{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:O6LADTEAME3MTJITFZG7HIIQJO","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":"bb2ba33032223b089cbb6e16dab3e585b9b064c133203e299b596a3fb81f13d9","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-01-12T18:03:53Z","title_canon_sha256":"9a586496a8dd5489b790f2e8d7aeb53113c2e8662918f7e7cad3b76ecb938bf1"},"schema_version":"1.0","source":{"id":"math/0401120","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401120","created_at":"2026-05-18T02:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401120v4","created_at":"2026-05-18T02:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401120","created_at":"2026-05-18T02:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"O6LADTEAME3M","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"O6LADTEAME3MTJIT","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"O6LADTEA","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:8a652f084aecbc867c36537b9dfd0dcfd57acf5bbec6b7d9edd5eb922adca4c7","target":"graph","created_at":"2026-05-18T02:50:10Z","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":"Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\\Phi (c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly simple JSJ decomposition then the complement of $K$ has a finite-sheeted, noncyclic cover with at most $\\Phi (c)$ sheets.","authors_text":"Nathan Broaddus","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-01-12T18:03:53Z","title":"Noncyclic covers of knot complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401120","kind":"arxiv","version":4},"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:e61efbf52575ce526189cb87129d94023b7062995e9295d1185816cfbb1c6915","target":"record","created_at":"2026-05-18T02:50:10Z","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":"bb2ba33032223b089cbb6e16dab3e585b9b064c133203e299b596a3fb81f13d9","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-01-12T18:03:53Z","title_canon_sha256":"9a586496a8dd5489b790f2e8d7aeb53113c2e8662918f7e7cad3b76ecb938bf1"},"schema_version":"1.0","source":{"id":"math/0401120","kind":"arxiv","version":4}},"canonical_sha256":"779601cc806136c9a5132e4df3a1104b811154ad45b065aee1873ba27e995794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"779601cc806136c9a5132e4df3a1104b811154ad45b065aee1873ba27e995794","first_computed_at":"2026-05-18T02:50:10.979562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:10.979562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/nkluC+uMjZPkn38EXmJ/6SjCqw14W6yUB9ExlRAI+WzF1Bnny6/WQoMOn5gSe2B+RdXsNk7wns946lrGeNqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:10.980095Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401120","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e61efbf52575ce526189cb87129d94023b7062995e9295d1185816cfbb1c6915","sha256:8a652f084aecbc867c36537b9dfd0dcfd57acf5bbec6b7d9edd5eb922adca4c7"],"state_sha256":"68289a38318bdc406e69ab1201ba298cdca800aefa20e050ac4b78dfe18e7c1b"}