1033 matching entries · Page 10 of 21
Domina and Ceriotti give noncongruent atom-centered environments with identical complete correlations through seven-neighbor order, including three-dimensional lifts. For every finite correlation order and angular cutoff, they also construct indistinguishable noncongruent environments.
For a connected reductive group on a smooth projective connected curve over an algebraically closed field of characteristic p>0, the restricted geometric Langlands functor reaches every spectral component under either finite-field descent or, with p very good and p not dividing the Weyl-group order, an arbitrary algebraically closed base. Both regimes require a nondegenerate invariant Lie-algebra form (also on Levi centers), Chevalley restriction for every Levi, semisimple centralizers that are Levi, and nilpotents lying in parabolic unipotent radicals over every field extension.
Aletheia constructed planar n-point sets with no four cocircular in which every point determines fewer than 3n/4 distinct distances. These refute the near-n-distances question under that hypothesis.
There are absolute constants c>0 and C such that every A⊆{1,…,N} with no nonzero square difference satisfies |A|≤CN^(1−c) for all N≥1. The source gives no useful numerical value for c.
An Artin group on 116 generators, with off-diagonal labels only 2, 3 or infinity, has no proper cocompact isometric action on any nonempty proper CAT(0) metric space, in any dimension.
For every integer n≥3 and finite β>0, spin two-point correlations in finite free-boundary nearest-neighbor square-lattice O(n) models with edge strengths in [0,β] obey a uniform A exp(−m|x−y|) bound. Free-boundary limits inherit the decay.
For semifree noncommutative differential graded algebras over a nontrivial computable unital commutative ring, stable tame isomorphism, quasi-isomorphism and derived Morita equivalence are undecidable.
The Paley tournament on 43 vertices has predictability 181/301, above the five-voter threshold 3/5, yet cannot be induced by five voters. The proof uses a co-backing constraint for cyclic triangles and an exact finite shell-and-screen enumeration.
For finite-dimensional quantum states at trace distance at most δ and d=dim A, the optimal dimension-only conditional-entropy continuity modulus is h₂(δ)+δ log(d²−1) up to δ=1−d⁻², then 2 log d. Equality is attainable when dim B≥d.
For regular adjacent-transposition chains on S_n with n≥3, the second-largest eigenvalue has algebraic multiplicity M equal to the number N of neutral labels, except when N=n−2 or n, when M=n−1.
For every increasing antipodal function h on the Boolean cube and every nonnegative allocation of each nonempty Fourier coefficient’s squared mass among its coordinates, the induced linear function flows upward to h₊². This is Kahn’s flow conjecture.
For every odd integer base b>1, the fair {0,2} base-b Cantor measure admits no Fourier frame. The middle-third case answers Strichartz’s question.
A 1,280-word binary code of length 19 and minimum distance five inside a five-punctured extended Golay code extends Cohn and Li’s 10,668-point configuration. It gives the lower bound k(19)≥11,948.
For odd k≥3 and integers n with gcd(n,k)=gcd(n+1,k)=1, AxiomProver found a Jacobi-symbol reformulation and the floor-sum identity N_k(n)=F_k(n+1)−F_k(n). The authors combine that identity with classical Jacobi facts to establish the parity formula N_k(n)≡⌊(k+1)/4⌋ mod 2 and make the earlier genus-zero and genus-one k-differential formulas unconditional.
In a specified three-block Gaussian factor model with 96N true nulls and 4N nonnulls, ordinary Benjamini–Hochberg testing at level 0.01 has false discovery rate greater than 0.0104 for all sufficiently large N when applied to correlated two-sided Gaussian p-values.
Finite planar lattice sets can have an arbitrarily large ratio of ordered rectangles to ordered isosceles triangles, including degenerate configurations. Bennett, Kovač, Nakamura and Oliveira quantify the construction in a box [-N,N]² by a ratio at least (log N)^(c/log log log N), with an analogous cardinality bound.
The September 23 manuscript claims that the intersection of any two conjugates of standard parabolic subgroups is parabolic in every finite-rank Artin group, including nonspherical types and infinite Coxeter labels.
For positive rational u=c/d and r=a/b in lowest terms, with d even, d dividing lcm(b,2), and u≤r, the integer trace of the fractional Gaussian binomial coefficient at u dominates that at r coefficientwise for every k≥1. This proves the Han–Xiong comparison for every r≥1/2 and reduces the remaining parameters to 1/(2m).
