{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CLHECKG3ZXZUKLX4HL2RFQZTJ4","short_pith_number":"pith:CLHECKG3","schema_version":"1.0","canonical_sha256":"12ce4128dbcdf3452efc3af512c3334f151429a71b76534811115093c997becd","source":{"kind":"arxiv","id":"1901.09778","version":1},"attestation_state":"computed","paper":{"title":"A Diagrammatic Approach for Determining the Braid Index of Alternating Links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Claus Ernst, Gabor Hetyei, Pengyu Liu, Yuanan Diao","submitted_at":"2019-01-28T16:27:09Z","abstract_excerpt":"It is well known that the braid index of a link equals the minimum number of Seifert circles among all link diagrams representing it. For a link with a reduced alternating diagram $D$, $s(D)$, the number of Seifert circles in $D$, equals the braid index $\\textbf{b}(D)$ of $D$ if $D$ contains no {\\em lone crossings} (a crossing in $D$ is called a {\\em lone crossing} if it is the only crossing between two Seifert circles in $D$). If $D$ contains lone crossings, then $\\textbf{b}(D)$ is strictly less than $s(D)$. However in general it is not known how $s(D)$ is related to $\\textbf{b}(D)$. In this "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1901.09778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-01-28T16:27:09Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"21fd4138ef16c409d95a250a6897fc74ebd4efb348291024c35f7eb6169943fe","abstract_canon_sha256":"e8f2a2822c93a1c18d00f6d653dad0f9e8befe14249870d349e590437b1ad2a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:23.890984Z","signature_b64":"juu920Taf/v8RHE+3zHGxbbrMfL85GR+KsFhwvfvI1W/0ex/FWTZSHrbA3ftu/eXV8fW4YBOwLFrF1+e0KRwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12ce4128dbcdf3452efc3af512c3334f151429a71b76534811115093c997becd","last_reissued_at":"2026-05-17T23:55:23.890595Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:23.890595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Diagrammatic Approach for Determining the Braid Index of Alternating Links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Claus Ernst, Gabor Hetyei, Pengyu Liu, Yuanan Diao","submitted_at":"2019-01-28T16:27:09Z","abstract_excerpt":"It is well known that the braid index of a link equals the minimum number of Seifert circles among all link diagrams representing it. For a link with a reduced alternating diagram $D$, $s(D)$, the number of Seifert circles in $D$, equals the braid index $\\textbf{b}(D)$ of $D$ if $D$ contains no {\\em lone crossings} (a crossing in $D$ is called a {\\em lone crossing} if it is the only crossing between two Seifert circles in $D$). If $D$ contains lone crossings, then $\\textbf{b}(D)$ is strictly less than $s(D)$. However in general it is not known how $s(D)$ is related to $\\textbf{b}(D)$. In this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09778","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1901.09778","created_at":"2026-05-17T23:55:23.890657+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.09778v1","created_at":"2026-05-17T23:55:23.890657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09778","created_at":"2026-05-17T23:55:23.890657+00:00"},{"alias_kind":"pith_short_12","alias_value":"CLHECKG3ZXZU","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"CLHECKG3ZXZUKLX4","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"CLHECKG3","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4","json":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4.json","graph_json":"https://pith.science/api/pith-number/CLHECKG3ZXZUKLX4HL2RFQZTJ4/graph.json","events_json":"https://pith.science/api/pith-number/CLHECKG3ZXZUKLX4HL2RFQZTJ4/events.json","paper":"https://pith.science/paper/CLHECKG3"},"agent_actions":{"view_html":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4","download_json":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4.json","view_paper":"https://pith.science/paper/CLHECKG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.09778&json=true","fetch_graph":"https://pith.science/api/pith-number/CLHECKG3ZXZUKLX4HL2RFQZTJ4/graph.json","fetch_events":"https://pith.science/api/pith-number/CLHECKG3ZXZUKLX4HL2RFQZTJ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4/action/storage_attestation","attest_author":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4/action/author_attestation","sign_citation":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4/action/citation_signature","submit_replication":"https://pith.science/pith/CLHECKG3ZXZUKLX4HL2RFQZTJ4/action/replication_record"}},"created_at":"2026-05-17T23:55:23.890657+00:00","updated_at":"2026-05-17T23:55:23.890657+00:00"}