{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:W26SZMTIEA2VH7AIAWTAAWQCTH","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":"2c3aaab7b4e1efefb068c3eb6dbad4e5f3b6d1b154830ed9a40e9ad9bc1c10fd","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.RA","submitted_at":"2005-12-26T07:17:41Z","title_canon_sha256":"4582f388fbd4024d2311a4a22831374c6b8e9fb12e8fd36d88371f6b099f73b4"},"schema_version":"1.0","source":{"id":"math/0512566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512566","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512566v1","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512566","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"W26SZMTIEA2V","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"W26SZMTIEA2VH7AI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"W26SZMTI","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f646a50a6773645922ad9bc8ac9cbb12b738d3d580349ed0ec1da76125a9e52d","target":"graph","created_at":"2026-05-18T00:17:47Z","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":"A local ring $R$ is called $Z$-local if $J(R) = Z(R)$ and $J(R)^2 = 0$. In this paper the structures of a class of $Z$-local rings are determined.","authors_text":"Dancheng Lu, Tongsuo Wu","cross_cats":["math.AC"],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2005-12-26T07:17:41Z","title":"The structures of a class of $Z$-local rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512566","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":"sha256:1df4f91577fd46ac5af0274aef9eee6918d128b9517097d6421561537ac3a481","target":"record","created_at":"2026-05-18T00:17:47Z","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":"2c3aaab7b4e1efefb068c3eb6dbad4e5f3b6d1b154830ed9a40e9ad9bc1c10fd","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.RA","submitted_at":"2005-12-26T07:17:41Z","title_canon_sha256":"4582f388fbd4024d2311a4a22831374c6b8e9fb12e8fd36d88371f6b099f73b4"},"schema_version":"1.0","source":{"id":"math/0512566","kind":"arxiv","version":1}},"canonical_sha256":"b6bd2cb268203553fc0805a6005a0299d5e97e3584d00ef6fc71e82640bca699","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6bd2cb268203553fc0805a6005a0299d5e97e3584d00ef6fc71e82640bca699","first_computed_at":"2026-05-18T00:17:47.710939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:47.710939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uezg598ciby0VNmqltXgRCLYZYj33ty3iS4skCUU8BgovKOxneniu/XvxiwEn8nJPjFHTpED1O/tdJ3oM58FDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:47.711594Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1df4f91577fd46ac5af0274aef9eee6918d128b9517097d6421561537ac3a481","sha256:f646a50a6773645922ad9bc8ac9cbb12b738d3d580349ed0ec1da76125a9e52d"],"state_sha256":"6030bcd98cc512bfe3357ac296869d8dab18daac0718e9858516b53020c62782"}