{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TO26DFAY2D5Z4JB7NGYQIOMHUI","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":"45abb719a0d6db3c8cad917643b752aa7e17be6865806f648a6aae69b1f949df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-05T10:26:53Z","title_canon_sha256":"ab497753061fd3e218141073e6357fb163c75a602ca61a4bd044aadad48a4d1f"},"schema_version":"1.0","source":{"id":"1506.01854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01854","created_at":"2026-05-18T01:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01854v2","created_at":"2026-05-18T01:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01854","created_at":"2026-05-18T01:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"TO26DFAY2D5Z","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TO26DFAY2D5Z4JB7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TO26DFAY","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:f57a3f71be141bffbe3d425397391cf520e7eebc4a1e5683ea06a699c4ba20fc","target":"graph","created_at":"2026-05-18T01:28:38Z","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 generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in degrees 0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra by quiver and relations, and show that the ideal of relations has a quadratic Gr\\\"obner basis; this enables us to give a regrading of the Ext algebra under which the regraded Ext algebra is a Koszul algebra.","authors_text":"Joanne Leader, Nicole Snashall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-05T10:26:53Z","title":"The Ext algebra and a new generalisation of D-Koszul algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01854","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":"sha256:09a90f58db1ff7597f6336258bf30a5d9e10236568a39a1111139908a298858c","target":"record","created_at":"2026-05-18T01:28:38Z","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":"45abb719a0d6db3c8cad917643b752aa7e17be6865806f648a6aae69b1f949df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-05T10:26:53Z","title_canon_sha256":"ab497753061fd3e218141073e6357fb163c75a602ca61a4bd044aadad48a4d1f"},"schema_version":"1.0","source":{"id":"1506.01854","kind":"arxiv","version":2}},"canonical_sha256":"9bb5e19418d0fb9e243f69b1043987a21b20e93fcfa885f0bcd07f8c0bb6c9c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bb5e19418d0fb9e243f69b1043987a21b20e93fcfa885f0bcd07f8c0bb6c9c9","first_computed_at":"2026-05-18T01:28:38.340226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:38.340226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qTJgCv18oweavH0mHE1+4fbbdbaPCb01Ovo6Ai6Y6eHY9iqIdBySeeQ1tzGBdcsIsJdt/+iGgVUmTHLMOifVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:38.340957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09a90f58db1ff7597f6336258bf30a5d9e10236568a39a1111139908a298858c","sha256:f57a3f71be141bffbe3d425397391cf520e7eebc4a1e5683ea06a699c4ba20fc"],"state_sha256":"b885df62db6da0f9d0b22037b3f972c2a30f60c1ec7966491403b3ce2d854e6b"}