{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XGOTT6WF3DUILH4Z4YWEL2ELRI","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":"c57241f74e34976075de5b488a1ae1c0ea34f41ec39b211b7c7ceefcff093be5","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-05-13T07:43:18Z","title_canon_sha256":"2bfd8d62eff4f31f1771f89f13f72872e0589e6ef6b62358819cc65f612d6a83"},"schema_version":"1.0","source":{"id":"1105.2633","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2633","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2633v2","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2633","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"pith_short_12","alias_value":"XGOTT6WF3DUI","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XGOTT6WF3DUILH4Z","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XGOTT6WF","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:be3552fd964f1ffd7b93b0e0784e82e39ab4d9c1941348b3292c5ffc4e1bf8ec","target":"graph","created_at":"2026-05-18T02:28:29Z","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":"We give a classification of Wada-type representations of the braid groups, and solutions of a variant of the set-theoretical Yang-Baxter equation adapted to the free-product group structure. As a consequence, we prove Wada's conjecture: There are only seven types of Wada-type representations up to certain symmetries.","authors_text":"Tetsuya Ito","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-05-13T07:43:18Z","title":"The classification of Wada-type representations of braid groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2633","kind":"arxiv","version":2},"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":"sha256:74dfe60245e30a61499d069c8f8b140a421b2dc942371ebc090fda543047864a","target":"record","created_at":"2026-05-18T02:28:29Z","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":"c57241f74e34976075de5b488a1ae1c0ea34f41ec39b211b7c7ceefcff093be5","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-05-13T07:43:18Z","title_canon_sha256":"2bfd8d62eff4f31f1771f89f13f72872e0589e6ef6b62358819cc65f612d6a83"},"schema_version":"1.0","source":{"id":"1105.2633","kind":"arxiv","version":2}},"canonical_sha256":"b99d39fac5d8e8859f99e62c45e88b8a356520b8acff891a78d21e4805f36242","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b99d39fac5d8e8859f99e62c45e88b8a356520b8acff891a78d21e4805f36242","first_computed_at":"2026-05-18T02:28:29.631266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:29.631266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dfBYJalei5HhJUYWhzwzpIRXRjOrmvDHE6UBzH4aAmh8RryNBPp4ez7UY1lvHuqtc3vLFUYi67fAKai9YHuPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:29.631700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2633","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74dfe60245e30a61499d069c8f8b140a421b2dc942371ebc090fda543047864a","sha256:be3552fd964f1ffd7b93b0e0784e82e39ab4d9c1941348b3292c5ffc4e1bf8ec"],"state_sha256":"5e2df91d5bbc31e797d015d9e144a76a0add5787409a7c3e718d4284fe319c34"}