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This gives counterexamples to a conjecture of Morimoto and Moriah on tunnel number under connected sum and meridionally primitive knots."},"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":"1310.5054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-18T15:18:01Z","cross_cats_sorted":[],"title_canon_sha256":"987ada890680f94cf430605f5d8f6be62d790b2455b2a9532e51235bbfda7387","abstract_canon_sha256":"a75d3fca39b74ede13d87627588a114eaded6da0a07547fd16591f11b00a4c4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:32.777009Z","signature_b64":"uXWYWlgvCUAC/bIz12aUqIR5P/18rXW609J60bUy+9g629KelKx3YZPcjbZC5kakSF03cwx0O6qu/gJP6lEjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"004a299c2b819f8b25053d3f5888992c7fcc77d1ccb6b58282683f698f6996cd","last_reissued_at":"2026-05-18T03:09:32.776157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:32.776157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the degeneration of tunnel numbers under connected sum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ruifeng Qiu, Tao Li","submitted_at":"2013-10-18T15:18:01Z","abstract_excerpt":"We show that, for any integer $n\\ge 3$, there is a prime knot $k$ such that (1) $k$ is not meridionally primitive, and (2) for every $m$-bridge knot $k'$ with $m\\leq n$, the tunnel numbers satisfy $t(k\\# k')\\le t(k)$. 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