{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:4HL7QNZE6EQNOWYM4DARBIADQA","short_pith_number":"pith:4HL7QNZE","schema_version":"1.0","canonical_sha256":"e1d7f83724f120d75b0ce0c110a0038000133e331aaa38c7e24255043b9271dc","source":{"kind":"arxiv","id":"0712.2962","version":1},"attestation_state":"computed","paper":{"title":"The first Hochschild cohomology group of a schurian cluster-tilted algebra","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Ibrahim Assem, Maria Julia Redondo","submitted_at":"2007-12-18T13:51:56Z","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}}."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0712.2962","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2007-12-18T13:51:56Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a36269bfac777cb3bce3491f9d6c0cf704f72b0ffd50948c107cd836df0c77b6","abstract_canon_sha256":"6f06a341af828b3fffc7021fe33bcd0ab87c9b24bdf5ba6b0f73e416d684b94a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:14.550807Z","signature_b64":"tOSEEMmkI1dJPSkYzMKJtFojVqIGnV44L58WUJJPjjHe8whFSW7LQtCB/2faVVt6cEQomQj9en1xShkLQuIrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1d7f83724f120d75b0ce0c110a0038000133e331aaa38c7e24255043b9271dc","last_reissued_at":"2026-05-18T04:38:14.550235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:14.550235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The first Hochschild cohomology group of a schurian cluster-tilted algebra","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Ibrahim Assem, Maria Julia Redondo","submitted_at":"2007-12-18T13:51:56Z","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}}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2962","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0712.2962","created_at":"2026-05-18T04:38:14.550339+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.2962v1","created_at":"2026-05-18T04:38:14.550339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.2962","created_at":"2026-05-18T04:38:14.550339+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HL7QNZE6EQN","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HL7QNZE6EQNOWYM","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HL7QNZE","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA","json":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA.json","graph_json":"https://pith.science/api/pith-number/4HL7QNZE6EQNOWYM4DARBIADQA/graph.json","events_json":"https://pith.science/api/pith-number/4HL7QNZE6EQNOWYM4DARBIADQA/events.json","paper":"https://pith.science/paper/4HL7QNZE"},"agent_actions":{"view_html":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA","download_json":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA.json","view_paper":"https://pith.science/paper/4HL7QNZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.2962&json=true","fetch_graph":"https://pith.science/api/pith-number/4HL7QNZE6EQNOWYM4DARBIADQA/graph.json","fetch_events":"https://pith.science/api/pith-number/4HL7QNZE6EQNOWYM4DARBIADQA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA/action/storage_attestation","attest_author":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA/action/author_attestation","sign_citation":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA/action/citation_signature","submit_replication":"https://pith.science/pith/4HL7QNZE6EQNOWYM4DARBIADQA/action/replication_record"}},"created_at":"2026-05-18T04:38:14.550339+00:00","updated_at":"2026-05-18T04:38:14.550339+00:00"}