{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7YKQIHF5C6TNN2BC5LTU5NAHB5","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":"9d0f5ceea5b4e08047202c2edf3b4a11e9d930bb919763dedb9db7895cf4aaa4","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-05T19:50:29Z","title_canon_sha256":"a301d26dc563ce31b7312e8598b4d77bcaf988a76f99dff67736f86f3c505672"},"schema_version":"1.0","source":{"id":"1605.01711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01711","created_at":"2026-05-18T00:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01711v1","created_at":"2026-05-18T00:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01711","created_at":"2026-05-18T00:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"7YKQIHF5C6TN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7YKQIHF5C6TNN2BC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7YKQIHF5","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:c833f4a3eab31756805d29d8c51339a9bb6a1f7be52ddf032f61d3024a211ac4","target":"graph","created_at":"2026-05-18T00:17:46Z","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 show that every quasipositive link has a quasipositive minimal braid representative, partially resolving a question posed by Orevkov. These quasipositive minimal braids are used to show that the maximal self-linking number of a quasipositive link is bounded below by the negative of the minimal braid index, with equality if and only if the link is an unlink. This implies that the only amphicheiral quasipositive links are the unlinks, answering a question of Rudolph's.","authors_text":"Kyle Hayden","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-05T19:50:29Z","title":"Minimal braid representatives of quasipositive links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01711","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:e2bfbf348b557512ed190980230e2eb1d4af5543f14add0435ca5f65b1d524da","target":"record","created_at":"2026-05-18T00:17:46Z","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":"9d0f5ceea5b4e08047202c2edf3b4a11e9d930bb919763dedb9db7895cf4aaa4","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-05T19:50:29Z","title_canon_sha256":"a301d26dc563ce31b7312e8598b4d77bcaf988a76f99dff67736f86f3c505672"},"schema_version":"1.0","source":{"id":"1605.01711","kind":"arxiv","version":1}},"canonical_sha256":"fe15041cbd17a6d6e822eae74eb4070f41a6ef5d854ff8ee77d5b32b255d8239","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe15041cbd17a6d6e822eae74eb4070f41a6ef5d854ff8ee77d5b32b255d8239","first_computed_at":"2026-05-18T00:17:46.504682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:46.504682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P70wWVmajQNlnyxsgUZCU92pE8iTLtUdktUhzwbK4/AQ0NXMjBfCtyMjl/bVctXKVx7oJ4vBXu1ZOeA47KOyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:46.505327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2bfbf348b557512ed190980230e2eb1d4af5543f14add0435ca5f65b1d524da","sha256:c833f4a3eab31756805d29d8c51339a9bb6a1f7be52ddf032f61d3024a211ac4"],"state_sha256":"e57f59449abeaea27c9dbdd037b2e37da47b1f961933a82d2142094ce498f5b0"}