{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:44X33XSKD7K3KMYUXGKU3E7X7Q","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":"b7c8b9c3fabdb7176d0121a1ce7aacb0f40d7a265287abfac39e575360500e28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-29T19:40:50Z","title_canon_sha256":"f2f37e2b09262a34cfad05eceae9b0dcfc9eb5ec04c8a683a94f4a3ab6c8ec4d"},"schema_version":"1.0","source":{"id":"1705.10373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10373","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10373v1","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10373","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"44X33XSKD7K3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"44X33XSKD7K3KMYU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"44X33XSK","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:bfb01d94212a51ec7a53977d36a86b94068aad9e239d3c63ffeef26ef8ed4794","target":"graph","created_at":"2026-05-17T23:41:47Z","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":"Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\\{K_n\\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n) \\to 1$ as $n \\to \\infty$, then either the winding number of $K$ about $c$ is zero or the winding number equals the wrapping number. As a key application, if $\\{K_n\\}$ or the mirror twist family $\\{\\overline{K_n}\\}$ contains infinitely many tight fiber","authors_text":"Kenneth L. Baker, Kimihiko Motegi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-29T19:40:50Z","title":"Seifert vs slice genera of knots in twist families and a characterization of braid axes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10373","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":"sha256:56bac121d52c4b1c3ec7b7f78ba32d5df88237d98b425479202f3111442b232a","target":"record","created_at":"2026-05-17T23:41:47Z","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":"b7c8b9c3fabdb7176d0121a1ce7aacb0f40d7a265287abfac39e575360500e28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-29T19:40:50Z","title_canon_sha256":"f2f37e2b09262a34cfad05eceae9b0dcfc9eb5ec04c8a683a94f4a3ab6c8ec4d"},"schema_version":"1.0","source":{"id":"1705.10373","kind":"arxiv","version":1}},"canonical_sha256":"e72fbdde4a1fd5b53314b9954d93f7fc0231f916369fe7ad11b4a6912a6d9ec1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e72fbdde4a1fd5b53314b9954d93f7fc0231f916369fe7ad11b4a6912a6d9ec1","first_computed_at":"2026-05-17T23:41:47.216667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:47.216667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kePjioFuZp4zgipgW7GJwA3N81Od2tPW0vMqpbhwMW0yBhZ7HyCLw6Bvd+nX101pzzHgcwRHgrSu4/c9OEnFAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:47.217399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56bac121d52c4b1c3ec7b7f78ba32d5df88237d98b425479202f3111442b232a","sha256:bfb01d94212a51ec7a53977d36a86b94068aad9e239d3c63ffeef26ef8ed4794"],"state_sha256":"4b504bb923d0f821c13598abe4ea4cec0642f790cd0cb7cc5ad7a10960b41c79"}