{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KKPSDW2IUEWQGZTOIKC4P54LNA","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":"7b9c83c5b59af323b63a98dc5f8c2a1123b9ae2164d3515ed312e62b814ba26c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-11-12T03:47:46Z","title_canon_sha256":"783fae665700f7ef042452b8bb55c3b03a20ae86e2c7ccbdf76efdb9b524568e"},"schema_version":"1.0","source":{"id":"1811.04542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04542","created_at":"2026-05-18T00:01:04Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04542v1","created_at":"2026-05-18T00:01:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04542","created_at":"2026-05-18T00:01:04Z"},{"alias_kind":"pith_short_12","alias_value":"KKPSDW2IUEWQ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KKPSDW2IUEWQGZTO","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KKPSDW2I","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:b6c6ceeaa7b010818f9736d5f2a4b7c9b87f22980fc7f08afff57b2fc5d0c7d8","target":"graph","created_at":"2026-05-18T00:01:04Z","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":"For a certain finite graph E, we consider the corresponding finite dimensional algebra A with radical square zero. An explicit compact generator for the homotopy category of acyclic complexes of injective (resp. projective) modules over A, called the injective (resp. projective) Leavitt complex of E, was constructed in [18] (resp. [19]). We overview the connection between the injective (resp. projective) Leavitt complex and the Leavitt path algebra of E. A differential graded bimodule structure, which is right quasi-balanced, is endowed to the injective (resp. projective) Leavitt complex in [1","authors_text":"Huanhuan Li","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-11-12T03:47:46Z","title":"The injective and projective Leavitt complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04542","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":"sha256:2bdf24edd490a368e27339cfdfcbdc5cf13b9f356fc14db3a72c1f0f4da253ef","target":"record","created_at":"2026-05-18T00:01:04Z","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":"7b9c83c5b59af323b63a98dc5f8c2a1123b9ae2164d3515ed312e62b814ba26c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-11-12T03:47:46Z","title_canon_sha256":"783fae665700f7ef042452b8bb55c3b03a20ae86e2c7ccbdf76efdb9b524568e"},"schema_version":"1.0","source":{"id":"1811.04542","kind":"arxiv","version":1}},"canonical_sha256":"529f21db48a12d03666e4285c7f78b6828eb6ec608e288cda0a74c55134060b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"529f21db48a12d03666e4285c7f78b6828eb6ec608e288cda0a74c55134060b5","first_computed_at":"2026-05-18T00:01:04.847890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:04.847890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2WZ6e2LLemb87FAe94hIraHHak62dwMrzVs3ouuvbDqs800S3YYrimk4tXmCbju1I7OZmKCUNJ0AW6rfQNRKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:04.848540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bdf24edd490a368e27339cfdfcbdc5cf13b9f356fc14db3a72c1f0f4da253ef","sha256:b6c6ceeaa7b010818f9736d5f2a4b7c9b87f22980fc7f08afff57b2fc5d0c7d8"],"state_sha256":"fcbf813e49a7b721e0314e738a6481c86da3417ce971c85678140cc678748dbc"}