{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:O6IQKT6QBKQRUNKBUN2PBNWNZQ","short_pith_number":"pith:O6IQKT6Q","schema_version":"1.0","canonical_sha256":"7791054fd00aa11a3541a374f0b6cdcc1bad73430db3d8f8ef28c82f2822edfc","source":{"kind":"arxiv","id":"1506.00387","version":3},"attestation_state":"computed","paper":{"title":"On the Ext Ring of Koszul Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Adrian Manea","submitted_at":"2015-06-01T08:37:12Z","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"},"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":"1506.00387","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-01T08:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"a43492415094940034f7fd26431c1cdbbf1edd58efd253a7216b4dd9d7004d53","abstract_canon_sha256":"984b9e45057cf9bfad9b18b3f97c15a8058eec9517f6374a77c87fa19c6f7d12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:58.297046Z","signature_b64":"rcvcu+PrY1CkLtxx0bwfyQr/yX63pwr4qFGHhpv0mlvDyx0ENdNqW4ymfW+a9tI9FRS6Njrc/MDX7rHOApdRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7791054fd00aa11a3541a374f0b6cdcc1bad73430db3d8f8ef28c82f2822edfc","last_reissued_at":"2026-05-18T01:33:58.296514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:58.296514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Ext Ring of Koszul Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Adrian Manea","submitted_at":"2015-06-01T08:37:12Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00387","kind":"arxiv","version":3},"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":"1506.00387","created_at":"2026-05-18T01:33:58.296582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00387v3","created_at":"2026-05-18T01:33:58.296582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00387","created_at":"2026-05-18T01:33:58.296582+00:00"},{"alias_kind":"pith_short_12","alias_value":"O6IQKT6QBKQR","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"O6IQKT6QBKQRUNKB","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"O6IQKT6Q","created_at":"2026-05-18T12:29:34.919912+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/O6IQKT6QBKQRUNKBUN2PBNWNZQ","json":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ.json","graph_json":"https://pith.science/api/pith-number/O6IQKT6QBKQRUNKBUN2PBNWNZQ/graph.json","events_json":"https://pith.science/api/pith-number/O6IQKT6QBKQRUNKBUN2PBNWNZQ/events.json","paper":"https://pith.science/paper/O6IQKT6Q"},"agent_actions":{"view_html":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ","download_json":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ.json","view_paper":"https://pith.science/paper/O6IQKT6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00387&json=true","fetch_graph":"https://pith.science/api/pith-number/O6IQKT6QBKQRUNKBUN2PBNWNZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/O6IQKT6QBKQRUNKBUN2PBNWNZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ/action/storage_attestation","attest_author":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ/action/author_attestation","sign_citation":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ/action/citation_signature","submit_replication":"https://pith.science/pith/O6IQKT6QBKQRUNKBUN2PBNWNZQ/action/replication_record"}},"created_at":"2026-05-18T01:33:58.296582+00:00","updated_at":"2026-05-18T01:33:58.296582+00:00"}