{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NVIAS4SOC2CAZE4ZX7KC4UZ4QF","short_pith_number":"pith:NVIAS4SO","schema_version":"1.0","canonical_sha256":"6d5009724e16840c9399bfd42e533c814fdebd2e5adee8162d819c79b5707bc5","source":{"kind":"arxiv","id":"1412.3874","version":3},"attestation_state":"computed","paper":{"title":"Width of a satellite knot and its companion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Qilong Guo, Zhenkun Li","submitted_at":"2014-12-12T03:17:12Z","abstract_excerpt":"In the paper we prove the conjecture by Alexander Zupan that $w(K) \\geqslant n^2w(J)$ where w denote the width and $K$ and $J$ are satellite knot and its companion with winding number $n$. Also we proved that for satellite knot with braid pattern, the equality holds."},"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":"1412.3874","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-12-12T03:17:12Z","cross_cats_sorted":[],"title_canon_sha256":"49eac515da8d1c7a938d94a47a69bd70983a7bd1dbfef9ca66ead0c5b4a28965","abstract_canon_sha256":"a5f9afd85fd91d46e6f833ee677963a83c20ab8977ce30abd0637bffbbae184c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:00.686105Z","signature_b64":"iTVA9NvYoyvbPnBKzQDovEBFqR+5RyUx/qXwXBEPT2pOco9khnkH6Di2Uga0OnwT8Cl3ew8SviPX8eB9k/yODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d5009724e16840c9399bfd42e533c814fdebd2e5adee8162d819c79b5707bc5","last_reissued_at":"2026-05-18T00:21:00.685610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:00.685610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Width of a satellite knot and its companion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Qilong Guo, Zhenkun Li","submitted_at":"2014-12-12T03:17:12Z","abstract_excerpt":"In the paper we prove the conjecture by Alexander Zupan that $w(K) \\geqslant n^2w(J)$ where w denote the width and $K$ and $J$ are satellite knot and its companion with winding number $n$. Also we proved that for satellite knot with braid pattern, the equality holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3874","kind":"arxiv","version":3},"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":"1412.3874","created_at":"2026-05-18T00:21:00.685682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.3874v3","created_at":"2026-05-18T00:21:00.685682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3874","created_at":"2026-05-18T00:21:00.685682+00:00"},{"alias_kind":"pith_short_12","alias_value":"NVIAS4SOC2CA","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NVIAS4SOC2CAZE4Z","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NVIAS4SO","created_at":"2026-05-18T12:28:41.024544+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/NVIAS4SOC2CAZE4ZX7KC4UZ4QF","json":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF.json","graph_json":"https://pith.science/api/pith-number/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/graph.json","events_json":"https://pith.science/api/pith-number/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/events.json","paper":"https://pith.science/paper/NVIAS4SO"},"agent_actions":{"view_html":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF","download_json":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF.json","view_paper":"https://pith.science/paper/NVIAS4SO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.3874&json=true","fetch_graph":"https://pith.science/api/pith-number/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/graph.json","fetch_events":"https://pith.science/api/pith-number/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/action/storage_attestation","attest_author":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/action/author_attestation","sign_citation":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/action/citation_signature","submit_replication":"https://pith.science/pith/NVIAS4SOC2CAZE4ZX7KC4UZ4QF/action/replication_record"}},"created_at":"2026-05-18T00:21:00.685682+00:00","updated_at":"2026-05-18T00:21:00.685682+00:00"}