{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RQSKM5EL4CN7CKCMBYPWWQLAMK","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":"dbc7d295f2701c023a9e30010192315d8a20b616fecc65504dc5edec4cfc2f49","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-22T16:21:57Z","title_canon_sha256":"dc14e677d07f99e9080b67094bb083d037dbdb1889719b6873276aa10d72c771"},"schema_version":"1.0","source":{"id":"1412.7040","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7040","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7040v3","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7040","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"RQSKM5EL4CN7","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RQSKM5EL4CN7CKCM","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RQSKM5EL","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:228fbda390b06f5439f5ab8b5019e5b0301476c7b508ac1d0bf38858b488ef68","target":"graph","created_at":"2026-05-17T23:54:27Z","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":"The vertices of any (combinatorial) Kashiwara crystal graph carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomorphic components of the crystal. Working on a purely combinatorial and monoid-theoretical level, we prove some foundational results for these crystal monoids, including the observation that they have decidable word problem when their weight monoid is a finite rank free abelian group. The problem of constructing finite complete rewriting systems, and biautomatic structures, for crystal monoids is then investigated. In","authors_text":"Alan J. Cain, Ant\\'onio Malheiro, Robert D. Gray","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-22T16:21:57Z","title":"Crystal monoids \\& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types $A_{n}$, $B_{n}$, $C_{n}$, $D_{n}$, and $G_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7040","kind":"arxiv","version":3},"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":"sha256:63a1ad14071aa2c9b7aa77bad179b08e004984a9b3d0741aa4cb5017d9770504","target":"record","created_at":"2026-05-17T23:54:27Z","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":"dbc7d295f2701c023a9e30010192315d8a20b616fecc65504dc5edec4cfc2f49","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-22T16:21:57Z","title_canon_sha256":"dc14e677d07f99e9080b67094bb083d037dbdb1889719b6873276aa10d72c771"},"schema_version":"1.0","source":{"id":"1412.7040","kind":"arxiv","version":3}},"canonical_sha256":"8c24a6748be09bf1284c0e1f6b41606283c0097db7a41639753d815067a09fc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c24a6748be09bf1284c0e1f6b41606283c0097db7a41639753d815067a09fc3","first_computed_at":"2026-05-17T23:54:27.323006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:27.323006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SwI33cVoQCT7Tf4tkcCZWi9X6/UD8Be4LtEGrKpiUxG4mC0hzskjbLlVMdS6pHa3v6oLBT62q/jj9PrS6906CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:27.323639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7040","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63a1ad14071aa2c9b7aa77bad179b08e004984a9b3d0741aa4cb5017d9770504","sha256:228fbda390b06f5439f5ab8b5019e5b0301476c7b508ac1d0bf38858b488ef68"],"state_sha256":"6c216d5672c42d008da9858ab01e9eeb482985bd7f86d090603b4c2a7a42d660"}