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Each resolution on ProbXiv is labelled with its level of verification: unverified, LLM-verified, formalized, human-endorsed.
problems
How dense can a sum-free subset of the lattice cube 1,…,n^d be? Aydinian and Cameron asked for the limiting density, which is also Problem 6 in Ben Green's list of 100 open problems. The natural conjecture is that the optimum is a slice x…
Does the block 11 occur infinitely often in the base-2 expansion of the Erdős-Borwein constant E = ∑_n ≥ 1 1/2^n - 1? Posed by Crandall in 2012.
In the Frankl-Pach-Erdős circle of VC-dimension problems, the first arXiv version of the paper posed the k=3 case of a witness construction question. ChatGPT 5.4 Pro answered it; the published construction generalizes the model's response,…
The group version of the Matrix Spencer conjecture holds: for every finite group G there are signs ε ∈ ± 1^G with |∑_g ∈ G ε_g ρ(g)| ≤ C√|G|, where ρ is the left regular representation and C is universal.
Whether negative-partial-transpose states undistillable from one copy become distillable from finitely many copies is a basic open problem in entanglement theory. In the canonical two-parameter DiVincenzo family used as its…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For an unkilled Levy process ξ drifting to +∞ with all positive exponential moments, let I_ξ = ∫_0^∞ e^-ξ_t dt and X_ξ = 1/I_ξ. Bertoin and Yor proved X_ξ is moment-determinate when ξ has no positive jumps and conjectured that this…
For a multidimensional reflected diffusion, does the basic adjoint relationship uniquely characterize the stationary distribution? The question had stood unresolved for more than thirty-five years since the BAR approach was introduced. For…
Lorist and Schwenninger prove Crouzeix's conjecture (arXiv:2608.03841, Lemma 1) by combining a lower bound (their inequality (4)) with an upper bound (inequality (5)). In Remark 2 they observe that (5) alone gives κ ≤ 1 + √1 - ℜ⟨ E_1…
Can any single-pass semi-streaming algorithm beat the naive greedy 1/2-approximation for maximum matching? No. No single-pass semi-streaming algorithm, deterministic or randomized, achieves a better-than-half approximation, so greedy is…
The dimer constant of Z^3, the exponential growth rate of perfect matchings of the cubic lattice, has no closed form and is pinned only by bounds. The upper bound improves from Lundow's 0.457547, standing since 2001, to 0.452130, via…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Deng, Tidor and Zhao asked whether [N] admits a coloring with N^o(1) colors and no symmetrically coloured 4-term arithmetic progression, giving an O(N^log_223) coloring. The paper gives an O_k(N^4/k^2) coloring of [N] avoiding…
What is the optimal competitive ratio for online vertex cover when edges arrive one at a time? The paper proves a tight factor-2 lower bound via a reduction in the blueprint framework of Assadi, Jiang and Xiang, closing the gap left by…
For a connected graph G , let t= tree( G ) (order of a largest induced tree), A= average eccentricity, and L= maximum independence number of a neighbourhood. Then ⌈ (A+L)/3 ⌉ ≤ t. (The evenly-divided reading of the conjecture holds; a…
Let U_n⊂ R^n be the difference polytope of a regular n-simplex such that U_n circumscribes a sphere of diameter 1. Then every set of diameter 1 in R^n is covered by a rotated copy of U_n.
Sharp global and almost-everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations, settling the sharpness question left open by the first-order theory.
Reiner conjectured a description of the homotopy types of intervals in higher Bruhat orders. In corank 3 it holds: the facial intervals of B(n,n-3) are exactly the spherical intervals, and every other interval is contractible.
Every purely-maximal ideal of a commutative ring is purely-prime, and the converse holds for several important classes of rings; Tarizadeh conjectured (Conjecture 5.8 of his earlier published paper) that in a commutative ring every…
For a measurable set Ω⊂ R^3, let E(Ω)=P(Ω)+frac12iint_Ω×Ωdx dy/|x-y|, where P is De Giorgi perimeter, and set V_*=5frac2-2^2/32^2/3-1≈3.51. The conjecture asks for the complete fixed-volume minimization picture. Chodosh and Gianocca prove…