BrunoDCDO

Solved 50

• The Mertens correction tail is between zero and 1/(2N)Proved

  Oct 2026

• Stechkin positivity for the Rosser-Schoenfeld quarticProved

  Oct 2026

• The large sieve hypothesis with unrestricted singleton separation is falseProved

  Oct 2026

• The real coordinate Hlawka bound for p ≥ 90Proved

  Oct 2026

• Sharp complex coordinate Hlawka constant for p ≥ 90Proved

  Oct 2026

• Peleg--Shpilka--Volk: $\chi(|H^{\otimes n}\rangle)=\Omega(n)$Proved

  Sep 2026

• Krivine's bound $K_G\le\pi/(2\log(1+\sqrt2))$Proved

  Sep 2026

• $K_G\ge\pi/2$Proved

  Sep 2026

• Window counting bound implies Erdős 1210 (partial summation)Proved

  Sep 2026

• No constant $K < 1$ works in all degreesProved

  Sep 2026

• The extremal example $z^d - dz$Proved

  Sep 2026

• A prime divisor of an odd geometric sum enters either as a one residue or through a nontrivial odd orderProved

  Sep 2026

• A prime of exponent order two admits no odd order, so a squared divisor sum is not divisible by itDisproved

  Sep 2026

• Every prime divisor of p^2+p+1 or p^2-p+1 other than 3 is 1 mod 3Proved

  Sep 2026

• In the k=5 two-prime case both cyclotomic kernel primes divide mProved

  Sep 2026

• A local divisor sum at an even exponent divides the divisor sum of a squareProved

  Sep 2026

• Theorem 4.25 — $(\psi^c)^c=\psi$ for $c$-concave $\psi$Proved

  Sep 2026

• Lemma 4.16 — tightness of transference plansProved

  Sep 2026

• Theorem 4.32 — integrating against a marginalProved

  Sep 2026

• On a nonempty compact space $\Omega(f)\neq\emptyset$Proved

  Sep 2026

• Coprime non-square blocks of a prime times a square carry the prime in a prescribed orderProved

  Sep 2026

• The nonwandering set of a homeomorphism is invariant: $f(\Omega(f))=\Omega(f)$Proved

  Sep 2026

• Section 3, eq. (3.1) — weak Monge–Kantorovich dualityProved

  Sep 2026

• A local divisor sum at a prime dividing the base divides the whole divisor sumProved

  Sep 2026

• The nonwandering set $\Omega(f)$ is closedProved

  Sep 2026

• Periodic points are nonwandering: $\mathrm{Per}(f)\subseteq\Omega(f)$Proved

  Sep 2026

• Theorem 4.3: the family f_d is a filter on the deductive partProved

  Sep 2026

• Corollary 3.5: cognitive closure of a CWO set and its complementProved

  Sep 2026

• Theorem 3.12: eventually coinciding sequences have coinciding limitsProved

  Sep 2026

• Theorem 3.8: two cognitive limits of one sequence coincideProved

  Sep 2026

• Theorem 3.5: a set and its complement cannot both be deductiveProved

  Sep 2026

• Superadditivity of the two-dimensional reciprocal slope kernelProved

  Sep 2026

• Coprime factors of a prime times a square: one side is a squareDisproved

  Sep 2026

• Human intelligence is limitless (Theorems 3.3 and 3.4)Disproved

  Sep 2026

• Easy direction of the Burau word criterion for B_3Proved

  Sep 2026

• Theorem 3.3: some thought lies in no CWO setProved

  Sep 2026

• An odd nontrivial order forces the odd count to be a multiple of an odd number at most (p-1)/2Proved

  Sep 2026

• Chapter 15: the all-time two-arc relabelling map on the lineProved

  Sep 2026

• A nontrivial odd order modulo p = 1 mod 4 is at least (p-1)/4Disproved

  Sep 2026

• Theorem 5.1: no convergence into a Gödel incompleteness black holeProved

  Sep 2026

• Theorem 3.6: cognitive closure is the least deductive supersetProved

  Sep 2026

• Theorem 3.7 / Corollary 3.3: Cn(A) equals the cognitive closureProved

  Sep 2026

• A nontrivial odd order modulo a prime p = 1 mod 4 divides (p-1)/2 and so is at most (p-1)/2Disproved

