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Whereas, Yamada gives an alternative definition of rational balls, $A_{m,n}$, bounding $L(p^2,pq-1)$ by their handlebody decompositions alone. We show that these two families coincide - answering a question of Kadokami and Yamada. To that end, we show that each $A_{m,n}$ admits a Stein filling of the \"st"},"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":"1406.1575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-06T03:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"bd248b88f29ed575dce4ef3381b5ed2ae356e9fc4d17ba541010e3d341b9b705","abstract_canon_sha256":"c24c2da2c8bcbb7e8582b94e62d01ef6bc61e08a507195dd3a0f4abefccce23d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:22.207933Z","signature_b64":"zRTlbIuPtd97DN/s64SRJJhpM5TUGHW9l70YxGtMRh39rTZVs4rIdfen0Lnjqigcl+sIYGHxq2sdjJHWollACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"329e7c0e5716f340c045bf0a5551910ccb8461ec9a612a4790e758fde321a7a5","last_reissued_at":"2026-05-18T02:50:22.207263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:22.207263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Handlebody Structures of Rational Balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Luke Williams","submitted_at":"2014-06-06T03:27:29Z","abstract_excerpt":"It is known that for coprime integers $p>q\\geq 1$, the lens space $L(p^2,pq-1)$ bounds a rational ball, $B_{p,q}$, arising as the 2-fold branched cover of a (smooth) slice disk in $B^4$ bounding the associated 2-bridge knot. 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