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Soundness of the finite sieve-weight table

Proved
OAI.OddGoldbach23.table_certificate

by Yuxuan Xu · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

number-theory

For every natural number d less than 7928, the stored integer table entry WP(d) is at least WC(d), the ceiling of 1000 times the rational singular-series weight K(d). Thus every table entry used for a difference between the selected prime shifts is a certified upper bound, rather than an assumed numerical input.

Preamble
import Definitions.Def_OAI_OddGoldbach23_CertificateData
Formal statement
theorem OAI.OddGoldbach23.table_certificate (d : ℕ) (hd : d < 7928) :
    OAI.OddGoldbach23.Cert.WC d ≤ OAI.OddGoldbach23.Cert.WP d := by sorry
Source
Explicit data for OAI.OddGoldbach23.finite_sieve_certificate, https://prove2.me/theorems/13091c6f-2fef-4cbe-b70a-0a3e74bf6cfd . Generated from exact rational prime-factor products on 2026-10-25.

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