{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:4HL7QNZE6EQNOWYM4DARBIADQA","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":"6f06a341af828b3fffc7021fe33bcd0ab87c9b24bdf5ba6b0f73e416d684b94a","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.RA","submitted_at":"2007-12-18T13:51:56Z","title_canon_sha256":"a36269bfac777cb3bce3491f9d6c0cf704f72b0ffd50948c107cd836df0c77b6"},"schema_version":"1.0","source":{"id":"0712.2962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.2962","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"0712.2962v1","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.2962","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"4HL7QNZE6EQN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"4HL7QNZE6EQNOWYM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"4HL7QNZE","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:5bf49cd2d29e9f78b59bbb8c9c82b3cd28e9951c8fc48a5940a6a1b50b58ba2b","target":"graph","created_at":"2026-05-18T04:38:14Z","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":"Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH^1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type \\tilde{\\mathbb{A}}.","authors_text":"Ibrahim Assem, Maria Julia Redondo","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2007-12-18T13:51:56Z","title":"The first Hochschild cohomology group of a schurian cluster-tilted algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2962","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":"sha256:83098a2a7293556927b95fc07578d25f0c95787f8aae97dd1c46c0fadf904c74","target":"record","created_at":"2026-05-18T04:38:14Z","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":"6f06a341af828b3fffc7021fe33bcd0ab87c9b24bdf5ba6b0f73e416d684b94a","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.RA","submitted_at":"2007-12-18T13:51:56Z","title_canon_sha256":"a36269bfac777cb3bce3491f9d6c0cf704f72b0ffd50948c107cd836df0c77b6"},"schema_version":"1.0","source":{"id":"0712.2962","kind":"arxiv","version":1}},"canonical_sha256":"e1d7f83724f120d75b0ce0c110a0038000133e331aaa38c7e24255043b9271dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1d7f83724f120d75b0ce0c110a0038000133e331aaa38c7e24255043b9271dc","first_computed_at":"2026-05-18T04:38:14.550235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:14.550235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tOSEEMmkI1dJPSkYzMKJtFojVqIGnV44L58WUJJPjjHe8whFSW7LQtCB/2faVVt6cEQomQj9en1xShkLQuIrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:14.550807Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.2962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83098a2a7293556927b95fc07578d25f0c95787f8aae97dd1c46c0fadf904c74","sha256:5bf49cd2d29e9f78b59bbb8c9c82b3cd28e9951c8fc48a5940a6a1b50b58ba2b"],"state_sha256":"025e66e40f44ae31733eff928f36987efdb62030b65ac12532306beccaa57223"}