{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:M75RLZCJK7X44J7LHHS6Z7A5SN","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":"e1c9107630fbdc5c2e216ab055085ffcd86a3c87048fdf0e37a649c3d7a19a80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-30T16:58:01Z","title_canon_sha256":"84390d232d713fcf72993f4bfd00c2482a407b93d6e8e40fc1d7844cbc45b8f5"},"schema_version":"1.0","source":{"id":"1309.7917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7917","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7917v2","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7917","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"pith_short_12","alias_value":"M75RLZCJK7X4","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M75RLZCJK7X44J7L","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M75RLZCJ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:c9011321153feb8749f52c7a614f27bb2509ae6d854ae8b862ea029fd1095b8e","target":"graph","created_at":"2026-05-18T02:49:03Z","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":"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","authors_text":"Kulumani M. Rangaswamy, Pere Ara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-30T16:58:01Z","title":"Leavitt path algebras with at most countably many irreducible representatios"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7917","kind":"arxiv","version":2},"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":"sha256:62920540d30d462d5893f4a0488bc46cfa5394a98a69f72fd1fd79af9064b7d8","target":"record","created_at":"2026-05-18T02:49:03Z","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":"e1c9107630fbdc5c2e216ab055085ffcd86a3c87048fdf0e37a649c3d7a19a80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-30T16:58:01Z","title_canon_sha256":"84390d232d713fcf72993f4bfd00c2482a407b93d6e8e40fc1d7844cbc45b8f5"},"schema_version":"1.0","source":{"id":"1309.7917","kind":"arxiv","version":2}},"canonical_sha256":"67fb15e44957efce27eb39e5ecfc1d9361340c16042c504aaf8bd1daa8a43cc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67fb15e44957efce27eb39e5ecfc1d9361340c16042c504aaf8bd1daa8a43cc6","first_computed_at":"2026-05-18T02:49:03.282949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:03.282949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZH082MCcV/6ts6rueOGd+GrM7aDTeK3mJTlFEKriFJlkQZGT5NDAg5vh0p/wkrHF+/qec1vwAd8wzNwfI2+XAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:03.283629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62920540d30d462d5893f4a0488bc46cfa5394a98a69f72fd1fd79af9064b7d8","sha256:c9011321153feb8749f52c7a614f27bb2509ae6d854ae8b862ea029fd1095b8e"],"state_sha256":"f81bad3972c32fe66a68b8942b460669f1f3df7fa792ecd6a10a5be5e3dfe23d"}