1033 matching entries · Page 13 of 21
There is a smooth compactly supported probability density on ℝ³, with smooth compactly supported square root, whose finite three-marginal Coulomb Kantorovich minimum is attained by a coupling but by no pair of measure-preserving Borel maps; nevertheless the Monge and Kantorovich infima are equal.
If a smooth almost complex structure on a closed connected smooth four-manifold is tamed by a symplectic form, then the same almost complex structure is compatible with some smooth symplectic form.
Every smooth normalized positive triple of closed two-forms on a closed connected oriented four-manifold deforms smoothly through positive closed triples to a hyperkähler triple while preserving each of its three cohomology classes.
OpenAI gives an adaptive-anchor and weighted-tree proof that every nonexpansive selfmap of a nonempty closed bounded convex subset of a real reflexive Banach space has a fixed point in the given norm; the manuscript also derives the commuting-family retract corollary from Bruck’s theorem.
For uniformly signed proper random 3-SAT clauses sampled independently with replacement, the finite positive limiting satisfiability threshold is a computable real: one deterministic machine takes a requested precision and returns a rational approximation within that error.
At the critical honeycomb self-avoiding-walk activity, the total weight of unrooted polygons of diameter at least r is r^{-2+o(1)}, their length-weighted tail is r^{-2/3+o(1)}, and the truncated second-length-moment mass through diameter r is at most r^{2/3+o(1)}.
For zero-field Sherrington–Kirkpatrick heat-bath dynamics at β=1, stationary and fair-spin quench autocorrelations converge jointly as random functions after multiplying correlations by n^{1/3} and scaling waiting times and lags by n^{2/3}; Gaussian and Rademacher couplings have the same limiting law, and the quench limit relaxes to the stationary limit as waiting time grows.
Assuming the scalar, annealed Cardy crossing formula for fair-colored critical Poisson–Voronoi percolation on every bounded Jordan quadrilateral, the jointly coupled near-critical crossing thresholds of rational polygonal quadrilaterals, normalized by each model’s expected number of unit-square color-pivotal sites, have conditional laws that converge in probability over Voronoi tessellations to the triangular-lattice limit.
For the Ising perceptron with independent Gaussian patterns, every bounded Borel real log-potential and each fixed positive temperature and pattern density have a limiting normalized free energy given by the manuscript’s explicit overlap-path variational formula, with convergence in expectation and probability.
For planar Ising bonds J_e=1+εξ_e with any fixed bounded, nondegenerate, mean-zero iid disorder law and sufficiently small ε>0, the full oriented interface law at the spontaneous-magnetization threshold converges in probability over environments to chordal SLE₃ in deterministic Jordan-domain approximations.
For the nearest-neighbor two-dimensional O(3) spin model with no external field or topological term, normalization by susceptibility and second-moment correlation length yields a unique continuum Schwinger hierarchy as the bare inverse coupling tends to infinity through all positive real values; the reconstructed field theory has a positive mass gap and a nonzero connected four-point function.
For critical spherical FK–Ising planar maps with n edges, stationary random walks using every incident half-edge converge jointly with the rescaled map metric and degree measure to Liouville Brownian motion on the unit-area √3-quantum sphere when time is accelerated by exactly n; the convergence holds for any fixed finite number of conditionally independent walks.
For every degree k≥2 there is c_k>0 such that, for each fixed intersective integer polynomial h of degree k with positive leading coefficient, every A⊆{1,…,N} avoiding nonzero differences h(m), m≥1, has |A|=O_h(N^{1−c_k}).
For every quartic Salem number β with 1<β<2, the unbiased Bernoulli convolution with contraction parameter λ=β⁻¹ is singular with respect to Lebesgue measure.
For a compact connected smooth manifold of dimension at least three with smooth boundary and any nonempty open boundary patch, equality of zero-frequency same-patch boundary measurements for two smooth metrics and smooth unitary connections on the trivial rank-two Hermitian bundle implies they differ only by a patch-fixing diffeomorphism and a patch-identity unitary gauge.
