{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:P2RGQXQ4T4FJ7U3Q73Y4XM5UMB","short_pith_number":"pith:P2RGQXQ4","schema_version":"1.0","canonical_sha256":"7ea2685e1c9f0a9fd370fef1cbb3b46042d072d386de94db3dea92fcba9ca91b","source":{"kind":"arxiv","id":"1109.3761","version":1},"attestation_state":"computed","paper":{"title":"Piecewise-Koszul algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Diming Lu, Jiafeng Lu, Jiwei He","submitted_at":"2011-09-17T09:19:34Z","abstract_excerpt":"It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are, in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra $A$ to be piecewise-Koszul in terms of its Yoneda-Ext algebra $E(A)$, and show an $A_{\\infty}$-structure on $E(A)$. Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos' [6]."},"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":"1109.3761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-17T09:19:34Z","cross_cats_sorted":[],"title_canon_sha256":"1312e4e6683fe454820973d447aea8e3ee5aa941223aa18711f3d6b0270f7b6f","abstract_canon_sha256":"7e4cd874468e8a24170edc9db757fdecd6f9ed1567c05cdd6c162ede7fbca002"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:45.951196Z","signature_b64":"PKIqbbLu+SCdmpIGccQPUfGg9YQ3bKLUCU1qIhO9Jvl7QaKhog/ognNLtcppOz6qXPt5GI0IKPAhhZEzSU36CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ea2685e1c9f0a9fd370fef1cbb3b46042d072d386de94db3dea92fcba9ca91b","last_reissued_at":"2026-05-18T04:12:45.950615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:45.950615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Piecewise-Koszul algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Diming Lu, Jiafeng Lu, Jiwei He","submitted_at":"2011-09-17T09:19:34Z","abstract_excerpt":"It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are, in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra $A$ to be piecewise-Koszul in terms of its Yoneda-Ext algebra $E(A)$, and show an $A_{\\infty}$-structure on $E(A)$. Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos' [6]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3761","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":"1109.3761","created_at":"2026-05-18T04:12:45.950715+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.3761v1","created_at":"2026-05-18T04:12:45.950715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3761","created_at":"2026-05-18T04:12:45.950715+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2RGQXQ4T4FJ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2RGQXQ4T4FJ7U3Q","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2RGQXQ4","created_at":"2026-05-18T12:26:39.201973+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/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB","json":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB.json","graph_json":"https://pith.science/api/pith-number/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/graph.json","events_json":"https://pith.science/api/pith-number/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/events.json","paper":"https://pith.science/paper/P2RGQXQ4"},"agent_actions":{"view_html":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB","download_json":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB.json","view_paper":"https://pith.science/paper/P2RGQXQ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.3761&json=true","fetch_graph":"https://pith.science/api/pith-number/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/graph.json","fetch_events":"https://pith.science/api/pith-number/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/action/storage_attestation","attest_author":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/action/author_attestation","sign_citation":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/action/citation_signature","submit_replication":"https://pith.science/pith/P2RGQXQ4T4FJ7U3Q73Y4XM5UMB/action/replication_record"}},"created_at":"2026-05-18T04:12:45.950715+00:00","updated_at":"2026-05-18T04:12:45.950715+00:00"}