For every nonempty inclusion-free hypergraph on n vertices, every d≥1 and arbitrary real edge offsets, Faber and Harris prove that at least n times the sum of j^(n−1) for j=0,…,d−1 assignments in [d]^n isolate a unique minimum edge. The n-singleton hypergraph attains equality.
Astra proved in Lean that a complex polynomial p exists with p(0)=0 and p′(0)=1 such that |p(c)/c|>1 at every critical point c. Thus the universal K=1 mean-value inequality fails at z=0.
The smooth Fermat quintic Calabi–Yau threefold has a faithful action of (μ₅)⁵/Δ, an elementary abelian 5-group of rank four. Since 4>15/4, this refutes Moraga’s proposed odd-dimensional extension of a rank bound.
The Laurent polynomial f(x,z)=(1−z⁻¹)((1−x)+xz) has zero pure product-integral moments for every positive n but marked moment (−1)^(n−1)/(n+1). It refutes xz(1,1), with padding for all mixed k,l≥1. Its SU(2) lift F=(1+c)(ad+b), G=−c has the same pure and marked Haar moments and refutes the SU(2) Mathieu conjecture.
For k≥2 in any positive integer dimension, the magnitude of the kth hard-sphere Mayer coefficient, multiplied by k!, equals a sum of no-broken-circuit region volumes over spanning trees. In dimension three, each tree-region volume is at most (17/32)^ν(T)κ^(k−1), where κ is unit-ball volume and ν(T) is the largest packing of disjoint ordered forks a<b<c with tree edges ab and ac.
For Borel-definable global Keisler measures over a model of a discrete first-order theory, the authors prove the reverse implications: self-averaging gives a definable measure whose canonical random extension is generically stable, which in turn gives a frequency interpretation measure. Together with earlier forward implications, these yield equivalence.
A ten-word code in F₃⁴ and an eight-degree lift give square-difference-free polynomial sets of size 810ᵉ below degree 8e and 27·810ᵉ below degree 8e+4. They refute Naslund’s Conjecture 13 at q=3, k=2 for every n divisible by four with n≥8, and imply a growth-exponent lower bound of 16/21.
Allen, Dhawan and Noel prove that for every fixed girth g≥4 there are d-degenerate graphs of girth at least g with fractional chromatic number at least (1−o(1))d/log d as d grows. ChatGPT solved the authors’ optimization problem for the fractional clique function used in this lower-bound proof.
Liehr, Taylor and Yu prove that every countable Bessel sequence of bound 1 in a complex Hilbert space has its full Gram matrix, including diagonal entries, represented by correlations of complex functions on [0,1] bounded in modulus by 1.
For infinitely many n=q+1 with q a prime power, Ho constructs n points in R^(n²−n) whose distances for distinct pairs differ by at least one but whose diameter is at most (1−1/π²+o(1))n².
For an ordinary mean-payoff game of complete binary input length L with arbitrary signed binary edge weights, the September 25 deterministic manuscript reports a 2^O((log(L+2))²)-bit-operation algorithm for the exact winning set, values and optimal positional strategies.
Wang and collaborators report a second unstable self-similar Córdoba–Córdoba–Fontelos (CCF) profile, stable and three unstable incompressible porous media (IPM) profiles, and stable and three unstable 2D Boussinesq profiles. They test residuals and linearized modes on dense grids. A fourth Boussinesq profile remains an unvalidated candidate.
The free Heyting algebra F₂ on two generators cannot be the lattice of subterminal objects of an elementary topos. The obstruction extends to any Heyting algebra surjecting onto F₂, including free F_N for N≥2.
For integers r≥3, k≥4 and n≥72, the maximum ordinary-line count Fᵣ,ₖ(n) is at least n²/12−(10/3)n. The elliptic-curve construction has no four collinear points and a bipartite ordinary-line graph.
For F(q)=Σₙ≥₁1/(qⁿ−1), a degree criterion excludes polynomial relations of degree at most e over Q(q) when eλ log M(q)<log q, where λ=(42963+428220/π²)/202140. It gives nonquadraticity for every integer q≥2 and irrationality for rational q=a/b>1 when log b/log a<0.5728; a certified refinement reaches 0.573290.
For a fixed n×d real matrix U with UᵀU=I, d≥1, 0<ε≤1 and 0<δ≤1, the fully independent signed-hash SparseStack construction gives failure probability at most δ with column sparsity below 1356 max(1,⌈log₂(d/δ)⌉)/ε and row count below 306456(d+max(1,⌈log₂(d/δ)⌉))/ε².
