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We focus on the second-order SU(3)-breaking quantity $[1 - f_+(0)]$, which is necessary to extract $|V_{us}|$ from $K_{\\ell 3}$ decays. For this quantity we show that it is possible to reach the percent precision which is the required one for a significant determination of $|V_{us}|$. The leading quenched chiral logarithms are corrected for by using analytic calculations in quenched chiral perturbation theory. Our final result, $f_+^{K^0\\pi^-}(0) = 0.960"},"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":"hep-ph/0403217","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2004-03-19T16:53:08Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"23ea73c438321be0475c36ca7e22ee426221e9dd6b2327740a797e4f3eedb195","abstract_canon_sha256":"fe73496488858cf2cade9145489078a7fe9b103f80013db8a1a2b6d416c6a8de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:48:09.661514Z","signature_b64":"N1t9rSrHC4Jap3AvFCvO7ahbZoGqSMOGGmRyXMZX4BIX3BBoBTbPSGD1xUwHhuGX08HKzsBE8E2N8ZZhQh2WAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a18aada679b00ad4865b0e0dcaa400985735241cd41847defda0f1905234403b","last_reissued_at":"2026-07-04T16:48:09.661106Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:48:09.661106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The K -> pi vector form factor at zero momentum transfer on the lattice","license":"","headline":"","cross_cats":["hep-lat"],"primary_cat":"hep-ph","authors_text":"C. 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