The three-dimensional periodic hard-sphere Boltzmann equation has one nonnegative initial density with bounded velocity support and finite mass, energy and absolute entropy that yields two distinct global entropy solutions, both satisfying exact local conservation of mass, momentum and kinetic energy and strong L¹ continuity.
For every integer n≥2 and real κ, a complete separable metric space is an n-dimensional Alexandrov space of curvature at least κ exactly when its Hausdorff-measure metric space has full support, is RCD((n−1)κ,n), and has Gigli distributional sectional curvature at least κ on the original global test classes.
Every connected closed Einstein four-manifold with positive Einstein constant and nonnegative sectional curvature that has even one zero-curvature two-plane has universal Riemannian cover isometric to a product of two equal-radius round two-spheres.
A uniformly discrete bounded-geometry coarse disjoint union of finite connected uniformly bounded-degree graphs has an infinite-order class in degree-one coarse K-homology that maps to zero under maximal coarse assembly, so that map is not rationally injective.
Every action of a countable discrete amenable group on a simple, separable, unital, infinite-dimensional, nuclear, stably finite, Jiang–Su-stable complex C∗-algebra absorbs the trivial Jiang–Su action up to cocycle conjugacy, with no condition on its action on traces.
For every unital expected inclusion N⊂M of von Neumann algebras with separable preduals, there is an expected unital amenable subalgebra P⊂N with P′∩c(M)=N′∩c(M), where c(M) is the continuous core.
For the zero-field Gaussian Sherrington–Kirkpatrick model, as system size tends to infinity first and QAOA depth then grows, the best limiting expected energy per spin approaches the Parisi ground-state value. For every accuracy, one finite depth and deterministic angles work independently of system size and disorder.
Every simple unitary strongly rational complex vertex operator algebra has polynomial energy bounds and CKLW strong locality; its smeared fields generate an irreducible conformal net.
An explicit entangled state on C¹⁰⊗C¹⁰ has zero distillable secret key against an eavesdropper holding a purification and the full public transcript, for completed local-instrument protocols with joint processing of copies and unlimited two-way public communication. Every admitted bit-output protocol remains at trace distance at least 1/10 from an ideal secret bit.
For any fixed nuclei at distinct positions with real charges at least one, total nuclear charge Z and M nuclei, the full two-spin nonrelativistic Coulomb Hamiltonian can strictly bind no more than Z+CM electrons, where C is universal and independent of the nuclear positions and charges.
Every nonzero one-homogeneous global minimizer of the one-phase Bernoulli energy in ℝᵈ is a flat half-space solution for each dimension 1≤d≤6.
There is a nonquadratic smooth entire function on ℝ¹⁰ with pointwise positive-definite Hessian that solves the classical affine maximal equation.
For each integer m≥1, there is a simply connected closed Kähler manifold of real dimension 22 with stable Morse number 80+1968m and a Hamiltonian diffeomorphism with exactly 80+1952m fixed points, all nondegenerate with contractible orbit loops.
Assuming the continuum hypothesis, there are infinite-dimensional real and complex Banach spaces with no bounded linear surjection onto any infinite-dimensional separable Banach space.
For every Grothendieck coherator in the Ara–Henry convention, every boundary-cellular infinity-groupoid model X, every n≥0 and every n-cell a of X, adjoining an (n+1)-disk along the source n-face of a gives a weak equivalence X→X⁺.
For separable nuclear complex C∗-algebras A and B, any isomorphism between their topological cones of all extended lower-semicontinuous tracial weights is realized by an isomorphism A⊗W⊗K ≅ B⊗W⊗K, where W is the Razak–Jacelon algebra and K the compact operators.
For every fixed positive half-integer spin and every nonnegative symmetric finite-range interaction generating ℤ³, the spontaneous magnetization deficit of the three-dimensional quantum Heisenberg ferromagnet is asymptotic to ζ(3/2)T^{3/2}/(8π^{3/2}√det D), where D is the positive quadratic one-magnon dispersion matrix.
