{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MVI6XMPVMQ46HEHAO5XJ5N2A7V","short_pith_number":"pith:MVI6XMPV","canonical_record":{"source":{"id":"1111.7281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T19:31:30Z","cross_cats_sorted":[],"title_canon_sha256":"ce39edc065e01b562bb89ebe048395346ec2b5a20db25877c39b94659309eeaa","abstract_canon_sha256":"3b3bbcb1964e7aa1084f4c90ecca7949d0c00fc096f40ad43247131f18d16fa8"},"schema_version":"1.0"},"canonical_sha256":"6551ebb1f56439e390e0776e9eb740fd4c0c6de4f84687e96d1b380c707e4932","source":{"kind":"arxiv","id":"1111.7281","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7281","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7281v2","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7281","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"MVI6XMPVMQ46","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MVI6XMPVMQ46HEHA","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MVI6XMPV","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MVI6XMPVMQ46HEHAO5XJ5N2A7V","target":"record","payload":{"canonical_record":{"source":{"id":"1111.7281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T19:31:30Z","cross_cats_sorted":[],"title_canon_sha256":"ce39edc065e01b562bb89ebe048395346ec2b5a20db25877c39b94659309eeaa","abstract_canon_sha256":"3b3bbcb1964e7aa1084f4c90ecca7949d0c00fc096f40ad43247131f18d16fa8"},"schema_version":"1.0"},"canonical_sha256":"6551ebb1f56439e390e0776e9eb740fd4c0c6de4f84687e96d1b380c707e4932","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:17.718297Z","signature_b64":"Gzapp3E/v6JTNRUfyvq1HzGEk05sDoGRK+KNMothzWSUilRj9Rma3P5vIOaK1Ycah5na7dEIKLdD1DGdtg+5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6551ebb1f56439e390e0776e9eb740fd4c0c6de4f84687e96d1b380c707e4932","last_reissued_at":"2026-05-18T03:14:17.717725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:17.717725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.7281","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":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8nayv9r8Od10f3cHZxje0BZdjSihl9zJL1saLrcA0V0L50M3VZXlJxcmZLTxuVOVxZgpFuFZAOJD2nZNu2QNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:50:29.232673Z"},"content_sha256":"07f1d12822b8c866bcdada6e1ba3e6db3c3a99c9be15655a7ab8ab7fedd1ee61","schema_version":"1.0","event_id":"sha256:07f1d12822b8c866bcdada6e1ba3e6db3c3a99c9be15655a7ab8ab7fedd1ee61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MVI6XMPVMQ46HEHAO5XJ5N2A7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finitistic Extension Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kosmas Diveris","submitted_at":"2011-11-30T19:31:30Z","abstract_excerpt":"We introduce the finitistic extension degree of a ring and investigate rings for which it is finite. The Auslander-Reiten Conjecture is proved for rings of finite finitistic extension degree and these rings are also shown to have finite finitistic dimension. We apply these results to better understand a gen- eralized version of the Auslander-Reiten Condition for Gorenstein rings. We also record how the finitistic extension degree behaves with respect to many change of ring procedures that arise frequently in the commutative setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7281","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":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7skXBZA9RC3zb5xOhiY2dH9T1pcTlIIRGrlcE9WVRqsSd2hUol2wywC4AQNjxxwrZNSBa9PTPax25HtNJTZYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:50:29.233016Z"},"content_sha256":"a1204d7b098313dd628672616a004da5ad8badabe9014877452bc60b266ae70c","schema_version":"1.0","event_id":"sha256:a1204d7b098313dd628672616a004da5ad8badabe9014877452bc60b266ae70c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVI6XMPVMQ46HEHAO5XJ5N2A7V/bundle.json","state_url":"https://pith.science/pith/MVI6XMPVMQ46HEHAO5XJ5N2A7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVI6XMPVMQ46HEHAO5XJ5N2A7V/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":"2026-06-21T15:50:29Z","links":{"resolver":"https://pith.science/pith/MVI6XMPVMQ46HEHAO5XJ5N2A7V","bundle":"https://pith.science/pith/MVI6XMPVMQ46HEHAO5XJ5N2A7V/bundle.json","state":"https://pith.science/pith/MVI6XMPVMQ46HEHAO5XJ5N2A7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVI6XMPVMQ46HEHAO5XJ5N2A7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MVI6XMPVMQ46HEHAO5XJ5N2A7V","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":"3b3bbcb1964e7aa1084f4c90ecca7949d0c00fc096f40ad43247131f18d16fa8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T19:31:30Z","title_canon_sha256":"ce39edc065e01b562bb89ebe048395346ec2b5a20db25877c39b94659309eeaa"},"schema_version":"1.0","source":{"id":"1111.7281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7281","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7281v2","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7281","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"MVI6XMPVMQ46","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MVI6XMPVMQ46HEHA","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MVI6XMPV","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:a1204d7b098313dd628672616a004da5ad8badabe9014877452bc60b266ae70c","target":"graph","created_at":"2026-05-18T03:14:17Z","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 introduce the finitistic extension degree of a ring and investigate rings for which it is finite. The Auslander-Reiten Conjecture is proved for rings of finite finitistic extension degree and these rings are also shown to have finite finitistic dimension. We apply these results to better understand a gen- eralized version of the Auslander-Reiten Condition for Gorenstein rings. We also record how the finitistic extension degree behaves with respect to many change of ring procedures that arise frequently in the commutative setting.","authors_text":"Kosmas Diveris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T19:31:30Z","title":"Finitistic Extension Degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7281","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":"sha256:07f1d12822b8c866bcdada6e1ba3e6db3c3a99c9be15655a7ab8ab7fedd1ee61","target":"record","created_at":"2026-05-18T03:14:17Z","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":"3b3bbcb1964e7aa1084f4c90ecca7949d0c00fc096f40ad43247131f18d16fa8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T19:31:30Z","title_canon_sha256":"ce39edc065e01b562bb89ebe048395346ec2b5a20db25877c39b94659309eeaa"},"schema_version":"1.0","source":{"id":"1111.7281","kind":"arxiv","version":2}},"canonical_sha256":"6551ebb1f56439e390e0776e9eb740fd4c0c6de4f84687e96d1b380c707e4932","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6551ebb1f56439e390e0776e9eb740fd4c0c6de4f84687e96d1b380c707e4932","first_computed_at":"2026-05-18T03:14:17.717725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:17.717725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gzapp3E/v6JTNRUfyvq1HzGEk05sDoGRK+KNMothzWSUilRj9Rma3P5vIOaK1Ycah5na7dEIKLdD1DGdtg+5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:17.718297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07f1d12822b8c866bcdada6e1ba3e6db3c3a99c9be15655a7ab8ab7fedd1ee61","sha256:a1204d7b098313dd628672616a004da5ad8badabe9014877452bc60b266ae70c"],"state_sha256":"f9a3cac5337a2b15986ff886cdcc2b0096940faf80e45cc52fe3f7dab9952dd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cMIOq1Ws0RFyD7Ol5agnpMIaDtIuKqhnxq449lUxnADJNen1C7U5TKtSOEJuCR/JU/HitSEXI+20tUYFxPsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T15:50:29.235007Z","bundle_sha256":"c3015bc0431ed7cff630f485261668f08afa08468c992745c790fcc6e46d19cc"}}