1033 matching entries · Page 5 of 21
AlphaEvolve found explicit witness words that Riestenberg, Taha, Trettel and Wienhard use to prove that the degree-six symplectic hypergeometric monodromy groups C-47 and C-55 have finite index in their ambient integral symplectic groups and are arithmetic.
For uniform real nearest-neighbor Lipschitz heights on triangular-lattice approximations of smooth simply connected domains, the October 6 manuscript claims a centered and normalized Dirichlet Gaussian free-field limit. With a tuned opposite two-arc boundary amplitude, the zero-height interface converges to chordal SLE₄ in uniform curve distance.
Defant’s manuscript claims that, for every alternating sign matrix A, gradedness of [e,A], the corresponding equal-length condition and equidimensionality of all X_B in that interval are equivalent to Cohen–Macaulayness of all those ASM varieties. The new direction establishes Escobar–Klein–Weigandt Conjecture 3.21.
Defant’s manuscript displays an interval in the weak order on six-by-six alternating sign matrices whose Möbius value is 1, although it has none of the specified parabolic forms. Its open-interval order complex is therefore not contractible, contrary to the Hamaker–Reiner dichotomy.
For any field extension K⊂L, associative L-algebra A and A-module M, Greenfeld’s manuscript states that amenability of M over A viewed as a K-algebra is equivalent to amenability over L. This also applies to amenable and fully amenable algebras.
Larson gives a rank-nine binary matroid on 18 elements whose complementary basis pairs occupy disconnected symmetric-exchange classes. It refutes Farber’s two-base conjecture and White’s toric-ideal symmetric-exchange generation conjecture.
For finite-dimensional unitaries satisfying approximate order-two and orbit-commutator relations through 2M, with M polynomial in the target tolerance, Dogon and Vidick prove nearby exact lamplighter relations. Their argument gives polynomial upper bounds on Hilbert–Schmidt stability rate and radius.
The AlphaProof Nexus report says its agent ruled out monochromatic quantum graphs for the diagonal four-, six- and ten-particle cases N=d=4, 6 and 10 in the Krenn–Gu perfect-matching model.
Meiburg constructs a total Boolean function on 2,017,584 variables with block sensitivity at least 14,011 and spectral sensitivity at most 89.0162. Composition yields an exponent of at least 2.127, refuting a proposed quadratic upper bound.
For every finite simple connected graph G, the maximum number L_S(G) of leaves in a spanning tree is at least 2(ℓ(G)−1), where ℓ(G) is the average local independence number.
A released AI-generated sum-of-squares and Lean candidate encodes Φ(A)≤1226/625−||A−U₅||²_F/625 for nonnegative 5×5 matrices whose entries sum to five. If its encoding matches the original problem, it implies unique equality at U₅.
Protti’s planar acyclic four-terminal instance needs upper overload at least 335 when the largest demand is 294 if cost cannot increase. A rational family gives a lower bound (299−41√41)/32≈1.139747 for the unrestricted planar constant.
Rethlas found a representable rank-seven binary projective-deletion matroid whose Kazhdan–Lusztig polynomial is not real-rooted, with a convolution and degree approach. Cheng and Liu later used that direction to construct representable matroids over every finite field with nonunimodal Kazhdan–Lusztig polynomials.
Das, Ferenczi and Rosendal prove that no hyperplane of the real Kalton–Peck space Z₂ admits a complex structure; hence Z₂ is not isomorphic to its hyperplanes. A symplectic operator rank-parity theorem supplies the obstruction.
For odd n=2k+1>1 and doubly stochastic A, Lavi proves max per(I−A)=3·2^(k−2). Every maximizer is a simultaneous permutation conjugate of the half-weight triangle block plus k−1 swap blocks.
A connected 13-vertex graph formed by joining an independent seven-vertex set to two disjoint triangles has independence number 7, largest induced bipartite subgraph size 9 and Havel–Hakimi residue 2. These values violate Conjecture 109’s proposed bound of 6.
For subsets of {1,…,N} in which no element divides a nonempty subset sum of the others, Xeff proves the maximum size is N^(1/5+o(1)). The new upper bound matches the known lower exponent.
