{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JDB6Y652FL5TCNX4I3AF6THSMH","short_pith_number":"pith:JDB6Y652","schema_version":"1.0","canonical_sha256":"48c3ec7bba2afb3136fc46c05f4cf261df19c41e2327a4b18d89a5828bd11286","source":{"kind":"arxiv","id":"1810.03502","version":1},"attestation_state":"computed","paper":{"title":"The unbearable hardness of unknotting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Arnaud de Mesmay, Eric Sedgwick, Martin Tancer, Yo'av Rieck","submitted_at":"2018-10-08T14:47:41Z","abstract_excerpt":"We prove that deciding if a diagram of the unknot can be untangled using at most $k$ Riedemeister moves (where $k$ is part of the input) is NP-hard. We also prove that several natural questions regarding links in the $3$-sphere are NP-hard, including detecting whether a link contains a trivial sublink with $n$ components, computing the unlinking number of a link, and computing a variety of link invariants related to four-dimensional topology (such as the $4$-ball Euler characteristic, the slicing number, and the $4$-dimensional clasp number)."},"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":"1810.03502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-10-08T14:47:41Z","cross_cats_sorted":[],"title_canon_sha256":"a2604ea58409c68d5d3cb84f20abf4d3d775e753da75ca8faa895f62f33fe4aa","abstract_canon_sha256":"14f70f27f28968967afc055e49534ca46e34c6e32051f9b99967bf3e1913c032"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:51.099282Z","signature_b64":"kuHunrJsOYQuJH9qjqoQa5DyhRa5lJBSEOGIPhitJusPuoM5QuqqBoXM25p070nJ97STt7IGFWb4EQVhVX0HBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48c3ec7bba2afb3136fc46c05f4cf261df19c41e2327a4b18d89a5828bd11286","last_reissued_at":"2026-05-18T00:03:51.098516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:51.098516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The unbearable hardness of unknotting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Arnaud de Mesmay, Eric Sedgwick, Martin Tancer, Yo'av Rieck","submitted_at":"2018-10-08T14:47:41Z","abstract_excerpt":"We prove that deciding if a diagram of the unknot can be untangled using at most $k$ Riedemeister moves (where $k$ is part of the input) is NP-hard. We also prove that several natural questions regarding links in the $3$-sphere are NP-hard, including detecting whether a link contains a trivial sublink with $n$ components, computing the unlinking number of a link, and computing a variety of link invariants related to four-dimensional topology (such as the $4$-ball Euler characteristic, the slicing number, and the $4$-dimensional clasp number)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03502","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":"1810.03502","created_at":"2026-05-18T00:03:51.098642+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.03502v1","created_at":"2026-05-18T00:03:51.098642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03502","created_at":"2026-05-18T00:03:51.098642+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDB6Y652FL5T","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDB6Y652FL5TCNX4","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDB6Y652","created_at":"2026-05-18T12:32:31.084164+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/JDB6Y652FL5TCNX4I3AF6THSMH","json":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH.json","graph_json":"https://pith.science/api/pith-number/JDB6Y652FL5TCNX4I3AF6THSMH/graph.json","events_json":"https://pith.science/api/pith-number/JDB6Y652FL5TCNX4I3AF6THSMH/events.json","paper":"https://pith.science/paper/JDB6Y652"},"agent_actions":{"view_html":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH","download_json":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH.json","view_paper":"https://pith.science/paper/JDB6Y652","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.03502&json=true","fetch_graph":"https://pith.science/api/pith-number/JDB6Y652FL5TCNX4I3AF6THSMH/graph.json","fetch_events":"https://pith.science/api/pith-number/JDB6Y652FL5TCNX4I3AF6THSMH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH/action/storage_attestation","attest_author":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH/action/author_attestation","sign_citation":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH/action/citation_signature","submit_replication":"https://pith.science/pith/JDB6Y652FL5TCNX4I3AF6THSMH/action/replication_record"}},"created_at":"2026-05-18T00:03:51.098642+00:00","updated_at":"2026-05-18T00:03:51.098642+00:00"}