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Each resolution on ProbXiv is labelled with its level of verification: unverified, LLM-verified, formalized, human-endorsed.
problems
Banks and Martin conjectured in 2013 that for a primitive set A and any set Q of primes, the Erdos sum of the members of A composed only of primes in Q is at most the corresponding sum over Q itself. The unrestricted form turned out to be…
Is the irreversibility of entanglement manipulation robust in the strong-converse sense - a strict separation between the exponential strong-converse distillable entanglement and the entanglement cost, as conjectured by Lami and Regula?…
A graph G on n vertices with k edges is t-edge-balanced if every graph on n vertices with t edges is contained in exactly the same number of subgraphs of K_n isomorphic to G. Infinite families were known for t = 2, but no example was known…
How large can a measurable A ⊆ [0,R]^2 be while avoiding the vertices of upward-oriented axis-aligned right triangles of area 1/2? At most O_c(R^2/(log R)^c), with a matching-shaped lower bound construction.
Can online vector balancing in the Spencer setting achieve the optimal order of prefix discrepancy with an efficient algorithm?
Does the finite signed basic adjoint relation determine the invariant signed measure uniquely, and how far beyond the Harrison-Reiman class can uniqueness extend?
Monteiro and Svaiter gave a second-order method for smooth monotone variational inequalities converging at O(T^-1.5), later improved to O(T^-1.75) for the convex-concave minimax subset. Whether the conjectured complexity for general…
Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge with a path on n-2 vertices is the unique planar graph of maximum adjacency spectral radius for every n ≥ 9. Tait and Tobin proved it for sufficiently…
Nesterov's accelerated gradient method (1983) is a cornerstone of optimization, yet whether its iterates themselves converge to a minimizer, rather than just the function values, stayed open for over forty years. Jang and Ryu resolve it in…
The total Chern class of Sym^d(C^n) as a torus representation is a symmetric polynomial whose coefficients were conjectured positive, with a binomial log-concavity refinement. Both are established.
What is the shortest curve guaranteed to reach the boundary of the golden gnomon - the isosceles triangle with equal sides 1 and apex angle 108^∘ - from an unknown starting position and heading? The optimum is a symmetric seven-piece path…
For every zonotope Z ⊂ R^d and vectors v_1,…,v_n ∈ Z, there are signs with ∑_i x_i v_i ∈ C√d Z for a universal constant C. This resolves a 2002 conjecture on vector balancing in zonotopes.
Is the density of Chernoff's distribution - the law of argmax_t W(t) - t^2 for two-sided Brownian motion W - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?
Is the maximum size of a set A⊆ 1,…,N such that ab+1 is never squarefree (for all a,b∈ A) achieved by taking those n≡ 7pmod25? Resolved for all sufficiently large N: any near-maximal A is contained in n≡ 7pmod25 or n≡ 18pmod25, leaving…
At the critical inverse temperature β=1 in the Sherrington-Kirkpatrick spin glass model, Talagrand conjectured that the expected squared overlap of two independent Gibbs replicas has an exact N^-2/3 scaling: there exists a constant a>0…
Frankl, Peng, Rodl and Talbot asked in 2007 whether the set of Turan densities of families of r-graphs contains intervals. It does: for every r ≥ 3 the set contains non-degenerate intervals, including one of the form [1-δ_r, 1].
Let F(n) be the largest A⊆1,…,n with anmid bc for distinct a,b,c∈ A. Is F(n)=π(n)+(C+o(1)) n^2/3(log n)^-2 for some constant C?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
After L^2 normalization, stable phase retrieval holds over the L^2-spans of independent real-valued centered random variables exactly when all but possibly one coordinate satisfies a uniform two-sided L^1 bound. This confirms the…
Klopp and Zadik gave an exponential-time node-private algorithm for exact community recovery in stochastic block models and asked whether a polynomial-time algorithm could match it. One can: a Lipschitz surrogate for the penalized…