4fd6c5fb4a20fe009d7de51492343ae0c52982945ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-01T15:04:11Z","title_canon_sha256":"1b6da52f43bfc4035d7cf3b79e99df0dec65f301a34316bbf7de083bb5531f2a"},"schema_version":"1.0","source":{"id":"1610.00144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00144","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00144v2","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00144","created_at":"2026-05-18T01:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"MG4AAHTCLPPF","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MG4AAHTCLPPFGZYN","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MG4AAHTC","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:a8a3e8018a88a27a3aee4b8526e1b785985a0aa97a07ebdd49587d873c101c51","target":"graph","created_at":"2026-05-18T01:02:51Z","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":"Let Q be a finite quiver without sources, and A be the corresponding algebra with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of projective A-modules. We call such a generator the projective Leavitt complex of Q. This terminology is justified by the following result: the opposite differential graded endomorphism algebra of the projective Leavitt complex of Q is quasi-isomorphic to the Leavitt path algebra of Q^{ op}. Here, Q^{op} is the opposite quiver of Q and the Leavitt path algebra of Q^{op} is naturally Z-graded and viewed","authors_text":"Huanhuan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-01T15:04:11Z","title":"The projective Leavitt complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00144","kind":"arxiv","version":2},"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":"sha256:345ea18cf6dabab679e2f22c3e080fc00c68a64825d8eae62321e664cce5d792","target":"record","created_at":"2026-05-18T01:02:51Z","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":"f401474e260fb867ae15d4fd6c5fb4a20fe009d7de51492343ae0c52982945ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-01T15:04:11Z","title_canon_sha256":"1b6da52f43bfc4035d7cf3b79e99df0dec65f301a34316bbf7de083bb5531f2a"},"schema_version":"1.0","source":{"id":"1610.00144","kind":"arxiv","version":2}},"canonical_sha256":"61b8001e625bde53670d08f040c8be57dba95ec1a39046c82c5154d801a0bf62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61b8001e625bde53670d08f040c8be57dba95ec1a39046c82c5154d801a0bf62","first_computed_at":"2026-05-18T01:02:51.651072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:51.651072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gy4HbmtTwUtzfJCO3Jfp8tksqsD9vfiaYr3PiYuudKWdrm9MQImlKHI5EW7V7KbYotIXTgnvDVDApTk5fxjyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:51.651704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:345ea18cf6dabab679e2f22c3e080fc00c68a64825d8eae62321e664cce5d792","sha256:a8a3e8018a88a27a3aee4b8526e1b785985a0aa97a07ebdd49587d873c101c51"],"state_sha256":"40e8411b4169972676b4893e39d77be1fc109cef64759480151636e1cab8a05f"}