Harman sieve and Lean-verified certificate for the \(n^{1.323}\) bound on the greatest prime factor of \(n^2+1\).
Manuscript, certified computations and data for "Sums of two squares with few prime factors via theta series of quaternary forms": level of distribution 2/5 for r(n)r(N-n) from Waibel's theta-series bound, giving Omega(n(N-n)) <= 9 and max side <= 6.
Manuscript, certified computations and data for "Recovering the level of distribution x^{1/2} for the orders of y² = x³ − x modulo p": the Iwaniec–Jiménez Urroz P₂ theorem holds as stated, and Xie's prime-power bounds improve to P₃ and ⌊2.05(ℓ−1)+1.2⌋.
Primes p ≤ N with N − p an almost prime sum of two squares (Ω ≤ 9): paper, semi-linear vector sieve with Richert weights and switching, and an interval-arithmetic certification script.
Prime quintuplets and the sextuplet boundary for Q(n)=n^47-(n-1)^47 (Titan Project, Part III). Exact Bateman-Horn singular series via Dirichlet L-functions mod 47; parameter-free prediction of 7 quintuplets / 0 sextuplets up to 2e11; first sextuplet expected near N*~1e13. Paper, data, scripts. v2 DOI 10.5281/zenodo.23178170
N = n₁ + n₂ with n₁, n₂ sums of two squares (or values of any class number one form) and Ω(n₁n₂) ≤ 11, max Ω(nᵢ) ≤ 8: paper, linear vector sieve with switching and Richert weights, interval-arithmetic certification.
Finite local sieves for shifted even squares, with exact CRT densities and prime-square extensions.
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