{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:M75RLZCJK7X44J7LHHS6Z7A5SN","short_pith_number":"pith:M75RLZCJ","schema_version":"1.0","canonical_sha256":"67fb15e44957efce27eb39e5ecfc1d9361340c16042c504aaf8bd1daa8a43cc6","source":{"kind":"arxiv","id":"1309.7917","version":2},"attestation_state":"computed","paper":{"title":"Leavitt path algebras with at most countably many irreducible representatios","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kulumani M. Rangaswamy, Pere Ara","submitted_at":"2013-09-30T16:58:01Z","abstract_excerpt":"Let E be an arbitrary directed graph with no restrictions on the number of vertices and edges and let K be any field. We give necessary and sufficient conditions for the Leavitt path algebra L_K(E) to be of countable irreducible representation type, that is, we determine when L_K(E)has at most countably many distinct isomorphism classes of simple left L_K(E-modules. It is also shown that L_K(E) has dinitely many isomorphism classes of simple left modules if and only if L_K(E) is a semi-artinian von Neumann regular ring with at most finitely many ideals. Equivalent conditions on the graph E are"},"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":"1309.7917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-30T16:58:01Z","cross_cats_sorted":[],"title_canon_sha256":"84390d232d713fcf72993f4bfd00c2482a407b93d6e8e40fc1d7844cbc45b8f5","abstract_canon_sha256":"e1c9107630fbdc5c2e216ab055085ffcd86a3c87048fdf0e37a649c3d7a19a80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:03.283629Z","signature_b64":"ZH082MCcV/6ts6rueOGd+GrM7aDTeK3mJTlFEKriFJlkQZGT5NDAg5vh0p/wkrHF+/qec1vwAd8wzNwfI2+XAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67fb15e44957efce27eb39e5ecfc1d9361340c16042c504aaf8bd1daa8a43cc6","last_reissued_at":"2026-05-18T02:49:03.282949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:03.282949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Leavitt path algebras with at most countably many irreducible representatios","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kulumani M. Rangaswamy, Pere Ara","submitted_at":"2013-09-30T16:58:01Z","abstract_excerpt":"Let E be an arbitrary directed graph with no restrictions on the number of vertices and edges and let K be any field. We give necessary and sufficient conditions for the Leavitt path algebra L_K(E) to be of countable irreducible representation type, that is, we determine when L_K(E)has at most countably many distinct isomorphism classes of simple left L_K(E-modules. It is also shown that L_K(E) has dinitely many isomorphism classes of simple left modules if and only if L_K(E) is a semi-artinian von Neumann regular ring with at most finitely many ideals. Equivalent conditions on the graph E are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7917","kind":"arxiv","version":2},"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":"1309.7917","created_at":"2026-05-18T02:49:03.283059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7917v2","created_at":"2026-05-18T02:49:03.283059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7917","created_at":"2026-05-18T02:49:03.283059+00:00"},{"alias_kind":"pith_short_12","alias_value":"M75RLZCJK7X4","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"M75RLZCJK7X44J7L","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"M75RLZCJ","created_at":"2026-05-18T12:27:51.066281+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/M75RLZCJK7X44J7LHHS6Z7A5SN","json":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN.json","graph_json":"https://pith.science/api/pith-number/M75RLZCJK7X44J7LHHS6Z7A5SN/graph.json","events_json":"https://pith.science/api/pith-number/M75RLZCJK7X44J7LHHS6Z7A5SN/events.json","paper":"https://pith.science/paper/M75RLZCJ"},"agent_actions":{"view_html":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN","download_json":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN.json","view_paper":"https://pith.science/paper/M75RLZCJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7917&json=true","fetch_graph":"https://pith.science/api/pith-number/M75RLZCJK7X44J7LHHS6Z7A5SN/graph.json","fetch_events":"https://pith.science/api/pith-number/M75RLZCJK7X44J7LHHS6Z7A5SN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN/action/storage_attestation","attest_author":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN/action/author_attestation","sign_citation":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN/action/citation_signature","submit_replication":"https://pith.science/pith/M75RLZCJK7X44J7LHHS6Z7A5SN/action/replication_record"}},"created_at":"2026-05-18T02:49:03.283059+00:00","updated_at":"2026-05-18T02:49:03.283059+00:00"}