{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BXOMCZKDZW6G7ZOXOM65ILIIMO","short_pith_number":"pith:BXOMCZKD","schema_version":"1.0","canonical_sha256":"0ddcc16543cdbc6fe5d7733dd42d086399d108d273654cddd9774fade3a7b6a6","source":{"kind":"arxiv","id":"1606.00938","version":1},"attestation_state":"computed","paper":{"title":"Cluster-tilted and quasi-tilted algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Ibrahim Assem, Khrystyna Serhiyenko, Ralf Schiffler","submitted_at":"2016-06-03T00:48:08Z","abstract_excerpt":"In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so that any two local slices can be reached one from the other by a sequence of reflections and coreflections. We then give an algorithmic procedure for constructing the tubes of a cluster-tilted algebra of euclidean type. Our main result characterizes quasi-tilted algebras whose relation-extensions are cluster-tilted of euclidean type."},"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":"1606.00938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-06-03T00:48:08Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"328d9076fcd764d2b33444336b30ac3246d144bdc7d5494ef8b69a5259b2f31f","abstract_canon_sha256":"69d4ea8a2626ea6c78373904a39b4eaa08a4b869abacc042781132133811978f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:00.046342Z","signature_b64":"Sk92s3F76Z6oP+wqXR3SGYSJh/z/F7zY3uzkV7y6jrs9QyZkrdmtbXF01aJtFtpKUMZTyPdI0cdOKBDNWEkSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ddcc16543cdbc6fe5d7733dd42d086399d108d273654cddd9774fade3a7b6a6","last_reissued_at":"2026-05-18T01:13:00.045892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:00.045892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster-tilted and quasi-tilted algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Ibrahim Assem, Khrystyna Serhiyenko, Ralf Schiffler","submitted_at":"2016-06-03T00:48:08Z","abstract_excerpt":"In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so that any two local slices can be reached one from the other by a sequence of reflections and coreflections. We then give an algorithmic procedure for constructing the tubes of a cluster-tilted algebra of euclidean type. Our main result characterizes quasi-tilted algebras whose relation-extensions are cluster-tilted of euclidean type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00938","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":"1606.00938","created_at":"2026-05-18T01:13:00.045974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00938v1","created_at":"2026-05-18T01:13:00.045974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00938","created_at":"2026-05-18T01:13:00.045974+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXOMCZKDZW6G","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXOMCZKDZW6G7ZOX","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXOMCZKD","created_at":"2026-05-18T12:30:09.641336+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/BXOMCZKDZW6G7ZOXOM65ILIIMO","json":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO.json","graph_json":"https://pith.science/api/pith-number/BXOMCZKDZW6G7ZOXOM65ILIIMO/graph.json","events_json":"https://pith.science/api/pith-number/BXOMCZKDZW6G7ZOXOM65ILIIMO/events.json","paper":"https://pith.science/paper/BXOMCZKD"},"agent_actions":{"view_html":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO","download_json":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO.json","view_paper":"https://pith.science/paper/BXOMCZKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00938&json=true","fetch_graph":"https://pith.science/api/pith-number/BXOMCZKDZW6G7ZOXOM65ILIIMO/graph.json","fetch_events":"https://pith.science/api/pith-number/BXOMCZKDZW6G7ZOXOM65ILIIMO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO/action/storage_attestation","attest_author":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO/action/author_attestation","sign_citation":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO/action/citation_signature","submit_replication":"https://pith.science/pith/BXOMCZKDZW6G7ZOXOM65ILIIMO/action/replication_record"}},"created_at":"2026-05-18T01:13:00.045974+00:00","updated_at":"2026-05-18T01:13:00.045974+00:00"}