For the fermionic V₁ Laughlin Hamiltonian at flux q=3(N−1), sufficiently weak projected bounded real scalar one-body potentials leave a unique ground state and a spectral gap bounded below uniformly for all sufficiently large N and all potential profiles of sup norm at most one.
For each hard-sphere radius a>0 and every sufficiently small fixed density ρ>0, there is a temperature T(a,ρ)>0 independent of volume at which the exact three-dimensional canonical Gibbs state has a positive condensate fraction in the constant orbital as N/L³ tends to ρ.
For every finite matrix size and 1/2<γ<3/2, a measurable positive semidefinite Hermitian matrix potential saturates the sharp one-dimensional Lieb–Thirring inequality exactly when one constant unitary basis makes it a direct sum of independent one-bound-state scalar sech² profiles and zero channels.
There is a finite connected aspherical complex with a linear combinatorial disk-filling bound whose word-hyperbolic fundamental group has no proper cocompact isometric action on any nonempty proper complete CAT(0) space.
For any group G and any finite system of m equations in n unknowns, with 1≤m≤n, if the exponent-sum matrix has row rank m over the rationals, then G embeds in the group formed by adjoining the unknowns and imposing the equations. Thus the system has a simultaneous solution in an overgroup.
For every fixed 0<κ<8, there is a deterministic Hausdorff gauge that almost surely gives positive finite measure to every nontrivial compact positive-time segment of ordinary chordal SLE_κ.
For the ferromagnetic four-state Potts broadcast model on every regular d-ary tree with d≥2 and every observed Poisson Galton–Watson tree of mean d>0, reconstruction occurs exactly when dλ²>1, including nonreconstruction at equality.
For every stationary ergodic, uniformly elliptic, finite-range-dependent nearest-neighbor environment on Z^d with d≥3, the annealed probability of escape in any fixed nonzero direction is either zero or one.
For every discrete group G, the Hattori–Stallings trace of every idempotent matrix over the complex Banach algebra ℓ¹(G) has finite support, contained in conjugacy classes of finite-order elements.
A finite nonempty lattice is the full congruence lattice of some finite algebra exactly when it admits the finite colored-graph witness specified in the manuscript, whose edge colors encode the required congruence relations.
There are fixed constants η,c>0 such that, for every sufficiently large n, n points can be placed in the unit square with every triangle of area at least c n^{-2+η}.
A real circulant Hadamard matrix of positive order n exists exactly when n=1 or n=4.
Every regular language over a finite alphabet has a generalized regular expression over that same alphabet whose Kleene-star nesting height is at most thirteen, with complement taken relative to the same free monoid.
For each k≥4, an explicit construction maps a finite compatible-choice system to two equal-size simple uncolored graphs that are k-dimensional Weisfeiler–Leman equivalent exactly when the system has no successful choice; a successful choice is detected after two joint-refinement rounds or one separate-refinement round.
Every exact affine semidefinite lift of the perfect-matching polytope of the complete graph on n vertices has matrix size at least 2^{c n} for some absolute c>0 and all sufficiently large even n.
For every binary string of known length n and known rational deletion retention probability p, one randomized algorithm reconstructs the string with probability at least 2/3 using an explicit sample budget and bit time polynomial in that budget and the binary input length; for each fixed p, both are quasipolynomial in n.
Given a prime p in binary and positive n,s in unary, one deterministic polynomial-bit-time machine outputs a tuple of matrices over F_p of dimension O(n³s⁶) that detects every nonzero division-free noncommutative formula of size at most s in n variables over every field of characteristic p.
For stable finite-range radial pair potentials in the stated regularity class, grand-canonical Newtonian gases started from spatially summable C¹ data with Gaussian density and spatial-gradient bounds have every fixed scaled factorial marginal converge in full phase-space L¹, uniformly on any finite interval where the corresponding nonlinear Boltzmann equation has a nonnegative classical solution with the required Gaussian bound.
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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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