avi

Solved 3

• Theorem 4.2 — resampling identity $\mathcal T\mathcal P_s\mathcal F_s=\mathcal P_t\mathcal F_t\mathcal S$Proved

  Oct 2026

• Lemma 4.6 — $\|\mathcal E\|<2.01\,e^{-\pi\alpha^2\theta/2}<2^{-\alpha^2\theta}$Proved

  Oct 2026

• Lemma 4.5 — $\|\mathcal S\|<1+\alpha^{-1}$Proved

  Oct 2026

Posted 15

• HvdH Proposition 5.4: $M(n) < \frac{12T}{r}M(3rp) + O(n\log n)$Open

  Oct 2026

• Rosser–Schoenfeld upper bound $\vartheta(y) < y + y/(2\log y)$ for $y \ge 563$Open

  Oct 2026

• Corollary 5.5 — $\mathsf T(n)<\frac{1728}{d-1/2}\mathsf T(3rp)+O(1)$ for the recursive multiplication algorithmOpen

  Oct 2026

• Rosser–Schoenfeld: $|\vartheta(y)-y|<y/(2\log y)$ for $y\ge 563$Open

  Oct 2026

• Jain round six — multiplication in time $O(n(\lg n)^{1-\kappa})$, $\kappa=3666565558019/10^{17}>2^{-15}$Open

  Oct 2026

• Colkitt — multiplication in time $O(n(\lg n)^{1-\kappa})$, $\kappa=2^{-30}$Open

  Oct 2026

• OpenAI Theorem 1 — multiplication in time $O(n(\lg n)^{1-\kappa})$, $\kappa=2^{-182}$Open

  Oct 2026

• Theorem 1.1 — integer multiplication in time $O(n\log n)$Open

  Oct 2026

• Theorem 1.1 in the $\kappa$-framework — $\mathrm{KappaBound}(0)$: multiplication in time $O(n\lg n)$Open

  Oct 2026

• Lemma 5.1 — at least $\eta x/(2\log x)$ primes in $((1-2\eta)x,(1-\eta)x]$Open

  Oct 2026

• Lemma 4.6 — $\|\mathcal E\|<2.01\,e^{-\pi\alpha^2\theta/2}<2^{-\alpha^2\theta}$Proved

  Oct 2026

• Lemma 4.5 — $\|\mathcal S\|<1+\alpha^{-1}$Proved

  Oct 2026

• Theorem 4.2 — resampling identity $\mathcal T\mathcal P_s\mathcal F_s=\mathcal P_t\mathcal F_t\mathcal S$Proved

  Oct 2026

• Gaussian resampling maps $\mathcal S,\mathcal T,\mathcal P_s,\mathcal P_t,\mathcal C,\mathcal D,\mathcal N,\mathcal E$ of Harvey–van der HoevenDefinition

  Oct 2026

• Multitape Turing machines and exact integer multiplication in time $O(g(n))$Definition

  Oct 2026