{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ELDOMADCYKQVDEGX6AUGJVJD3B","short_pith_number":"pith:ELDOMADC","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"},"canonical_sha256":"22c6e60062c2a15190d7f02864d523d84ef42718011de8be974298a9a2fa5df4","source":{"kind":"arxiv","id":"1607.05594","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05594","created_at":"2026-05-18T00:41:12Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05594v2","created_at":"2026-05-18T00:41:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05594","created_at":"2026-05-18T00:41:12Z"},{"alias_kind":"pith_short_12","alias_value":"ELDOMADCYKQV","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ELDOMADCYKQVDEGX","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ELDOMADC","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ELDOMADCYKQVDEGX6AUGJVJD3B","target":"record","payload":{"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"},"canonical_sha256":"22c6e60062c2a15190d7f02864d523d84ef42718011de8be974298a9a2fa5df4","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"},"source_kind":"arxiv","source_id":"1607.05594","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EcGC7IRFsUCrR43iOHmf/rGx+fM3uZPAhrZN6YmrMupsgBJBaeAnQqKzHKtRqJ7Xdw6G+cZs9dOYaWd48tX7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:25:40.774520Z"},"content_sha256":"02cdbdf0a57158984d47184f2c556241d9823f0a4aa7a022921c5484f1de49a6","schema_version":"1.0","event_id":"sha256:02cdbdf0a57158984d47184f2c556241d9823f0a4aa7a022921c5484f1de49a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ELDOMADCYKQVDEGX6AUGJVJD3B","target":"graph","payload":{"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. Kustin, Liana M. Sega","submitted_at":"2016-07-19T14:19:09Z","abstract_excerpt":"We define a notion of compressed local Artinian ring that does not require the ring to contain a field. 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 $R$."},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gbh6PIMpftYe/E5EccquONsDL+zGJyUT+BeArfQHHNCyAt5563I2LtMNNgG/8YA/ReR+f5ixVYoyZ1EuZFFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:25:40.774922Z"},"content_sha256":"e8f272876de9b8386b22600da2859dbcad1aac4a527c14b6e2f8d6ec35b4b3ed","schema_version":"1.0","event_id":"sha256:e8f272876de9b8386b22600da2859dbcad1aac4a527c14b6e2f8d6ec35b4b3ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/bundle.json","state_url":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T00:25:40Z","links":{"resolver":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B","bundle":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/bundle.json","state":"https://pith.science/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELDOMADCYKQVDEGX6AUGJVJD3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ELDOMADCYKQVDEGX6AUGJVJD3B","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":"02bb4af4ace0d7c405c261ec61fe48cb46c5859862470eb8121d491149ddaf87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-07-19T14:19:09Z","title_canon_sha256":"487113448987bfb020c5639a1fd0e6c3adc34ae9af79d7ca579ce892d7195c90"},"schema_version":"1.0","source":{"id":"1607.05594","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05594","created_at":"2026-05-18T00:41:12Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05594v2","created_at":"2026-05-18T00:41:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05594","created_at":"2026-05-18T00:41:12Z"},{"alias_kind":"pith_short_12","alias_value":"ELDOMADCYKQV","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ELDOMADCYKQVDEGX","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ELDOMADC","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:e8f272876de9b8386b22600da2859dbcad1aac4a527c14b6e2f8d6ec35b4b3ed","target":"graph","created_at":"2026-05-18T00:41:12Z","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 define a notion of compressed local Artinian ring that does not require the ring to contain a field. 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 $R$.","authors_text":"Adela Vraciu, Andrew R. Kustin, Liana M. Sega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-07-19T14:19:09Z","title":"Poincar\\'e series of compressed local Artinian rings with odd top socle degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05594","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":"sha256:02cdbdf0a57158984d47184f2c556241d9823f0a4aa7a022921c5484f1de49a6","target":"record","created_at":"2026-05-18T00:41:12Z","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":"02bb4af4ace0d7c405c261ec61fe48cb46c5859862470eb8121d491149ddaf87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-07-19T14:19:09Z","title_canon_sha256":"487113448987bfb020c5639a1fd0e6c3adc34ae9af79d7ca579ce892d7195c90"},"schema_version":"1.0","source":{"id":"1607.05594","kind":"arxiv","version":2}},"canonical_sha256":"22c6e60062c2a15190d7f02864d523d84ef42718011de8be974298a9a2fa5df4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22c6e60062c2a15190d7f02864d523d84ef42718011de8be974298a9a2fa5df4","first_computed_at":"2026-05-18T00:41:12.941248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:12.941248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6obEq4Ok6V2w0e0BX/jMxZEUAqi6862YoTMs4cCZx7/SEG3iJQVuhNMJr3JWA68xLse6uDj4TrZhULesuSoqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:12.942002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05594","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02cdbdf0a57158984d47184f2c556241d9823f0a4aa7a022921c5484f1de49a6","sha256:e8f272876de9b8386b22600da2859dbcad1aac4a527c14b6e2f8d6ec35b4b3ed"],"state_sha256":"4fd5ca4a9624e7c66eeafca6890065b30a2f708cf59a13d6490e0038d151171d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/+y6vRTVSW6by1sTC0y40DQdntQrNejw6Vl0qgV4bsGKUliDQh93tJa7hewS4TR4YOMNeadzP71lw39AmCFCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:25:40.778375Z","bundle_sha256":"bc4e6fa55c2b177c3d934b9d77a7845cb634f8c03e94050ccff3f10d859e16c6"}}