{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TW33RZVKQ77YMIND6A35PFD47H","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":"54b5c5d99044a1777d249af1f3431257a844dad1e521d4d6af8e473a9caf1f82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-10T17:58:26Z","title_canon_sha256":"4ada9fbcc5bbded44f030be79e348bb81e55f2f2caf0119eae8856f927fd601f"},"schema_version":"1.0","source":{"id":"1902.03641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03641","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03641v1","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03641","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"TW33RZVKQ77Y","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TW33RZVKQ77YMIND","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TW33RZVK","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:c10b1630e9be471fc9b4578f40b69ae95cada1d24286775f91ae9a07325334d0","target":"graph","created_at":"2026-05-17T23:54:20Z","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":"We achieve an extremely useful description (up to isomorphism) of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a field $K$ as a direct sum of matrix rings over $K$, direct sum with a corner of the Leavitt path algebra $L_K(F)$ of a graph $F$ for which every regular vertex is the base of a loop. Moreover, in this case one may transform the graph $E$ into the graph $F$ via some step-by-step procedure, using the \"source elimination\" and \"collapsing\" processes. We use this to establish the main result of the article, that every nonzero corner of a Leavitt path algeb","authors_text":"Gene Abrams, T. G. Nam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-10T17:58:26Z","title":"Corners of Leavitt path algebras of finite graphs are Leavitt path algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03641","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":"sha256:9aa9b0c30a2eb5c480ec2a07e723bbf0dbcdc6e282b63033ca619e59a826474b","target":"record","created_at":"2026-05-17T23:54:20Z","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":"54b5c5d99044a1777d249af1f3431257a844dad1e521d4d6af8e473a9caf1f82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-10T17:58:26Z","title_canon_sha256":"4ada9fbcc5bbded44f030be79e348bb81e55f2f2caf0119eae8856f927fd601f"},"schema_version":"1.0","source":{"id":"1902.03641","kind":"arxiv","version":1}},"canonical_sha256":"9db7b8e6aa87ff8621a3f037d7947cf9e088a344cae5e8ac167ecc095963fb31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9db7b8e6aa87ff8621a3f037d7947cf9e088a344cae5e8ac167ecc095963fb31","first_computed_at":"2026-05-17T23:54:20.081913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:20.081913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1evob4+jiLSZn4cssTanMT21G1IWRcsisNASqLopUw0iQ7MsQATKJzfhsdnx29ZI5tH445V+USo5XI3XdnHvBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:20.082556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9aa9b0c30a2eb5c480ec2a07e723bbf0dbcdc6e282b63033ca619e59a826474b","sha256:c10b1630e9be471fc9b4578f40b69ae95cada1d24286775f91ae9a07325334d0"],"state_sha256":"b34fd7dcb1272c0be1805fbeff988fccbdc2c58538e1fd985178cf18a89996fd"}