{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:J7NT6A725XJ77FF62IXIQ4MOUB","short_pith_number":"pith:J7NT6A72","canonical_record":{"source":{"id":"1112.2353","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-11T13:23:29Z","cross_cats_sorted":[],"title_canon_sha256":"c8df1740a1d3d478bd30443f38f4a9872b3651c36a50ac2ffdad39ba181a60b2","abstract_canon_sha256":"e74ec3bc2f904c5e2467dd7df89ec87045edd2d65a3772a5400beca92cfa7543"},"schema_version":"1.0"},"canonical_sha256":"4fdb3f03faedd3ff94bed22e88718ea04c24790dbed9e82aeccd7f2a01d1cd6f","source":{"kind":"arxiv","id":"1112.2353","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2353","created_at":"2026-05-18T03:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2353v3","created_at":"2026-05-18T03:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2353","created_at":"2026-05-18T03:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"J7NT6A725XJ7","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J7NT6A725XJ77FF6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J7NT6A72","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:J7NT6A725XJ77FF62IXIQ4MOUB","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2353","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-11T13:23:29Z","cross_cats_sorted":[],"title_canon_sha256":"c8df1740a1d3d478bd30443f38f4a9872b3651c36a50ac2ffdad39ba181a60b2","abstract_canon_sha256":"e74ec3bc2f904c5e2467dd7df89ec87045edd2d65a3772a5400beca92cfa7543"},"schema_version":"1.0"},"canonical_sha256":"4fdb3f03faedd3ff94bed22e88718ea04c24790dbed9e82aeccd7f2a01d1cd6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:24.636257Z","signature_b64":"/u/YcYDBsFdpN7m5gSXTygZeKhXoubm/GwDOAsXbZTvx/4jwXdDKAI0Rl4YDoF3kLpX2WnjMIIJ/a28cZgu0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fdb3f03faedd3ff94bed22e88718ea04c24790dbed9e82aeccd7f2a01d1cd6f","last_reissued_at":"2026-05-18T03:57:24.635732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:24.635732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2353","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Sp7ufqZrNC8G+AImRa/3OCimUKRwTC4nT1tdydbbJpN1b6i/3j6AW+p3NQncAzrspfFWMXQLxhoM7rm4g7pDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:56:08.139698Z"},"content_sha256":"89b21850f7a6c0b37db85d00ac4efafa3036b2b7572ef7874b0088311c866fab","schema_version":"1.0","event_id":"sha256:89b21850f7a6c0b37db85d00ac4efafa3036b2b7572ef7874b0088311c866fab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:J7NT6A725XJ77FF62IXIQ4MOUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sequence of Exact Zero-Divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mohammad T. Dibaei, Mohsen Gheibi","submitted_at":"2011-12-11T13:23:29Z","abstract_excerpt":"The concept of a sequence of exact zero-divisors on a noetherian local ring is defined and studied. Some properties of sequences of exact zero-divisors are compared with regular sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2353","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lKd+4LphjmPfLIiFBuB6ovNP+oGjY1y4SeWh7ZUpud7vkBoIha+vrt9Sqw3iHs9BrmxcnUqkguxAobXQqNIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:56:08.140457Z"},"content_sha256":"87a6838d8f09ca1f4cf8509bd2005387704dff291ba1a592e2644d887f493d6a","schema_version":"1.0","event_id":"sha256:87a6838d8f09ca1f4cf8509bd2005387704dff291ba1a592e2644d887f493d6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7NT6A725XJ77FF62IXIQ4MOUB/bundle.json","state_url":"https://pith.science/pith/J7NT6A725XJ77FF62IXIQ4MOUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7NT6A725XJ77FF62IXIQ4MOUB/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":"2026-05-31T10:56:08Z","links":{"resolver":"https://pith.science/pith/J7NT6A725XJ77FF62IXIQ4MOUB","bundle":"https://pith.science/pith/J7NT6A725XJ77FF62IXIQ4MOUB/bundle.json","state":"https://pith.science/pith/J7NT6A725XJ77FF62IXIQ4MOUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7NT6A725XJ77FF62IXIQ4MOUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J7NT6A725XJ77FF62IXIQ4MOUB","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":"e74ec3bc2f904c5e2467dd7df89ec87045edd2d65a3772a5400beca92cfa7543","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-11T13:23:29Z","title_canon_sha256":"c8df1740a1d3d478bd30443f38f4a9872b3651c36a50ac2ffdad39ba181a60b2"},"schema_version":"1.0","source":{"id":"1112.2353","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2353","created_at":"2026-05-18T03:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2353v3","created_at":"2026-05-18T03:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2353","created_at":"2026-05-18T03:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"J7NT6A725XJ7","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J7NT6A725XJ77FF6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J7NT6A72","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:87a6838d8f09ca1f4cf8509bd2005387704dff291ba1a592e2644d887f493d6a","target":"graph","created_at":"2026-05-18T03:57:24Z","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":"The concept of a sequence of exact zero-divisors on a noetherian local ring is defined and studied. Some properties of sequences of exact zero-divisors are compared with regular sequences.","authors_text":"Mohammad T. Dibaei, Mohsen Gheibi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-11T13:23:29Z","title":"Sequence of Exact Zero-Divisors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2353","kind":"arxiv","version":3},"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":"sha256:89b21850f7a6c0b37db85d00ac4efafa3036b2b7572ef7874b0088311c866fab","target":"record","created_at":"2026-05-18T03:57:24Z","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":"e74ec3bc2f904c5e2467dd7df89ec87045edd2d65a3772a5400beca92cfa7543","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-11T13:23:29Z","title_canon_sha256":"c8df1740a1d3d478bd30443f38f4a9872b3651c36a50ac2ffdad39ba181a60b2"},"schema_version":"1.0","source":{"id":"1112.2353","kind":"arxiv","version":3}},"canonical_sha256":"4fdb3f03faedd3ff94bed22e88718ea04c24790dbed9e82aeccd7f2a01d1cd6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fdb3f03faedd3ff94bed22e88718ea04c24790dbed9e82aeccd7f2a01d1cd6f","first_computed_at":"2026-05-18T03:57:24.635732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:24.635732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/u/YcYDBsFdpN7m5gSXTygZeKhXoubm/GwDOAsXbZTvx/4jwXdDKAI0Rl4YDoF3kLpX2WnjMIIJ/a28cZgu0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:24.636257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2353","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89b21850f7a6c0b37db85d00ac4efafa3036b2b7572ef7874b0088311c866fab","sha256:87a6838d8f09ca1f4cf8509bd2005387704dff291ba1a592e2644d887f493d6a"],"state_sha256":"de7a8c6ce917cbac629c89787863f82f61ac070e0878677a46da3059a8e40e6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fFTBWQSf3bycdKsEiWKDY16zn4qga2WKu7B3BOMwvHALrI9jD71Yaxd0fbBKTQiBGngghUcyz0mNiMMG5PXlAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:56:08.144506Z","bundle_sha256":"8ec506d673a78f1b3678642d5f4cada224e180be507a8dbaac6221a41dee257e"}}