docs(formalization.yaml): cite Maynard Theorem 1.3 for the 600 bound - #8
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docs(formalization.yaml): cite Maynard Theorem 1.3 for the 600 bound#8morluto wants to merge 1 commit into
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The formal theorem bombieriVinogradov_implies_prime_gap_le_600 is the
Bombieri-Vinogradov-conditional bound on consecutive prime gaps, which is
Maynard's Theorem 1.3. Theorem 1.4 assumes level of distribution for every
theta < 1 (Elliott-Halberstam) and concerns liminf(p_{n+2} - p_n), so the
previous 'Theorem 1.4, second inequality' attribution matched neither the
hypothesis nor the conclusion of what is formalised.
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Fixes #7
What
Corrects the Maynard citation for
bombieriVinogradov_implies_prime_gap_le_600from "Theorem 1.4, second inequality" to "Theorem 1.3" in both places it appears:sources[].locationalignment.statements[].sourceWhy
The formalized theorem assumes$\theta$ for every $\theta<1$ (Elliott–Halberstam strength) and its second inequality bounds {n+2}-p_n$ — a stronger hypothesis and a different conclusion, so the previous attribution misdescribed the result in the registry metadata.
BombieriVinogradovand bounds consecutive gaps {n+1}-p_n$. That is precisely Maynard's Theorem 1.3 (Small gaps between primes, Annals 181(1):383–413). Theorem 1.4 instead assumes level of distributionThe implemented proof also matches Theorem 1.3's route (admissible 105-tuple of diameter 600, {105}>4$, BV supplying every$\theta<1/2$ ).
Validation
v0.4(checked programmatically).