{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XELTJLXHP2H4NBTRW6JHNHO7UC","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":"e30a818395a3c126c6708dfa89c9977c2282f0d338f57c943ce8a9995b0535de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-11-22T08:29:30Z","title_canon_sha256":"fa4a34ca4c95547ad5fb1aeeddd45bf9f0d35972bed1bc490c1cbc3f4c0e162f"},"schema_version":"1.0","source":{"id":"1811.09060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09060","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09060v1","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09060","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"XELTJLXHP2H4","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XELTJLXHP2H4NBTR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XELTJLXH","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:63ddae384179b2a42a7c48adf201bedd51b603bb63f4c67e5ba8ea48fbe87eea","target":"graph","created_at":"2026-05-18T00:00:07Z","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":"It is shown that the Hecke-Kiselman algebra associated to a finite directed graph is an automaton algebra in the sense of Ufnarovskii. Consequently, its Gelfand-Kirillov dimension is an integer if it is finite. As a consequence, it is proved that the Hecke-Kiselman algebra associated to an oriented cycle admits a finite Gr\\\"obner basis.","authors_text":"Arkadiusz M\\c{e}cel, Jan Okni\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-11-22T08:29:30Z","title":"Gr\\\"obner basis and the automaton property of Hecke--Kiselman algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09060","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":"sha256:3b43ed2cb7b4ed85f8ba8430c92e9fb1268bd4cdc8de9ef16968dfbceceeb178","target":"record","created_at":"2026-05-18T00:00:07Z","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":"e30a818395a3c126c6708dfa89c9977c2282f0d338f57c943ce8a9995b0535de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-11-22T08:29:30Z","title_canon_sha256":"fa4a34ca4c95547ad5fb1aeeddd45bf9f0d35972bed1bc490c1cbc3f4c0e162f"},"schema_version":"1.0","source":{"id":"1811.09060","kind":"arxiv","version":1}},"canonical_sha256":"b91734aee77e8fc68671b792769ddfa095d63c88be81d8051ca2a737d170e583","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b91734aee77e8fc68671b792769ddfa095d63c88be81d8051ca2a737d170e583","first_computed_at":"2026-05-18T00:00:07.193695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:07.193695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sddgne0Q3OwBZ14lXbKiGK1MMEm0S5gx0EDwUohBINK0PCbMfZmGRLf0iNDBX66WF/GjytLdRahBkoVii6QIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:07.194382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b43ed2cb7b4ed85f8ba8430c92e9fb1268bd4cdc8de9ef16968dfbceceeb178","sha256:63ddae384179b2a42a7c48adf201bedd51b603bb63f4c67e5ba8ea48fbe87eea"],"state_sha256":"1b3ea7928faeedbffb375a5b4b52579ab399036ac8d00731311e269fe63623a4"}