{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O6IQKT6QBKQRUNKBUN2PBNWNZQ","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":"984b9e45057cf9bfad9b18b3f97c15a8058eec9517f6374a77c87fa19c6f7d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-01T08:37:12Z","title_canon_sha256":"a43492415094940034f7fd26431c1cdbbf1edd58efd253a7216b4dd9d7004d53"},"schema_version":"1.0","source":{"id":"1506.00387","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00387","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00387v3","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00387","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"O6IQKT6QBKQR","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O6IQKT6QBKQRUNKB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O6IQKT6Q","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:711eb1dd959dd0a571cbf579997f2981bb420c3504bbe312be3fae6643380703","target":"graph","created_at":"2026-05-18T01:33:58Z","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":"The aim of this article is to study the Ext ring associated to a Koszul $R$-ring and to use it to provide further characterisations of the former. As such, for $R$ being a semisimple ring and $A$ a graded Koszul $R$-ring, we will prove that there is an isomorphism of DG rings between $\\mathcal{E}(A):=\\mathrm{Ext}^\\bullet_A(R,R)$ and $^{\\ast-\\text{gr}}\\mathrm{T}(A) \\simeq \\mathrm{E}(^{\\ast-\\text{gr}\\!} A)$. Also, the Ext $R$-ring will prove to be isomorphic to the shriek ring of the left graded dual of $A$, namely $\\mathcal{E}(A) \\simeq (^{\\ast-\\text{gr}\\!} A)^!$. As an application, these isomo","authors_text":"Adrian Manea","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-01T08:37:12Z","title":"On the Ext Ring of Koszul Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00387","kind":"arxiv","version":3},"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":"sha256:139a5ec17741c006cb8b557d8f9d5110c25d0edc8fd4145f42aff5983cef70df","target":"record","created_at":"2026-05-18T01:33:58Z","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":"984b9e45057cf9bfad9b18b3f97c15a8058eec9517f6374a77c87fa19c6f7d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-01T08:37:12Z","title_canon_sha256":"a43492415094940034f7fd26431c1cdbbf1edd58efd253a7216b4dd9d7004d53"},"schema_version":"1.0","source":{"id":"1506.00387","kind":"arxiv","version":3}},"canonical_sha256":"7791054fd00aa11a3541a374f0b6cdcc1bad73430db3d8f8ef28c82f2822edfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7791054fd00aa11a3541a374f0b6cdcc1bad73430db3d8f8ef28c82f2822edfc","first_computed_at":"2026-05-18T01:33:58.296514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:58.296514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rcvcu+PrY1CkLtxx0bwfyQr/yX63pwr4qFGHhpv0mlvDyx0ENdNqW4ymfW+a9tI9FRS6Njrc/MDX7rHOApdRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:58.297046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00387","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:139a5ec17741c006cb8b557d8f9d5110c25d0edc8fd4145f42aff5983cef70df","sha256:711eb1dd959dd0a571cbf579997f2981bb420c3504bbe312be3fae6643380703"],"state_sha256":"bcdb1eefff8a666c9f27855f87ac4e3c97a46c135b010d3134fe900fd621db9c"}