{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JBVA3R63PDVA6VMOLXP7HIKF6V","short_pith_number":"pith:JBVA3R63","canonical_record":{"source":{"id":"1107.0440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-03T09:25:14Z","cross_cats_sorted":[],"title_canon_sha256":"3ec269dc8c20c7f28884090543ab235a9b986fba8ed6538da549294c190cac25","abstract_canon_sha256":"00587ffd0eb9e2ff4118187ccdead2e2c76e87c5229bd123afa32a04c320ecb9"},"schema_version":"1.0"},"canonical_sha256":"486a0dc7db78ea0f558e5ddff3a145f5405f997f72ced0bcb764c096ee73e6e7","source":{"kind":"arxiv","id":"1107.0440","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0440","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0440v1","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0440","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"JBVA3R63PDVA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JBVA3R63PDVA6VMO","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JBVA3R63","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JBVA3R63PDVA6VMOLXP7HIKF6V","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-03T09:25:14Z","cross_cats_sorted":[],"title_canon_sha256":"3ec269dc8c20c7f28884090543ab235a9b986fba8ed6538da549294c190cac25","abstract_canon_sha256":"00587ffd0eb9e2ff4118187ccdead2e2c76e87c5229bd123afa32a04c320ecb9"},"schema_version":"1.0"},"canonical_sha256":"486a0dc7db78ea0f558e5ddff3a145f5405f997f72ced0bcb764c096ee73e6e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:53.966503Z","signature_b64":"gzS1aHdUswKnZHoIIiOVzMtU03skrqBvjUise0d9+m/Q6+AJBtxt2QBkymlvrffboYRWUUT+lraTU6sw1afxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"486a0dc7db78ea0f558e5ddff3a145f5405f997f72ced0bcb764c096ee73e6e7","last_reissued_at":"2026-05-18T04:18:53.966083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:53.966083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0440","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/gDlzFdfmrFLDYnK8jmCNQOf2vMlbIC3lG2zgSCn00hvneGHOvWYEzaiNl0/7c/qqWdtCtGE9+aznYlHgvzVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:35:44.044381Z"},"content_sha256":"bcd4a5eebde5bb2040bc69c73cb57ac09062426c1c702e357353a57b8218641a","schema_version":"1.0","event_id":"sha256:bcd4a5eebde5bb2040bc69c73cb57ac09062426c1c702e357353a57b8218641a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JBVA3R63PDVA6VMOLXP7HIKF6V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Conjecture on the weak global dimension of Gaussian rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Guram Donadze, Viji Thomas","submitted_at":"2011-07-03T09:25:14Z","abstract_excerpt":"Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is 0,1 or \\infty. In this paper, we prove their conjecture in all cases except when R is a non-reduced local Gaussian ring with nilradical $\\mathcal{N} satisfying $\\mathcal{N}^2=0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0440","kind":"arxiv","version":1},"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":"2026-05-18T04:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uu2cjIxS3Ct6Jt83424dFN/hKZ6/EM+MQEbPPVSuaDMbEQ4BenDROjLE4ZVoKoigJ07D8s/DDOYuxOQMDsQyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:35:44.045055Z"},"content_sha256":"21457fd9daa97e1bcb5e0ed274577e655285112ec8d6d83879ed8bdd3a5bc7aa","schema_version":"1.0","event_id":"sha256:21457fd9daa97e1bcb5e0ed274577e655285112ec8d6d83879ed8bdd3a5bc7aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JBVA3R63PDVA6VMOLXP7HIKF6V/bundle.json","state_url":"https://pith.science/pith/JBVA3R63PDVA6VMOLXP7HIKF6V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JBVA3R63PDVA6VMOLXP7HIKF6V/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":"2026-05-26T21:35:44Z","links":{"resolver":"https://pith.science/pith/JBVA3R63PDVA6VMOLXP7HIKF6V","bundle":"https://pith.science/pith/JBVA3R63PDVA6VMOLXP7HIKF6V/bundle.json","state":"https://pith.science/pith/JBVA3R63PDVA6VMOLXP7HIKF6V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JBVA3R63PDVA6VMOLXP7HIKF6V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JBVA3R63PDVA6VMOLXP7HIKF6V","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":"00587ffd0eb9e2ff4118187ccdead2e2c76e87c5229bd123afa32a04c320ecb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-03T09:25:14Z","title_canon_sha256":"3ec269dc8c20c7f28884090543ab235a9b986fba8ed6538da549294c190cac25"},"schema_version":"1.0","source":{"id":"1107.0440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0440","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0440v1","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0440","created_at":"2026-05-18T04:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"JBVA3R63PDVA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JBVA3R63PDVA6VMO","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JBVA3R63","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:21457fd9daa97e1bcb5e0ed274577e655285112ec8d6d83879ed8bdd3a5bc7aa","target":"graph","created_at":"2026-05-18T04:18:53Z","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":"Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is 0,1 or \\infty. In this paper, we prove their conjecture in all cases except when R is a non-reduced local Gaussian ring with nilradical $\\mathcal{N} satisfying $\\mathcal{N}^2=0$.","authors_text":"Guram Donadze, Viji Thomas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-03T09:25:14Z","title":"On a Conjecture on the weak global dimension of Gaussian rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0440","kind":"arxiv","version":1},"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:bcd4a5eebde5bb2040bc69c73cb57ac09062426c1c702e357353a57b8218641a","target":"record","created_at":"2026-05-18T04:18:53Z","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":"00587ffd0eb9e2ff4118187ccdead2e2c76e87c5229bd123afa32a04c320ecb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-03T09:25:14Z","title_canon_sha256":"3ec269dc8c20c7f28884090543ab235a9b986fba8ed6538da549294c190cac25"},"schema_version":"1.0","source":{"id":"1107.0440","kind":"arxiv","version":1}},"canonical_sha256":"486a0dc7db78ea0f558e5ddff3a145f5405f997f72ced0bcb764c096ee73e6e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"486a0dc7db78ea0f558e5ddff3a145f5405f997f72ced0bcb764c096ee73e6e7","first_computed_at":"2026-05-18T04:18:53.966083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:53.966083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gzS1aHdUswKnZHoIIiOVzMtU03skrqBvjUise0d9+m/Q6+AJBtxt2QBkymlvrffboYRWUUT+lraTU6sw1afxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:53.966503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcd4a5eebde5bb2040bc69c73cb57ac09062426c1c702e357353a57b8218641a","sha256:21457fd9daa97e1bcb5e0ed274577e655285112ec8d6d83879ed8bdd3a5bc7aa"],"state_sha256":"e49021b07ff5c0cceffc5c7b62436ca142b5885baa7cf85e24aeab577484624d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KQve3dEMOKmjSc/dl+GLRo0UxKvosHqtHdOgs3vpuLm2b63BbXAcdMw5rjxX4QoApctB6ErwPogaa3wazidbCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:35:44.048482Z","bundle_sha256":"5fd94cdea9e770562be8ef0d151fea64ea827feeb1a29bf5625d6708e6e12923"}}