{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:S3KK2MNCPVQS5G7F76W5WAFXYZ","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":"2fb247876a4be060a48b4f0a5459ed3c42d298561d23fc08a1509b3eddb0b89f","cross_cats_sorted":["math.MP","math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-03-18T16:16:19Z","title_canon_sha256":"7b8e1c06cfe40f8d28293cb3e398c0a6482aea9af6a4ecd7d72fee4e2464eb3c"},"schema_version":"1.0","source":{"id":"2003.08317","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.08317","created_at":"2026-07-05T03:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2003.08317v4","created_at":"2026-07-05T03:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.08317","created_at":"2026-07-05T03:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"S3KK2MNCPVQS","created_at":"2026-07-05T03:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"S3KK2MNCPVQS5G7F","created_at":"2026-07-05T03:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"S3KK2MNC","created_at":"2026-07-05T03:04:00Z"}],"graph_snapshots":[{"event_id":"sha256:0b3770c078d2d87beb477bc78a21168c28e5ebfbe8dc3339d32e063d36890f7a","target":"graph","created_at":"2026-07-05T03:04:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.08317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Connections between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and twisted algebras and we derive the associated defining algebra relations for $R$-matrices being Baxterized solutions of the $A$-type Hecke algebra ${\\cal H}_N(q=1)$. We show in the case of the reflection algebra that there exists a ``boundary'' finite sub-algebra for some special choice of ``boundary'' elements of the $B$-type Hecke algebra ${\\cal B}_N(q=1, Q)$.","authors_text":"Agata Smoktunowicz, Anastasia Doikou","cross_cats":["math.MP","math.QA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-03-18T16:16:19Z","title":"Set theoretic Yang-Baxter & reflection equations and quantum group symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.08317","kind":"arxiv","version":4},"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":"sha256:6f76f1a436f11bbab8cd32d4c3a57b4c53c8d4e4ef31a35c6b1e659b0137855e","target":"record","created_at":"2026-07-05T03:04:00Z","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":"2fb247876a4be060a48b4f0a5459ed3c42d298561d23fc08a1509b3eddb0b89f","cross_cats_sorted":["math.MP","math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-03-18T16:16:19Z","title_canon_sha256":"7b8e1c06cfe40f8d28293cb3e398c0a6482aea9af6a4ecd7d72fee4e2464eb3c"},"schema_version":"1.0","source":{"id":"2003.08317","kind":"arxiv","version":4}},"canonical_sha256":"96d4ad31a27d612e9be5ffaddb00b7c64b24295f10376ebe6ddb53e48170cf36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96d4ad31a27d612e9be5ffaddb00b7c64b24295f10376ebe6ddb53e48170cf36","first_computed_at":"2026-07-05T03:04:00.893827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:04:00.893827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zMpa0RD46AQlu8Kf0+S3+SNiBy8mJddHu3uFN702f20UzQCAbgPOVtc3+sz6BuAsnMrBCcVIYA5dZSTULBcaCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:04:00.894172Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.08317","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f76f1a436f11bbab8cd32d4c3a57b4c53c8d4e4ef31a35c6b1e659b0137855e","sha256:0b3770c078d2d87beb477bc78a21168c28e5ebfbe8dc3339d32e063d36890f7a"],"state_sha256":"04817a0364507e4f8907cccbbb4f8c0524519990651b4af5ee954b5350ae5487"}