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Let $(R,\\mathfrak m)$ be a compressed local Artinian ring with odd top socle degree $s$, at least five, and $\\operatorname{socle}(R)\\cap \\mathfrak m^{s-1}=\\mathfrak m^s$. We prove that the Poincar\\'e series of all finitely generated modules over $R$ are rational, sharing a common denominator, and that there is a Golod homomorphism from a complete intersection onto $R$."},"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":"1607.05594","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-07-19T14:19:09Z","cross_cats_sorted":[],"title_canon_sha256":"487113448987bfb020c5639a1fd0e6c3adc34ae9af79d7ca579ce892d7195c90","abstract_canon_sha256":"02bb4af4ace0d7c405c261ec61fe48cb46c5859862470eb8121d491149ddaf87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:12.942002Z","signature_b64":"6obEq4Ok6V2w0e0BX/jMxZEUAqi6862YoTMs4cCZx7/SEG3iJQVuhNMJr3JWA68xLse6uDj4TrZhULesuSoqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22c6e60062c2a15190d7f02864d523d84ef42718011de8be974298a9a2fa5df4","last_reissued_at":"2026-05-18T00:41:12.941248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:12.941248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poincar\\'e series of compressed local Artinian rings with odd top socle degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adela Vraciu, Andrew R. 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We prove that the Poincar\\'e series of all finitely generated modules over $R$ are rational, sharing a common denominator, and that there is a Golod homomorphism from a complete intersection onto $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05594","kind":"arxiv","version":2},"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":"1607.05594","created_at":"2026-05-18T00:41:12.941403+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05594v2","created_at":"2026-05-18T00:41:12.941403+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05594","created_at":"2026-05-18T00:41:12.941403+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELDOMADCYKQV","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELDOMADCYKQVDEGX","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELDOMADC","created_at":"2026-05-18T12:30:12.583610+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/ELDOMADCYKQVDEGX6AUGJVJD3B","json":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B.json","graph_json":"https://pith.science/api/pith-number/ELDOMADCYKQVDEGX6AUGJVJD3B/graph.json","events_json":"https://pith.science/api/pith-number/ELDOMADCYKQVDEGX6AUGJVJD3B/events.json","paper":"https://pith.science/paper/ELDOMADC"},"agent_actions":{"view_html":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B","download_json":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B.json","view_paper":"https://pith.science/paper/ELDOMADC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05594&json=true","fetch_graph":"https://pith.science/api/pith-number/ELDOMADCYKQVDEGX6AUGJVJD3B/graph.json","fetch_events":"https://pith.science/api/pith-number/ELDOMADCYKQVDEGX6AUGJVJD3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/action/storage_attestation","attest_author":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/action/author_attestation","sign_citation":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/action/citation_signature","submit_replication":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/action/replication_record"}},"created_at":"2026-05-18T00:41:12.941403+00:00","updated_at":"2026-05-18T00:41:12.941403+00:00"}