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The new conjecture implies that, for each fixed $y \\in \\mathbb{N}$, $$ \\limsup_{x \\to \\infty} \\frac{W(x,y)\\log\\log x}{\\log x} = 1. $$"},"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":"2607.07641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-08T17:00:03Z","cross_cats_sorted":[],"title_canon_sha256":"ee4632047a98ff8c1f52143d216ae91f0486362118592a902d35887cbbf0cadd","abstract_canon_sha256":"f0c0a85708d286841e8f58b706cfb168851d49b71999de1da7892319e11e3935"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:37.748945Z","signature_b64":"In2meSkV26CmugwjFKDgBzP1kykAJ6DbXQ9Wv+XE8pV+BmUXOaD/M0jF9UG5R1mzESXJWRudBQ2yIdvaMayxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c2823157d5d7a4b968a5908e419654da843c94d723e3d8ad44d73c087af34ab","last_reissued_at":"2026-07-09T01:20:37.748523Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:37.748523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $abc$ Conjecture Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Letendre","submitted_at":"2026-07-08T17:00:03Z","abstract_excerpt":"We propose a new abc-type conjecture. 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