{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:42FTM6CDWCOJCK5FTB5ADCEWQJ","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":"bbd8dbd7f1536c52a6036ee0108104c66e0334f5324e2eabfbc4f05c1ea3a560","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-14T19:37:22Z","title_canon_sha256":"24192fe3af7fb6adc07605ea05c5025e1c5c6b5c7d1c6266221e5c542b6a99e5"},"schema_version":"1.0","source":{"id":"1401.3302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3302","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3302v1","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3302","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"42FTM6CDWCOJ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"42FTM6CDWCOJCK5F","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"42FTM6CD","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:45795b9a038e013b272b6ac665895ef542842dcc4f1723607f62c0a12adafffc","target":"graph","created_at":"2026-05-18T03:02:18Z","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":"In connection with his interest in selfdistributive algebra, Richard Laver established two deep results with potential applications in low-dimensional topology, namely the existence of what is now known as the Laver tables and the well-foundedness of the standard ordering of positive braids. Here we present these results and discuss the way they could be used in topological applications.","authors_text":"Patrick Dehornoy (LMNO, PPS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-14T19:37:22Z","title":"Laver's results and low-dimensional topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3302","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:f73a7f81d2630ad65fddab9c4922467369885273a01b1a65380a5002128b3355","target":"record","created_at":"2026-05-18T03:02:18Z","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":"bbd8dbd7f1536c52a6036ee0108104c66e0334f5324e2eabfbc4f05c1ea3a560","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-14T19:37:22Z","title_canon_sha256":"24192fe3af7fb6adc07605ea05c5025e1c5c6b5c7d1c6266221e5c542b6a99e5"},"schema_version":"1.0","source":{"id":"1401.3302","kind":"arxiv","version":1}},"canonical_sha256":"e68b367843b09c912ba5987a018896824d399e61b9ba3e26dc647019d65b31b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e68b367843b09c912ba5987a018896824d399e61b9ba3e26dc647019d65b31b6","first_computed_at":"2026-05-18T03:02:18.861022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:18.861022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HeJgN/tgltjqE47axohGghzyib+HQ6PfYekExh4o4vC/4e9BXG/TCdcsUeLpf+81tOG8ou4tpnT6qSQ5EtohCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:18.861909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f73a7f81d2630ad65fddab9c4922467369885273a01b1a65380a5002128b3355","sha256:45795b9a038e013b272b6ac665895ef542842dcc4f1723607f62c0a12adafffc"],"state_sha256":"9a165778d1bb278dc006f83334ce3d20593ebf796ecfb9634cf841e0012623f9"}