{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C4CKL5U4SEPZCVQLB4UYN2O3D3","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":"1c93dd886003852731588af10eac6e368869e1eb0ffbd4f6a1b1c59a53d2e62d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-31T16:13:16Z","title_canon_sha256":"0dd56ddf8b686190edc863200125574d1a241f821f3797b20cc6c7f18fbbc3e0"},"schema_version":"1.0","source":{"id":"1701.09109","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.09109","created_at":"2026-05-18T00:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"1701.09109v3","created_at":"2026-05-18T00:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.09109","created_at":"2026-05-18T00:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"C4CKL5U4SEPZ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4CKL5U4SEPZCVQL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4CKL5U4","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:8063262972c11ff891ca50713ee8ef0676483435f45f98ac300044939ac72943","target":"graph","created_at":"2026-05-18T00:14:01Z","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 prove that a finite non-degenerate involutive set-theoretic solution (X,r) of the Yang-Baxter equation is a multipermutation solution if and only if its structure group G(X,r) admits a left ordering or equivalently it is poly-(infinite cyclic).","authors_text":"D. Bachiller, F. Ced\\'o, L. Vendramin","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-31T16:13:16Z","title":"A characterization of finite multipermutation solutions of the Yang-Baxter equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.09109","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":"sha256:849f7cbae000e65dfc1b25475a2042164b96391740aaf39f7979497bc363453a","target":"record","created_at":"2026-05-18T00:14:01Z","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":"1c93dd886003852731588af10eac6e368869e1eb0ffbd4f6a1b1c59a53d2e62d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-31T16:13:16Z","title_canon_sha256":"0dd56ddf8b686190edc863200125574d1a241f821f3797b20cc6c7f18fbbc3e0"},"schema_version":"1.0","source":{"id":"1701.09109","kind":"arxiv","version":3}},"canonical_sha256":"1704a5f69c911f91560b0f2986e9db1ee9a4ae40e2fbb073f63386f0da4ffb56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1704a5f69c911f91560b0f2986e9db1ee9a4ae40e2fbb073f63386f0da4ffb56","first_computed_at":"2026-05-18T00:14:01.354588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:01.354588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X9lEOjeltWnjKxIomgQ5ekEYMcupMDGy23CpW9qktwdJtzZTIbUGUNmIKlvDxr9efmDiZsuQL0NUVzQVn3XLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:01.355336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.09109","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:849f7cbae000e65dfc1b25475a2042164b96391740aaf39f7979497bc363453a","sha256:8063262972c11ff891ca50713ee8ef0676483435f45f98ac300044939ac72943"],"state_sha256":"e00083fb7ead181b9bb28823069e82d59c9e41a5733712660ce84e4f77e82a42"}