{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NF7AMSFYWRM7R47EOFB4M3RJJX","short_pith_number":"pith:NF7AMSFY","schema_version":"1.0","canonical_sha256":"697e0648b8b459f8f3e47143c66e294de5f522f9b9088eac4e24a7aa337e55de","source":{"kind":"arxiv","id":"2402.01129","version":3},"attestation_state":"computed","paper":{"title":"Satellite fully positive braid links are braided satellite of fully positive braid links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Tetsuya Ito","submitted_at":"2024-02-02T03:59:28Z","abstract_excerpt":"A link in $S^{3}$ is a fully positive braid link if it is the closure of a positive braid that contains at least one full-twist. We show that a fully positive braid link is a satellite link if and only if it is the satellite of a fully positive braid link $C$ such that the pattern is a positive braid that contains sufficiently many full twists, where the number of necessary full twists only depends on $C$. As an application, we give a characterization of the unknot by the property that certain braided satellite is a (fully) positive braid knot."},"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":"2402.01129","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-02-02T03:59:28Z","cross_cats_sorted":[],"title_canon_sha256":"fd8114e2d8b4754c7edbb4b9e2c5816be3a08ebede5ef737a74c7252258e2123","abstract_canon_sha256":"92f8ed17c70efef66b6bae431bf4d3478ad7385c14546c1752cdd00747244819"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:17:45.946717Z","signature_b64":"+Ui73glATjAsb9bHEhQ/P43XsAb5ppOz77V+W+haMlLhtoZCG+ekq1rCsepKNIqIo2JLnUDHizb1Q5dXFyljCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"697e0648b8b459f8f3e47143c66e294de5f522f9b9088eac4e24a7aa337e55de","last_reissued_at":"2026-07-05T10:17:45.946191Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:17:45.946191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Satellite fully positive braid links are braided satellite of fully positive braid links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Tetsuya Ito","submitted_at":"2024-02-02T03:59:28Z","abstract_excerpt":"A link in $S^{3}$ is a fully positive braid link if it is the closure of a positive braid that contains at least one full-twist. We show that a fully positive braid link is a satellite link if and only if it is the satellite of a fully positive braid link $C$ such that the pattern is a positive braid that contains sufficiently many full twists, where the number of necessary full twists only depends on $C$. As an application, we give a characterization of the unknot by the property that certain braided satellite is a (fully) positive braid knot."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.01129","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.01129/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2402.01129","created_at":"2026-07-05T10:17:45.946249+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.01129v3","created_at":"2026-07-05T10:17:45.946249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.01129","created_at":"2026-07-05T10:17:45.946249+00:00"},{"alias_kind":"pith_short_12","alias_value":"NF7AMSFYWRM7","created_at":"2026-07-05T10:17:45.946249+00:00"},{"alias_kind":"pith_short_16","alias_value":"NF7AMSFYWRM7R47E","created_at":"2026-07-05T10:17:45.946249+00:00"},{"alias_kind":"pith_short_8","alias_value":"NF7AMSFY","created_at":"2026-07-05T10:17:45.946249+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.20652","citing_title":"Hyperbolic knots with arbitrarily large torsion order in knot Floer homology","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX","json":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX.json","graph_json":"https://pith.science/api/pith-number/NF7AMSFYWRM7R47EOFB4M3RJJX/graph.json","events_json":"https://pith.science/api/pith-number/NF7AMSFYWRM7R47EOFB4M3RJJX/events.json","paper":"https://pith.science/paper/NF7AMSFY"},"agent_actions":{"view_html":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX","download_json":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX.json","view_paper":"https://pith.science/paper/NF7AMSFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.01129&json=true","fetch_graph":"https://pith.science/api/pith-number/NF7AMSFYWRM7R47EOFB4M3RJJX/graph.json","fetch_events":"https://pith.science/api/pith-number/NF7AMSFYWRM7R47EOFB4M3RJJX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX/action/storage_attestation","attest_author":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX/action/author_attestation","sign_citation":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX/action/citation_signature","submit_replication":"https://pith.science/pith/NF7AMSFYWRM7R47EOFB4M3RJJX/action/replication_record"}},"created_at":"2026-07-05T10:17:45.946249+00:00","updated_at":"2026-07-05T10:17:45.946249+00:00"}