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If K = Q, an explicit bound is 8 r g + 33 (g - 1) + 1.\n  The proof is based on Chabauty's method; the new ingredient is an estimate for the number of zeros of a logarithm in a p-adic `annulus' on the curve, which generalizes the standard bound on disks. The key observation is that for a p-adic field k, the set of k-points on C can be covered by a collection of disks and annul"},"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":"1307.1773","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-06T12:33:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0ac091f721558036e298da2b113179c26ead97f68fa5a40d57da618b157c0227","abstract_canon_sha256":"3366070f33c39844cd6f3cb8dc0bcf870c64bb3ad932b00e9fa96d2be994fe98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:03.195510Z","signature_b64":"wNYz7s+vdVDBuRO53FzIRQfE+k8PWAeOp4u2nn09ypucMPMUA/PLUkEMtNXt5MLfhL4qt5tfOUTgpDa42FrQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aba0d478b6fbec047a634f415c94860989fa02dce23e7e9d988368cfd3827a24","last_reissued_at":"2026-05-18T01:26:03.195030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:03.195030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Michael Stoll","submitted_at":"2013-07-06T12:33:02Z","abstract_excerpt":"We show that there is a bound depending only on g and [K:Q] for the number of K-rational points on a hyperelliptic curve C of genus g over a number field K such that the Mordell-Weil rank r of its Jacobian is at most g-3. 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