{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5A6FDLLULWE2XUOWRBJOJQZRZC","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":"e3336677a37dacecb2b727b1e696438f1772c8bc7369adaf2cb284e4d77bbfdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-18T15:37:30Z","title_canon_sha256":"a55209a0a74883a01731b4d670b8bd2819e55af8fb44bb4ae5100ccd64a43c68"},"schema_version":"1.0","source":{"id":"1902.06616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06616","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06616v1","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06616","created_at":"2026-05-17T23:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"5A6FDLLULWE2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5A6FDLLULWE2XUOW","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5A6FDLLU","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:77f68c5247be5f78e270269b27c2fa2d19a4043884a34fd9694f343c852ecff7","target":"graph","created_at":"2026-05-17T23:53:44Z","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":"Let $K$ be a tame knot embedded in $\\mathbf{S}^3$. We address the problem of finding the minimal degree non-cyclic cover $p:X \\rightarrow \\mathbf{S}^3 \\smallsetminus K$. When $K$ has non-trivial Alexander polynomial we construct finite non-abelian representations $\\rho:\\pi_1\\left(\\mathbf{S}^3 \\smallsetminus K\\right) \\rightarrow G$, and provide bounds for the order of $G$ in terms of the crossing number of $K$ which is an improvement on a result of Broaddus in this case. Using classical covering space theory along with the theory of Alexander stratifications we establish an upper and lower boun","authors_text":"Timothy Morris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-18T15:37:30Z","title":"Some non-abelian covers of knots with non-trivial Alexander polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06616","kind":"arxiv","version":1},"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:de690ad339b04d0ab6f2c130befbe59319f85d54534e66104d227685e70bb5c0","target":"record","created_at":"2026-05-17T23:53:44Z","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":"e3336677a37dacecb2b727b1e696438f1772c8bc7369adaf2cb284e4d77bbfdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-18T15:37:30Z","title_canon_sha256":"a55209a0a74883a01731b4d670b8bd2819e55af8fb44bb4ae5100ccd64a43c68"},"schema_version":"1.0","source":{"id":"1902.06616","kind":"arxiv","version":1}},"canonical_sha256":"e83c51ad745d89abd1d68852e4c331c89bf230c3c8c636dce07cb254c5343464","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e83c51ad745d89abd1d68852e4c331c89bf230c3c8c636dce07cb254c5343464","first_computed_at":"2026-05-17T23:53:44.966733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:44.966733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M3kvrNDeJ8PQKgPmPOunqfUp3Jr0r6zq4bMq+H4ToGT3qKXiXMuR4gVnhrCG1cf5FU3qEyb4/w4lHpa/sePkDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:44.967117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de690ad339b04d0ab6f2c130befbe59319f85d54534e66104d227685e70bb5c0","sha256:77f68c5247be5f78e270269b27c2fa2d19a4043884a34fd9694f343c852ecff7"],"state_sha256":"f0fb5853e11d73e273d97dbb0f314088c0a300a549ebd5e1620d74b59d0fb766"}