{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:MCNIVDV3IGTTIY6WIJN3CE7BSV","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":"1c3428150f1c65afa3b99b6e107255ab708ee631078cac97cdc6ec28b7fe0520","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2005-12-26T07:31:07Z","title_canon_sha256":"95acb1071d8a43ec10e78b5ff6fc9c946389f4c7397f78977cf27ce425047419"},"schema_version":"1.0","source":{"id":"math/0512568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512568","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512568v1","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512568","created_at":"2026-05-18T00:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"MCNIVDV3IGTT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MCNIVDV3IGTTIY6W","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MCNIVDV3","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:204e70ce4d1272a3294e4cbc7e49e41784d439e039b0e7ad21506111025b7dc4","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":"In this paper we study sub-semigroups of a zero-divisor semigroup $S$ determined by properties of the zero-divisor graph $\\Gamma(S)$. We use these sub-semigroups to study the correspondence between zero- divisor semigroups and zero-divisor graphs. We study properties of sub- semigroups of Boolean semigroups via the zero-divisor graph. As an application, we provide a characterization of the graphs which are zero- divisor graphs of Boolean rings.","authors_text":"Dancheng Lu, Tongsuo Wu","cross_cats":[],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2005-12-26T07:31:07Z","title":"Sub-semigroups determined by the zero-divisor graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512568","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":"sha256:2f7dbe6c521d65887f6c814597a629367ff277f16a7953bb05a56f3dcaaee963","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":"1c3428150f1c65afa3b99b6e107255ab708ee631078cac97cdc6ec28b7fe0520","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2005-12-26T07:31:07Z","title_canon_sha256":"95acb1071d8a43ec10e78b5ff6fc9c946389f4c7397f78977cf27ce425047419"},"schema_version":"1.0","source":{"id":"math/0512568","kind":"arxiv","version":1}},"canonical_sha256":"609a8a8ebb41a73463d6425bb113e195476134694378d108294695aaeb8efc06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"609a8a8ebb41a73463d6425bb113e195476134694378d108294695aaeb8efc06","first_computed_at":"2026-05-18T00:17:47.703392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:47.703392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6UQH2Kx5Gfxlb7dEZclDxPrW1F0I2fYRUsJHjZGG/+7HKpLV5JIjqHBHguJE53UnOpJxKKiS8aHuxfE1T6BOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:47.703958Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f7dbe6c521d65887f6c814597a629367ff277f16a7953bb05a56f3dcaaee963","sha256:204e70ce4d1272a3294e4cbc7e49e41784d439e039b0e7ad21506111025b7dc4"],"state_sha256":"92f0969afa11a6d18c9779ab6499849aaacaffcf4f3af5adfd473a373a9024a4"}