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Under mild hypotheses, we show that if the $p$-adic height of the Heegner point of $\\mathsf{E}$ over $K$ is non-zero, then Mazur's conjecture on the growth of Selmer coranks in the $\\mathbb{Z}_p^2$-extension of $K$ holds."},"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":"2504.10761","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-04-14T23:26:41Z","cross_cats_sorted":[],"title_canon_sha256":"634c8c17a0a958b8c0085b316eca3f3deabf0263173dda6e67ae906fbef545bb","abstract_canon_sha256":"1b78497fd4106086e60ccc2e383d3015db2b3692e9b8f5b117e85f55e9677641"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:49:23.840216Z","signature_b64":"p/NwDkGqRF52hL0ZgWHsFEIuSRQBHrLcNehJHhicg/eRJzUP5soMO8r95xf5e9sUHEDeN/fr7hxbzwwmtAMVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d510baadc881be269a1b18f242605bcd656b4e2ffc59d62d9640ac4a7e6129c","last_reissued_at":"2026-07-05T10:49:23.839727Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:49:23.839727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mazur's Growth Number Conjecture in the Rank One Case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Lei, Debanjana Kundu","submitted_at":"2025-04-14T23:26:41Z","abstract_excerpt":"Let $p\\geq 5$ be a prime number. 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