{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EKUZYGIYAIONMXMTAAEYLVS6D2","short_pith_number":"pith:EKUZYGIY","schema_version":"1.0","canonical_sha256":"22a99c1918021cd65d93000985d65e1eba7fe8ea4693388b6d811b047c6938e0","source":{"kind":"arxiv","id":"1412.4918","version":1},"attestation_state":"computed","paper":{"title":"Path algebras and monomial algebras of finite GK-dimension as noncommutative homogeneous coordinate rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Cody Holdaway","submitted_at":"2014-12-16T08:38:35Z","abstract_excerpt":"This article sets out to understand the categories $\\QGr A$ where $A$ is either a monomial algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: 1) What is the structure of the point modules up to isomorphism in $\\QGr A$? 2) When is $\\QGr A \\equiv \\QGr A'$? These two questions turn out to be intimately related.\n  It is shown that up to isomorphism in $\\QGr A$, there are only finitely many point modules and these give all the simple objects in the category. Then, a finite quiver $E_A$, which can be constructed from the algebra $A$ rather simply, is associa"},"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":"1412.4918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-16T08:38:35Z","cross_cats_sorted":[],"title_canon_sha256":"85df514140d4da17e94ba1407778ee646a202bc083820cb98556e20fc49fe4a5","abstract_canon_sha256":"4f348a3dfd79647003934013c153d625a75febf514542474a3818972ecad3ed2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:10.131498Z","signature_b64":"wUOoUOivO3RrlYmMku+2vPUbqriuLEKANCZ38il96r+grrVyB2FoHugC0KCKBQblrNhhwNYVifIaBnDEGqXwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22a99c1918021cd65d93000985d65e1eba7fe8ea4693388b6d811b047c6938e0","last_reissued_at":"2026-05-18T02:31:10.131010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:10.131010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Path algebras and monomial algebras of finite GK-dimension as noncommutative homogeneous coordinate rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Cody Holdaway","submitted_at":"2014-12-16T08:38:35Z","abstract_excerpt":"This article sets out to understand the categories $\\QGr A$ where $A$ is either a monomial algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: 1) What is the structure of the point modules up to isomorphism in $\\QGr A$? 2) When is $\\QGr A \\equiv \\QGr A'$? These two questions turn out to be intimately related.\n  It is shown that up to isomorphism in $\\QGr A$, there are only finitely many point modules and these give all the simple objects in the category. Then, a finite quiver $E_A$, which can be constructed from the algebra $A$ rather simply, is associa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4918","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":"1412.4918","created_at":"2026-05-18T02:31:10.131082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.4918v1","created_at":"2026-05-18T02:31:10.131082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4918","created_at":"2026-05-18T02:31:10.131082+00:00"},{"alias_kind":"pith_short_12","alias_value":"EKUZYGIYAION","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"EKUZYGIYAIONMXMT","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"EKUZYGIY","created_at":"2026-05-18T12:28:28.263976+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.13373","citing_title":"Growth in noncommutative algebras and entropy in derived categories","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2","json":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2.json","graph_json":"https://pith.science/api/pith-number/EKUZYGIYAIONMXMTAAEYLVS6D2/graph.json","events_json":"https://pith.science/api/pith-number/EKUZYGIYAIONMXMTAAEYLVS6D2/events.json","paper":"https://pith.science/paper/EKUZYGIY"},"agent_actions":{"view_html":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2","download_json":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2.json","view_paper":"https://pith.science/paper/EKUZYGIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.4918&json=true","fetch_graph":"https://pith.science/api/pith-number/EKUZYGIYAIONMXMTAAEYLVS6D2/graph.json","fetch_events":"https://pith.science/api/pith-number/EKUZYGIYAIONMXMTAAEYLVS6D2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2/action/storage_attestation","attest_author":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2/action/author_attestation","sign_citation":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2/action/citation_signature","submit_replication":"https://pith.science/pith/EKUZYGIYAIONMXMTAAEYLVS6D2/action/replication_record"}},"created_at":"2026-05-18T02:31:10.131082+00:00","updated_at":"2026-05-18T02:31:10.131082+00:00"}