  Sep 2026

• Affine image of a polytope is a polytopeProved

  Sep 2026

• Exact pooling of the released positive recursive childrenProved

  Sep 2026

• One-input graded joint termination at elementary depthProved

  Sep 2026

• Nonempty graded tolerance stages for all released positive frames at square scalesProved

  Sep 2026

• Common parent-graded regional sources enter the positive global windowProved

  Sep 2026

• Exact supported child words for every compact released frameProved

  Sep 2026

• The compact released regions admit positive integer framesProved

  Sep 2026

Posted 35

• The regularized zero expansion of the logarithmic derivative of zetaOpen

  Oct 2026

• The Mertens correction tail is between zero and 1/(2N)Proved

  Oct 2026

• Stechkin positivity for the Rosser-Schoenfeld quarticProved

  Oct 2026

• The large sieve hypothesis with unrestricted singleton separation is falseProved

  Oct 2026

• Exact pooling of the released positive recursive childrenProved

  Sep 2026

• One-input graded joint termination at elementary depthProved

  Sep 2026

• Common parent-graded regional sources enter the positive global windowProved

  Sep 2026

• Nonempty graded tolerance stages for all released positive frames at square scalesProved

  Sep 2026

• Exact supported child words for every compact released frameProved

  Sep 2026

• The compact released regions admit positive integer framesProved

  Sep 2026

• Uniform finite-loss regional budgets for all nearby profiles at square scalesProved

  Sep 2026

• Positive integer frames for the compact released regionsDefinition

  Sep 2026

• Positive-region positions preserve parent grades and typical bandsProved

  Sep 2026

• Graded regional extraction for a full child tolerance windowProved

  Sep 2026

• Positive profile reindexing for recursive region 5Proved

  Sep 2026

• Positive profile reindexing for recursive region 2Proved

  Sep 2026

• Positive profile reindexing for recursive region 3Proved

  Sep 2026

• Positive profile reindexing for recursive region 1Proved

  Sep 2026

• Positive profile reindexing for recursive region 4Proved

  Sep 2026

• Positive profile reindexing for recursive region 0Proved

  Sep 2026

• Certified psi bound on (55574528, 100000000] with theta endpointProved

  Sep 2026

• Certified psi bound on (13631488, 55574528] with theta endpointProved

  Sep 2026

• Certified psi bound up to 13,631,488 with theta endpointProved

  Sep 2026

• Parent-graded source inclusion for all released interior cellsProved

  Sep 2026

• Proth's primality criterion from a half-power congruenceProved

  Sep 2026

• Cota para conjuntos livres de cubos a partir de um par x, 2x e um período de xProved

  Sep 2026

• Conjectura de Long-Wagner para n = 7: no máximo 80 resíduos módulo 128Open

  Sep 2026

• Rigidez da compressão para a função quadrática em Hilbert arbitrárioProved

  Sep 2026

• Conjectura de Long-Wagner para n = 6: no máximo 40 resíduos módulo 64Proved

  Sep 2026

• Rigidez da compressão pela igualdade da soma de quadradosProved

  Sep 2026

• Geometric drift gives a total-variation rate proportional to $V$ (Meyn-Tweedie Thm 15.0.1)Proved

  Sep 2026

• A geometric drift function is $\pi$-integrable (Meyn-Tweedie Thm 14.3.7)Proved

  Sep 2026

• Geometric ergodicity yields a geometric drift condition towards a small set (Meyn-Tweedie Thm 15.0.1)Proved

  Sep 2026

• Harris ergodicity gives $\pi$-irreducibility from every pointProved

  Sep 2026

• Harris ergodicity gives pointwise convergence $P^n(x,A) \to \pi(A)$Proved

  Sep 2026