{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FFHZFXL4PTCQACGHI4HYE3AIWX","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":"c8555cc4b44a07cae05ccf3808856938b2649a523dae073841a8871c76ac1033","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-12-16T14:53:17Z","title_canon_sha256":"e47983fc0e8c99db952d12b2415460b93b19bcb1d8df4cc7ad90dd4270692fae"},"schema_version":"1.0","source":{"id":"1412.5024","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5024","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5024v3","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5024","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"pith_short_12","alias_value":"FFHZFXL4PTCQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FFHZFXL4PTCQACGH","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FFHZFXL4","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:659413940ba5ca71e66ca599ae4fd9d8930a23646d316411b48f0ba4df57cef9","target":"graph","created_at":"2026-05-18T00:09:42Z","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":"We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional topological surgery conjecture. The A-B slice problem, a reformulation of the surgery conjecture for free groups, is shown to admit a homotopy solution. We also exhibit a new collection of universal surgery problems, defined using ramifications of homotopically trivial links. More generally we show how n-Engel relations arise from higher order double points of surfaces in 4-space.","authors_text":"Michael Freedman, Vyacheslav Krushkal","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-12-16T14:53:17Z","title":"Engel relations in 4-manifold topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5024","kind":"arxiv","version":3},"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":"sha256:4574c73bf7eb8cdf06bfaf8276f7ecbfc7c92fba86db069d9cca2e5a6dbf4d6b","target":"record","created_at":"2026-05-18T00:09:42Z","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":"c8555cc4b44a07cae05ccf3808856938b2649a523dae073841a8871c76ac1033","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-12-16T14:53:17Z","title_canon_sha256":"e47983fc0e8c99db952d12b2415460b93b19bcb1d8df4cc7ad90dd4270692fae"},"schema_version":"1.0","source":{"id":"1412.5024","kind":"arxiv","version":3}},"canonical_sha256":"294f92dd7c7cc50008c7470f826c08b5dc1f3e42636289358f6b59039bed8ff4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"294f92dd7c7cc50008c7470f826c08b5dc1f3e42636289358f6b59039bed8ff4","first_computed_at":"2026-05-18T00:09:42.584161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:42.584161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vfpAPLuUKhVHRoLio6ej3DsFVDhrqAjoGhbQefptv8F9LtwY/8Z/Abc2XPRCeul0xIcZoKitRsRr4L3izN4EBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:42.584876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5024","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4574c73bf7eb8cdf06bfaf8276f7ecbfc7c92fba86db069d9cca2e5a6dbf4d6b","sha256:659413940ba5ca71e66ca599ae4fd9d8930a23646d316411b48f0ba4df57cef9"],"state_sha256":"ae64ba8a2735efba59838708cff69bbbcc1e584328fb53c8cc89b29223ca5b25"}