{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WPULX44HR5JWW6EX7QK73W2EZE","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":"6f1aaa86388e17332ac2a0f0fb0b095d0c74cbbcaace448af46dc1297b99a7a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-19T22:46:02Z","title_canon_sha256":"f7e80896172ea16aa8b167088aeaf175ff425d0355d1a09f79dd1fa34bbb2ad5"},"schema_version":"1.0","source":{"id":"1602.06339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06339","created_at":"2026-05-18T01:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06339v1","created_at":"2026-05-18T01:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06339","created_at":"2026-05-18T01:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"WPULX44HR5JW","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WPULX44HR5JWW6EX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WPULX44H","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:52de58bbd4b054b1b7a76082306ce9082c334d3ee665435793699d0c3f2a9e37","target":"graph","created_at":"2026-05-18T01:20:14Z","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":"Malcev described the congruences of the monoid $T_n$ of all full transformations on a finite set $X_n=\\{1, \\dots,n\\}$. Since then, congruences have been characterized in various other monoids of (partial) transformations on $X_n$, such as the symmetric inverse monoid $In_n$ of all injective partial transformations, or the monoid $PT_n$ of all partial transformations.\n  The first aim of this paper is to describe the congruences of the direct products $Q_m\\times P_n$, where $Q$ and $P$ belong to $\\{T, PT,In\\}$.\n  Malcev also provided a similar description of the congruences on the multiplicative","authors_text":"Gracinda Gomes, Jo\\~ao Ara\\'ujo, Wolfram Bentz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-19T22:46:02Z","title":"Congruences on Direct Products of Transformation and Matrix Monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06339","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:f3350eb746bd0cb4f439b20d14f89cf210b698d98a38722c0027a024b6bbebb5","target":"record","created_at":"2026-05-18T01:20:14Z","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":"6f1aaa86388e17332ac2a0f0fb0b095d0c74cbbcaace448af46dc1297b99a7a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-19T22:46:02Z","title_canon_sha256":"f7e80896172ea16aa8b167088aeaf175ff425d0355d1a09f79dd1fa34bbb2ad5"},"schema_version":"1.0","source":{"id":"1602.06339","kind":"arxiv","version":1}},"canonical_sha256":"b3e8bbf3878f536b7897fc15fddb44c92a36cb28e8dd956f2f4f0a8f89219e28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3e8bbf3878f536b7897fc15fddb44c92a36cb28e8dd956f2f4f0a8f89219e28","first_computed_at":"2026-05-18T01:20:14.358813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:14.358813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2o+RymmuM5OWRP0proqtdMUHqnWHtm7+qCRv9VSc+CVOS0LJ5V0sbjXlYSaa32lOjezDn4+Dx0PBo9ffPC8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:14.359403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3350eb746bd0cb4f439b20d14f89cf210b698d98a38722c0027a024b6bbebb5","sha256:52de58bbd4b054b1b7a76082306ce9082c334d3ee665435793699d0c3f2a9e37"],"state_sha256":"638f112ac13dac4dc191098e9dc4317984f4c646e31ad717d7449fc350cd5926"}