A repaired GPT-5.2 Pro argument uses prime cyclic groups to refute f(N)≤log₂N+o(log log N) for the random subset-sum covering threshold. Ma and Tang later prove the stronger lower bound f(p)≥log₂p+(1/(2 log 2)+o(1))log log p; the constant and quantitative refinement are their work.
For every discrete group G, OpenAI claims that the Hattori–Stallings trace of every class in K₀(C G) vanishes on each infinite-order conjugacy class. The claim concerns the complex group ring; an integral identity-only consequence needs a separate known finite-order input.
Tran, Xin and Yu construct a smooth periodic three-dimensional shear flow V=(0,0,f(x₁,x₂)) and direction (2,2,1) whose homogenized G-equation flame speed has c(0)=0 and positive right derivative as curvature diffusivity d tends to zero. For small d the cutoff is inactive, so the physical cutoff cell speed increases.
Kehoe’s working preprint recasts global cut conditions in the general-region half-collinear single-minus graviton recursion as positive directed-tree flows and open-root-cone membership. Retarded vertices become weighted sums over feasible spanning trees; directed Matrix-Tree determinants apply in chambers with a full arborescence family. It classifies four- and five-block chambers and gives one non-decay five-graviton identity.
Liu claims that a full-dimensional compact convex body in Rⁿ with barycenter zero, zero as its only interior lattice point and volume (n+1)ⁿ/n! is an integral unimodular image of the centered simplex (n+1)Δₙ−(1,…,1).
Jung constructs a 31-vertex simple plane triangulation with maximum induced forest 15, then simple maximal planar graphs Mₖ with 31k vertices, minimum degree five and maximum induced forest 15k for every k≥2. The ratio 15/31 refutes the Albertson–Berman half-forest conjecture.
Portier proves that an edge-minimal generically globally rigid graph in Rᵈ with at least d+3 vertices contains no K_(d+2) subgraph. Equivalently, the only minimally globally rigid graph containing that clique is K_(d+2) itself.
Cohen and Shusterman prove the Fₖ and FPₖ virtual-surjection conjectures for discrete groups. Their homological fibre-product theorem assumes the common quotient Q is finitely presented; they also give counterexamples without that condition.
Korsky proves that every sufficiently large prescribed length L admits full-chord sets in each compact convex body with finite piecewise C² boundary and discrepancy O((log L)^(3/2)). For the disk, every full-chord set has discrepancy Ω(log L).
Lee and Seo prove a degreewise lower bound for the multivariate independence polynomial at nonnegative vertex weights and a two-proper-colour semiproper partition-function bound. The model-origin Lemma 2.1 and dual-set ideas are retained central steps; the equality characterization in their first theorem is outside the Lean target.
Liu’s first release gives FC(4,9)=16 and a co-developed 3:1 core-petal charging argument yielding the nine-petal threshold and FC(4,n)=Θ(n²). A later version extends the asymptotic to FC(k,n)=Θₖ(n^(k−2)) for each fixed k≥2; that general proof is separate from the model-attributed first-release work.
Liu and Wang prove that a general pencil of plane cubics over C has exactly twelve common flex lines. They identify all twelve units of the degree-nine flex-line curve’s genus defect as ordinary nodes, each representing a line that is a flex of two distinct smooth members.
For every odd m≥3, the directed Cayley graph of (Z/mZ)^5 with the five positive coordinate generators decomposes into five directed Hamilton cycles.
For four colors, with x=y allowed, the reported proof gives R(c)=40c+41 for every integer c≥2 in x+y+c=z. It reduces the universal statement to R(2)=121 and two unsatisfiable spoke templates.
For every ε>0 and all sufficiently large even n, the complete graph K_n contains at least (1−ε)n edge-disjoint perfect matchings such that every pair forms a Hamilton cycle. This is the model-origin construction of Theorem 1.3.
For every α>0 and three positive point charges in R^n with n≥2, the potential has at most six nondegenerate equilibria. The new step proves a four-contact statement using separation at the unique saddle of a first integral.
Five positive point charges in R³ can have at least 24 nondegenerate electrostatic equilibria. A small perturbation makes all critical points nondegenerate and finite in number, exceeding Maxwell’s proposed (n−1)² bound of 16 when n=5.