For the centered Hardy–Littlewood maximal operator over axis-parallel cubes in R², the optimal weak-type (1,1) constant c₂ is at least Φ=1.6855099933…, so c₂>1.685.
For every n≥1, the integers 1 through n can be partitioned into nonempty blocks of at most three distinct integers, with each block summing to a power of three.
Guo, Fang and Lu prove the strict bound K_G^C>1.35584631827168 using a Gaussian Hermite multiplier, exact rational parameters and a weighted operator-norm criterion.
AlphaEvolve-generated graph searches report R(3,13)≥61, R(3,18)≥100, R(4,13)≥139, R(4,14)≥148, R(4,15)≥159, R(4,16)≥174, R(4,18)≥209, R(4,19)≥219 and R(4,20)≥237.
For a minimally four-generated numerical semigroup S=⟨n₀<n₁<n₂<n₃⟩, the minimal number of generators of its toric ideal is at most 2W over any field, where W=(n₃−n₀)/gcd(n₁−n₀,n₂−n₀,n₃−n₀). Consequently it is at most twice the ordinary width n₃−n₀.
For all sufficiently large k, the least n>2k for which (n−k)⋯(n−1) has no prime factor in (k,2k) exceeds exp((log k)²/(20 log log k)).
In an exact partition of any finite or infinite solvable group into at least two left cosets, two of the corresponding subgroups have the same index. The cardinality form of Erdős Problem 274 follows.
For the fermionic Laughlin state at filling 1/3 on the round sphere and flux 3(N−1), the unperturbed V1 Hamiltonian has a uniform gap for all sufficiently large particle numbers N. The released Lean scope gives a 1/25 Fock-space distance estimate and a 1/100 finite spherical gap.
For every deterministic fractional online vertex-cover algorithm and every ε>0, a finite bipartite edge-arrival instance forces a competitive ratio of at least 2−ε. The paper extends the lower bound to randomized integral or fractional algorithms against an oblivious adversary.
A 39-vertex dumbbell graph violates Graffiti Conjecture 143, which bounds the variance of positive adjacency eigenvalues by graph size divided by average distance. The witness works under both standard average-distance conventions.
For every origin-symmetric compact convex body K with nonempty interior in Rⁿ, n≥2, the Gromov width of int(K)×int(K°) is 4. Every symplectic ball of capacity c<4 embeds.
For the integer-normalized trigonometric permanents at prime p=29, s₂₉=1,053,859 is positive and s′₂₉=−4,806,838,304 is negative. These exact values contradict both sign predictions in Conjecture 4.6(ii).
Five simple 3-polytopes with 10 faces violate the printed IRIS Conjecture 6.1. One has four triangular, three pentagonal and three heptagonal faces, but no hexagonal faces, below the conjectured lower bound of 1/5.
A bipartite graph on 13 vertices has 22 edges and a unique minimum dominating set of size 4, exceeding the proposed bound m(13,4)=21 in Koch–Narayan Conjecture 1.
Lollipop graphs with 118 or 120 vertices violate Graffiti Conjecture 154 when “deviation” means the standard deviation of adjacency eigenvalues. A 144-vertex graph violates it under both standard average-distance conventions.
For every n>0, the Fubini number a(n), which counts ordered set partitions, equals the sum of A284005(k) for k from 0 through 2^(n−1)−1. The proposed proof counts partitions with each prescribed set of block minima.
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arXiv · algebra-geometry — last successful metadata check: 21/10/2026, 07:20:46 UTC
arXiv · algorithms-formal — last successful metadata check: 21/10/2026, 07:19:48 UTC
arXiv · analysis — last successful metadata check: 21/10/2026, 07:21:51 UTC
arXiv · combinatorics — last successful metadata check: 21/10/2026, 07:18:49 UTC
arXiv · geometry-topology — last successful metadata check: 21/10/2026, 07:22:23 UTC
arXiv · logic-foundations — last successful metadata check: 21/10/2026, 07:23:04 UTC
arXiv · optimization-information — last successful metadata check: 21/10/2026, 07:23:10 UTC
arXiv · probability-dynamics-physics — last successful metadata check: 21/10/2026, 07:22:36 UTC
arXiv · theoretical-physics — last successful metadata check: 21/10/2026, 07:22:50 UTC
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