{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XN6R6XXSZMCLHS6KIY4ERDXEKM","short_pith_number":"pith:XN6R6XXS","canonical_record":{"source":{"id":"1010.3338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-16T11:06:18Z","cross_cats_sorted":[],"title_canon_sha256":"59a38812edd93bc6b6c956da3bea8479b64e05f2ed95695ea3e9e8a1158b4b78","abstract_canon_sha256":"e97ce56da8dffe5a7b816c9e5c84c4ee0339ed36dfa6c58ec20b13d5fb17fc5a"},"schema_version":"1.0"},"canonical_sha256":"bb7d1f5ef2cb04b3cbca4638488ee45317c3e730bc60cdecf365a753cdf95204","source":{"kind":"arxiv","id":"1010.3338","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3338","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3338v1","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3338","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"XN6R6XXSZMCL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XN6R6XXSZMCLHS6K","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XN6R6XXS","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XN6R6XXSZMCLHS6KIY4ERDXEKM","target":"record","payload":{"canonical_record":{"source":{"id":"1010.3338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-16T11:06:18Z","cross_cats_sorted":[],"title_canon_sha256":"59a38812edd93bc6b6c956da3bea8479b64e05f2ed95695ea3e9e8a1158b4b78","abstract_canon_sha256":"e97ce56da8dffe5a7b816c9e5c84c4ee0339ed36dfa6c58ec20b13d5fb17fc5a"},"schema_version":"1.0"},"canonical_sha256":"bb7d1f5ef2cb04b3cbca4638488ee45317c3e730bc60cdecf365a753cdf95204","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:09.410125Z","signature_b64":"9VrYZN7nhdG6ARv2REeInaoTux/V/ZYz6RUloDqyZ5FyRK64Q4NZfBL/jt2VejveF5RIiuGsrmNBIgGCpWeqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb7d1f5ef2cb04b3cbca4638488ee45317c3e730bc60cdecf365a753cdf95204","last_reissued_at":"2026-05-18T04:39:09.409608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:09.409608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.3338","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aSNP0012sGX4oXaTLJqdC+TXRNhgTpiweGeEetWVPOsbfcuxJ1GPQ2Ltn1i5wJDGQvGHMp0mUbmA+62yEnY4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:19:51.414829Z"},"content_sha256":"62bb9e57f1adf7b85c07ed86ca88bb47e8a49caafe27561c8ff03ba28452f33e","schema_version":"1.0","event_id":"sha256:62bb9e57f1adf7b85c07ed86ca88bb47e8a49caafe27561c8ff03ba28452f33e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XN6R6XXSZMCLHS6KIY4ERDXEKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grobner-Shirshov bases for plactic algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jan Okninski, Lukasz Kubat","submitted_at":"2010-10-16T11:06:18Z","abstract_excerpt":"A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobner-Shirshov bases associated to the natural degree-lexicographic ordering on the corresponding free algebra. The latter is in contrast with the case of a strongly related class of algebras, called Chinese algebras, recently considered by Chen Yuqun and Qiu Jianjun."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3338","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIy4LqvEaH40hc76hTpkDiWuipVq1m/E0wxRk6lrmjQsdScyZyS23FIB5EezlemRlJ2WEiwwFUk3dsQwl4BIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:19:51.415443Z"},"content_sha256":"b5f028c78d731b6b901d7b6df1be462f16fbd0029ffe57df101fe28378d8b710","schema_version":"1.0","event_id":"sha256:b5f028c78d731b6b901d7b6df1be462f16fbd0029ffe57df101fe28378d8b710"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XN6R6XXSZMCLHS6KIY4ERDXEKM/bundle.json","state_url":"https://pith.science/pith/XN6R6XXSZMCLHS6KIY4ERDXEKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XN6R6XXSZMCLHS6KIY4ERDXEKM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T07:19:51Z","links":{"resolver":"https://pith.science/pith/XN6R6XXSZMCLHS6KIY4ERDXEKM","bundle":"https://pith.science/pith/XN6R6XXSZMCLHS6KIY4ERDXEKM/bundle.json","state":"https://pith.science/pith/XN6R6XXSZMCLHS6KIY4ERDXEKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XN6R6XXSZMCLHS6KIY4ERDXEKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XN6R6XXSZMCLHS6KIY4ERDXEKM","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":"e97ce56da8dffe5a7b816c9e5c84c4ee0339ed36dfa6c58ec20b13d5fb17fc5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-16T11:06:18Z","title_canon_sha256":"59a38812edd93bc6b6c956da3bea8479b64e05f2ed95695ea3e9e8a1158b4b78"},"schema_version":"1.0","source":{"id":"1010.3338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3338","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3338v1","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3338","created_at":"2026-05-18T04:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"XN6R6XXSZMCL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XN6R6XXSZMCLHS6K","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XN6R6XXS","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:b5f028c78d731b6b901d7b6df1be462f16fbd0029ffe57df101fe28378d8b710","target":"graph","created_at":"2026-05-18T04:39:09Z","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":"A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobner-Shirshov bases associated to the natural degree-lexicographic ordering on the corresponding free algebra. The latter is in contrast with the case of a strongly related class of algebras, called Chinese algebras, recently considered by Chen Yuqun and Qiu Jianjun.","authors_text":"Jan Okninski, Lukasz Kubat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-16T11:06:18Z","title":"Grobner-Shirshov bases for plactic algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3338","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":"sha256:62bb9e57f1adf7b85c07ed86ca88bb47e8a49caafe27561c8ff03ba28452f33e","target":"record","created_at":"2026-05-18T04:39:09Z","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":"e97ce56da8dffe5a7b816c9e5c84c4ee0339ed36dfa6c58ec20b13d5fb17fc5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-16T11:06:18Z","title_canon_sha256":"59a38812edd93bc6b6c956da3bea8479b64e05f2ed95695ea3e9e8a1158b4b78"},"schema_version":"1.0","source":{"id":"1010.3338","kind":"arxiv","version":1}},"canonical_sha256":"bb7d1f5ef2cb04b3cbca4638488ee45317c3e730bc60cdecf365a753cdf95204","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb7d1f5ef2cb04b3cbca4638488ee45317c3e730bc60cdecf365a753cdf95204","first_computed_at":"2026-05-18T04:39:09.409608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:09.409608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9VrYZN7nhdG6ARv2REeInaoTux/V/ZYz6RUloDqyZ5FyRK64Q4NZfBL/jt2VejveF5RIiuGsrmNBIgGCpWeqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:09.410125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62bb9e57f1adf7b85c07ed86ca88bb47e8a49caafe27561c8ff03ba28452f33e","sha256:b5f028c78d731b6b901d7b6df1be462f16fbd0029ffe57df101fe28378d8b710"],"state_sha256":"a9689e4215b2c5bc1ed709302b1e8dd4c670b038d29af2e0968592cffc38aa9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"alk7XKzc6CLXqFIlzABkEyUKkAn7G8HFvwak8ocQJCPO+o/RsDByEbk6UzCwzGDMRXsnTpQizxMNi7nxvSuaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:19:51.418727Z","bundle_sha256":"80b9c7cebbff30b568ab54f72643be2b1df689744a98b629cc9eda36a9b2fed7"}}