Feng, Fu and Guo give a fully polynomial randomized approximation scheme for s-to-t reachability probability in general directed graphs with independent edge-opening probabilities. An existing reduction extends it to undirected graphs.
For G_m=⟨a,t | [t,a[a,t]^(−m)]⟩, a Baumslag–Solitar group BS(m,m+1) is a retract. In particular, G_2 is non-Hopfian and non-residually finite, while G_1 is non-automatic. Literal commutator relators therefore do not force any of these properties.
AxiomProver generated Lean proofs of Ballantine–Beck–Feigon–Maurischat Conjectures 2, 5, 7, 8, 9 and the intended corrected reading of 10, covering coprimality, divisibility, special values and a recurrence. It also found an n=4 counterexample to a printed binary log-concavity claim.
A biconnected graph with nine vertices and ten edges, with s=1 and t=3, gives a longest path of six under MaxSTN and seven under MinSTN, refuting the proposed inequality for these algorithms.
For an absolute c>0, every family of subsets of [n] whose pairwise intersections contain a nontrivial three-term arithmetic progression has size at most (1/2−c)2^n. Keevash also proves this for 3-uniform hypergraphs with bounded pair-codegree.
Ignatev uses a Claude-origin max-term asymptotic lemma twice to prove Λ(T)=[0,1] for backward shifts on ℓ^p with strictly decreasing, positive, p′-summable weights.
For the two-layer solid standard Young-tableau shape [[n,n],[n,1]], Padhi gives an explicit two-term hypergeometric formula for the count g(n) and proves the conjectured second-order degree-12 recurrence for every n≥1.
For every fixed r,s≥1, both restricted-permutation count sequences a_(r,s)(n), forbidding π_(i+r)−π_i=s, and b_(r,s)(n), forbidding the corresponding absolute difference, are claimed to be holonomic. The argument uses an interleaving bijection with finitely many seams and D-finite closure.
For three-row tableaux with runs of length at least two, G(n)~C₁8ⁿ/n⁴; for odd runs, H(n)~C₂(7+5√2)ⁿ/n⁴. The constants are positive finite boundary sums, with numerical estimates about 0.52128605909 and 0.6389278129.
A connection from relaxed thin perfect matching to a single-tree cut sparsifier helps yield an O(log n log log n)-thin perfect matching relative to any fractional perfect matching, allowing edges outside its support. The separate O(n log n) bound requires support-constrained edges.
For the Geode G defined by S−1=(t₂+⋯+t₆)G, a coefficient-collapse identity reduces its diagonal coefficient to a one-dimensional integral and coefficient extraction. It enables an exact 8,367-digit computation of G[1000^(5)] using modular arithmetic and bounded Chinese remainder reconstruction.
For an n×n Hermitian positive semidefinite matrix A, an entropy-corrected concave Gram-factor relaxation P̂ satisfies e^(−γn)P̂≤per(A)≤P̂ and gives a deterministic polynomial-time e^((γ+ε)n)-approximation for every ε>0. The exponent is optimal up to lower-order terms under the cited NP-hardness, assuming P≠NP.
A measurable real-line set with finite average symmetric-difference measure under unit-interval translations is commensurate with exactly one of the empty set, the whole line, a right half-line or a left half-line. For free ergodic measure-preserving flows, this implies that abstractly isomorphic L¹ full groups determine conjugacy up to a nonzero scalar time change.
For the Lipschitz-function growth constant c(Q_d) of the d-dimensional hypercube, log c(Q_d)≤(3/4+o(1))(log d)/d. The argument compares graph homomorphisms with K_(d,d).
The 10×42 Chomp bar has exactly three winning first bites, at (5,36), (7,30) and (8,26), by exhaustive exact game-state computation.
For every finite uniformly dense rank-three matroid M with |E(M)|=3k and k>0, the version-2 Lean theorem constructs a cyclic ordering in which each consecutive triple is a basis. It includes non-simple and non-paving matroids.
These entries have recorded screening decisions and are not counted as curated contributions. Importance, evidence, interest, and date filters apply only to curated contributions.
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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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