{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3MKAXWZTVFBQHLBYBSVZHP7JXG","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":"41cfce4c21bed6d79a24e6b0b627f04a22aaa8df5ff2020aeab2e636584500c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-03T10:13:38Z","title_canon_sha256":"6f819ba88ca364d36d86bb42edcf83d19fe337986bb1a13209635d051c5bc10a"},"schema_version":"1.0","source":{"id":"1512.01023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01023","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01023v1","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01023","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"3MKAXWZTVFBQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3MKAXWZTVFBQHLBY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3MKAXWZT","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:9f940090389afdf90066ddd69c4e327c1e578b8cacf15643dde178cc9bba36f7","target":"graph","created_at":"2026-05-18T01:25:23Z","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":"Let H be a pseudovariety of groups in which the kappa-word problem is decidable. Here, kappa denotes the canonical implicit signature, which consists of the multiplication and the (omega-1)-power. We prove that the kappa-word problem is also decidable over DRH, the pseudovariety of all finite semigroups whose regular R-classes lie in H. Further, we present a canonical form for elements in the free kappa-semigroup over DRH, based on the knowledge of a canonical form for elements in the free kappa-semigroup over H. This extends work of Almeida and Zeitoun on the pseudovariety of all finite R-tri","authors_text":"C\\'elia Borlido","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-03T10:13:38Z","title":"The kappa-word problem over DRH"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01023","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":"sha256:6299a0fa263ba7c9aba1f09bfef00fe578855659d723a0b0dc1913add9ec142f","target":"record","created_at":"2026-05-18T01:25:23Z","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":"41cfce4c21bed6d79a24e6b0b627f04a22aaa8df5ff2020aeab2e636584500c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-03T10:13:38Z","title_canon_sha256":"6f819ba88ca364d36d86bb42edcf83d19fe337986bb1a13209635d051c5bc10a"},"schema_version":"1.0","source":{"id":"1512.01023","kind":"arxiv","version":1}},"canonical_sha256":"db140bdb33a94303ac380cab93bfe9b9b6194902070a2328e9304a3d34319d01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db140bdb33a94303ac380cab93bfe9b9b6194902070a2328e9304a3d34319d01","first_computed_at":"2026-05-18T01:25:23.574606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:23.574606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EEwDdh9Jcli/X5X9B9bUVc5BjVsWBfEvZcOqvEcoJHF6WFCSoIRz9taBiBGSTyT9uY1gPvoz0AQ2fRtfuOxzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:23.575053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6299a0fa263ba7c9aba1f09bfef00fe578855659d723a0b0dc1913add9ec142f","sha256:9f940090389afdf90066ddd69c4e327c1e578b8cacf15643dde178cc9bba36f7"],"state_sha256":"fcef710db417a079325eb8e54bc390070f315243c2e24d9ee8a07789a00742c2"}