{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KTHPEVWRDVODBJWAT2XOPQHNN3","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":"873629c3555243e040caa17dcc7504143e69c54ccf0036348ed1b9dfdc0b0ce5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-09T15:09:32Z","title_canon_sha256":"689b010b8c402087a4837a67ab16bee8f77a184c72f30ddaa4aec1bee14bd2b0"},"schema_version":"1.0","source":{"id":"1602.03020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03020","created_at":"2026-05-18T01:21:03Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03020v1","created_at":"2026-05-18T01:21:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03020","created_at":"2026-05-18T01:21:03Z"},{"alias_kind":"pith_short_12","alias_value":"KTHPEVWRDVOD","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KTHPEVWRDVODBJWA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KTHPEVWR","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:289edbf9a5afb93ff5dbf874ccc350ea2d6756fd1ddb4c8b725a8a782a46ac54","target":"graph","created_at":"2026-05-18T01:21:03Z","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":"This paper deals with the reducibility property of semidirect products of the form $\\bf V*\\bf D$ relatively to graph equation systems, where $\\bf D$ denotes the pseudovariety of definite semigroups. We show that, if the pseudovariety $\\bf V$ is reducible with respect to the canonical signature $\\kappa$ consisting of the multiplication and the $(\\omega-1)$-power, then $\\bf V*\\bf D$ is also reducible with respect to $\\kappa$.","authors_text":"Concei\\c{c}\\~ao Nogueira, Jos\\'e Carlos Costa, M. Lurdes Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-09T15:09:32Z","title":"On $\\kappa$-reducibility of pseudovarieties of the form $\\bf V*\\bf D$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03020","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":"sha256:59e8efc6f74dfda879eae148b9759a6a9d1be325151633ba2f68fd714fea2ee1","target":"record","created_at":"2026-05-18T01:21:03Z","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":"873629c3555243e040caa17dcc7504143e69c54ccf0036348ed1b9dfdc0b0ce5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-09T15:09:32Z","title_canon_sha256":"689b010b8c402087a4837a67ab16bee8f77a184c72f30ddaa4aec1bee14bd2b0"},"schema_version":"1.0","source":{"id":"1602.03020","kind":"arxiv","version":1}},"canonical_sha256":"54cef256d11d5c30a6c09eaee7c0ed6ed693a59bfe06dd47105e06fe1287d2e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54cef256d11d5c30a6c09eaee7c0ed6ed693a59bfe06dd47105e06fe1287d2e2","first_computed_at":"2026-05-18T01:21:03.642101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:03.642101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kLXJr2Qb7P7cTLlGtaay7K0gpxbMCIodpU9SPQFoqVodacD8SiaN7R54g94d/Tdi0FjAPAWFNSIy+AAdJ4RgAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:03.642632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e8efc6f74dfda879eae148b9759a6a9d1be325151633ba2f68fd714fea2ee1","sha256:289edbf9a5afb93ff5dbf874ccc350ea2d6756fd1ddb4c8b725a8a782a46ac54"],"state_sha256":"f059cec7dfd2c3f9131bfd93dfdebbc883ef58f006b8226833eb02eecc9960da"}