{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NA3UR6UBGQHRWSAAW4EDHEIPXJ","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":"854beb652559e07e146a6db01c6f2d9a973f0e0e9a628e2ba9ebb6ea88535100","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-05T19:27:14Z","title_canon_sha256":"f3c4338ffe00b65d09b58cb0a602bc7888b0a671af1362afaf54a1cc9284b342"},"schema_version":"1.0","source":{"id":"1908.01813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01813","created_at":"2026-07-04T23:52:06Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01813v2","created_at":"2026-07-04T23:52:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01813","created_at":"2026-07-04T23:52:06Z"},{"alias_kind":"pith_short_12","alias_value":"NA3UR6UBGQHR","created_at":"2026-07-04T23:52:06Z"},{"alias_kind":"pith_short_16","alias_value":"NA3UR6UBGQHRWSAA","created_at":"2026-07-04T23:52:06Z"},{"alias_kind":"pith_short_8","alias_value":"NA3UR6UB","created_at":"2026-07-04T23:52:06Z"}],"graph_snapshots":[{"event_id":"sha256:9f8d5b6d8406dd3e2c47527a1e86f8500158efa236da763f3a9d2be28fffd00f","target":"graph","created_at":"2026-07-04T23:52:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.01813/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalise a result of Isbell from commutative semigroups to H-commutative semigroups by showing that the dominion of an H-commutative semigroup is H-commutative. We then use this to generalise Howie and Isbell's result that any H-commutative semigroup satisfying the minimum condition on principal ideals is saturated.","authors_text":"Noor Alam, Noor Mohammad Khan, Peter M. Higgins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-05T19:27:14Z","title":"Epimorphisms, dominions and H-commutative semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01813","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":"sha256:77c12b1987b4bddba6f7c6da1d53fe3ea452bcab2837d806ec7e7ea59cf09ee2","target":"record","created_at":"2026-07-04T23:52:06Z","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":"854beb652559e07e146a6db01c6f2d9a973f0e0e9a628e2ba9ebb6ea88535100","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-05T19:27:14Z","title_canon_sha256":"f3c4338ffe00b65d09b58cb0a602bc7888b0a671af1362afaf54a1cc9284b342"},"schema_version":"1.0","source":{"id":"1908.01813","kind":"arxiv","version":2}},"canonical_sha256":"683748fa81340f1b4800b70833910fba4a638cbc51a327406d44f642d791d30d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"683748fa81340f1b4800b70833910fba4a638cbc51a327406d44f642d791d30d","first_computed_at":"2026-07-04T23:52:06.963140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:06.963140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VK49pXg1uPkJkxqN0x7EyJxrvi6UWPTmr2mK1BJfkL77b1qdrlbHaVsvm/e9EHzFvA1tbbH6E8EuA9lKyrNqDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:06.963495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77c12b1987b4bddba6f7c6da1d53fe3ea452bcab2837d806ec7e7ea59cf09ee2","sha256:9f8d5b6d8406dd3e2c47527a1e86f8500158efa236da763f3a9d2be28fffd00f"],"state_sha256":"182249a0cce15faaa6706b9f892e0c7683a757d7c2e266976ae4d95361322fd4"}