{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:R44QXFOEH45PDQTN3ATSTWJR3I","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":"77e05d01c6dc7d558813038a04f6ae2a7eb19cbbf3e3dc1448c670084320a11f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-05T12:24:01Z","title_canon_sha256":"531499deef9f23cd77faf51840b7872918d2337d2119d1425f1482265f4908c4"},"schema_version":"1.0","source":{"id":"1206.0898","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0898","created_at":"2026-05-18T03:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0898v2","created_at":"2026-05-18T03:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0898","created_at":"2026-05-18T03:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"R44QXFOEH45P","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"R44QXFOEH45PDQTN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"R44QXFOE","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:d9b2710e67fbf9b2db922f4fc7744873160ef305a659a9802e12fe213e9702f9","target":"graph","created_at":"2026-05-18T03:10:00Z","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"},"paper":{"abstract_excerpt":"In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually independent in a sense. A new proof of the monotonic simplification theorem for the unknot is given. It is shown that a minimal rectangular diagram maximizes the Thurston--Bennequin number for the corresponding Legendrian links. Jones' conjecture about the invariance of the algebraic number of intersections of a minimal braid representing a fixed link type is proved.","authors_text":"Ivan Dynnikov, Maxim Prasolov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-05T12:24:01Z","title":"Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0898","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:f9c51a54115060274275b8ba352604539b694efaeb0749aef492e27a0b648a1a","target":"record","created_at":"2026-05-18T03:10:00Z","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":"77e05d01c6dc7d558813038a04f6ae2a7eb19cbbf3e3dc1448c670084320a11f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-05T12:24:01Z","title_canon_sha256":"531499deef9f23cd77faf51840b7872918d2337d2119d1425f1482265f4908c4"},"schema_version":"1.0","source":{"id":"1206.0898","kind":"arxiv","version":2}},"canonical_sha256":"8f390b95c43f3af1c26dd82729d931da22c573ae2c50ea32d3831d6e8c9aea9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f390b95c43f3af1c26dd82729d931da22c573ae2c50ea32d3831d6e8c9aea9f","first_computed_at":"2026-05-18T03:10:00.160395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:00.160395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVhCua5lqKEBud8d71PDXvSr+cCrm1DxkHLkmxKrOBrNO7kTRG8ZBEVkFO82CDggDOkZftnmzE+4Wcaqsul5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:00.161048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0898","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9c51a54115060274275b8ba352604539b694efaeb0749aef492e27a0b648a1a","sha256:d9b2710e67fbf9b2db922f4fc7744873160ef305a659a9802e12fe213e9702f9"],"state_sha256":"0f65cc25b0559675f6c9fec0ddafe55fa0c95482172d5fb3c658c0e96ff10f20"}