{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MWQWN7ONYFHYN7OM7WKX4KGM3M","short_pith_number":"pith:MWQWN7ON","schema_version":"1.0","canonical_sha256":"65a166fdcdc14f86fdccfd957e28ccdb0a69a5fcb5ad727747fb395c9fc87507","source":{"kind":"arxiv","id":"1107.2640","version":1},"attestation_state":"computed","paper":{"title":"Tangle sums and factorization of A-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Koya Shimokawa, Masaharu Ishikawa, Thomas W. Mattman","submitted_at":"2011-07-13T19:37:34Z","abstract_excerpt":"We show that there exist infinitely many examples of pairs of knots, K_1 and K_2, that have no epimorphism $\\pi_1(S^3\\setminus K_1) \\to \\pi_1(S^3\\setminus K_2)$ preserving peripheral structure although their A-polynomials have the factorization $A_{K_2}(L,M) \\mid A_{K_1}(L,M)$. Our construction accounts for most of the known factorizations of this form for knots with 10 or fewer crossings. In particular, we conclude that while an epimorphism will lead to a factorization of A-polynomials, the converse generally fails."},"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":"1107.2640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-07-13T19:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"72ac632c75ad2aa2b3afb7448d74995003cd5a5a7a81ae15a40e863e2de5a79e","abstract_canon_sha256":"39c52a1f002e171c7eb85c34a58231e03f40ccb0222eb1dd2001b45113788e16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:22.717113Z","signature_b64":"RGszyIA/wcb+tEyY1j2h07JGuCRan6SlyRS+Rth6nOqADYVS3D1k3Hut7DQ9t97Mb4aJPAKVD+r0012AuMbcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65a166fdcdc14f86fdccfd957e28ccdb0a69a5fcb5ad727747fb395c9fc87507","last_reissued_at":"2026-05-18T04:18:22.716592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:22.716592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tangle sums and factorization of A-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Koya Shimokawa, Masaharu Ishikawa, Thomas W. Mattman","submitted_at":"2011-07-13T19:37:34Z","abstract_excerpt":"We show that there exist infinitely many examples of pairs of knots, K_1 and K_2, that have no epimorphism $\\pi_1(S^3\\setminus K_1) \\to \\pi_1(S^3\\setminus K_2)$ preserving peripheral structure although their A-polynomials have the factorization $A_{K_2}(L,M) \\mid A_{K_1}(L,M)$. Our construction accounts for most of the known factorizations of this form for knots with 10 or fewer crossings. In particular, we conclude that while an epimorphism will lead to a factorization of A-polynomials, the converse generally fails."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2640","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":"1107.2640","created_at":"2026-05-18T04:18:22.716680+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.2640v1","created_at":"2026-05-18T04:18:22.716680+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2640","created_at":"2026-05-18T04:18:22.716680+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWQWN7ONYFHY","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWQWN7ONYFHYN7OM","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWQWN7ON","created_at":"2026-05-18T12:26:37.096874+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/MWQWN7ONYFHYN7OM7WKX4KGM3M","json":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M.json","graph_json":"https://pith.science/api/pith-number/MWQWN7ONYFHYN7OM7WKX4KGM3M/graph.json","events_json":"https://pith.science/api/pith-number/MWQWN7ONYFHYN7OM7WKX4KGM3M/events.json","paper":"https://pith.science/paper/MWQWN7ON"},"agent_actions":{"view_html":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M","download_json":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M.json","view_paper":"https://pith.science/paper/MWQWN7ON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.2640&json=true","fetch_graph":"https://pith.science/api/pith-number/MWQWN7ONYFHYN7OM7WKX4KGM3M/graph.json","fetch_events":"https://pith.science/api/pith-number/MWQWN7ONYFHYN7OM7WKX4KGM3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M/action/storage_attestation","attest_author":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M/action/author_attestation","sign_citation":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M/action/citation_signature","submit_replication":"https://pith.science/pith/MWQWN7ONYFHYN7OM7WKX4KGM3M/action/replication_record"}},"created_at":"2026-05-18T04:18:22.716680+00:00","updated_at":"2026-05-18T04:18:22.716680+00:00"}