{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:P2RGQXQ4T4FJ7U3Q73Y4XM5UMB","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":"7e4cd874468e8a24170edc9db757fdecd6f9ed1567c05cdd6c162ede7fbca002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-17T09:19:34Z","title_canon_sha256":"1312e4e6683fe454820973d447aea8e3ee5aa941223aa18711f3d6b0270f7b6f"},"schema_version":"1.0","source":{"id":"1109.3761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3761","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3761v1","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3761","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"pith_short_12","alias_value":"P2RGQXQ4T4FJ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P2RGQXQ4T4FJ7U3Q","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P2RGQXQ4","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:a0f124671612865cd25f9bf5f71668be2c590471ef2bc2d969d05e947faa5c2f","target":"graph","created_at":"2026-05-18T04:12:45Z","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":"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].","authors_text":"Diming Lu, Jiafeng Lu, Jiwei He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-17T09:19:34Z","title":"Piecewise-Koszul algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3761","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":"sha256:5a0e3a46cea34a7725eba669d45f4b3a0fd7ec0693e83a7ec09236dc181fe1b5","target":"record","created_at":"2026-05-18T04:12:45Z","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":"7e4cd874468e8a24170edc9db757fdecd6f9ed1567c05cdd6c162ede7fbca002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-17T09:19:34Z","title_canon_sha256":"1312e4e6683fe454820973d447aea8e3ee5aa941223aa18711f3d6b0270f7b6f"},"schema_version":"1.0","source":{"id":"1109.3761","kind":"arxiv","version":1}},"canonical_sha256":"7ea2685e1c9f0a9fd370fef1cbb3b46042d072d386de94db3dea92fcba9ca91b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ea2685e1c9f0a9fd370fef1cbb3b46042d072d386de94db3dea92fcba9ca91b","first_computed_at":"2026-05-18T04:12:45.950615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:45.950615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PKIqbbLu+SCdmpIGccQPUfGg9YQ3bKLUCU1qIhO9Jvl7QaKhog/ognNLtcppOz6qXPt5GI0IKPAhhZEzSU36CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:45.951196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a0e3a46cea34a7725eba669d45f4b3a0fd7ec0693e83a7ec09236dc181fe1b5","sha256:a0f124671612865cd25f9bf5f71668be2c590471ef2bc2d969d05e947faa5c2f"],"state_sha256":"848127907d86aff45cde51344cd16ef1800fcc07c792c36f623abd25d8a3c896"}