1033 matching entries · Page 6 of 21
Testing whether a supplied family of meet-irreducibles is the complete canonical family of a finite implication closure system is coNP-complete, even with acyclic implications of premise size at most three and a genuine irredundant supplied family. The hard direction reduces 3-UNSAT to a missing member.
For n>2, Schlagenhauf constructs a bounded W¹,ⁿ map from the n-ball to Rⁿ⁺² that is discontinuous at the origin yet solves the critical n-Laplace system with an antisymmetric Lⁿ potential in distributions. The potential can lie in every L⁽ⁿ,ᑫ⁾ for q>2.
For exact pure and mixed ground states of a three-dimensional hard-sphere Bose gas, the nonzero-momentum occupation measure approaches the scaled Bogoliubov profile: first take the thermodynamic limit at fixed density, then the dilute limit. Its mass gives depletion 8/(3√π)√(ρa³)+o(√(ρa³)), uniformly over thermodynamic accumulation values.
Lorist and van Neerven construct two explicit 2^n-dimensional Banach-space families at p=2. One has Hilbert-transform constant of order n and UMD constant of order √n; the other reverses them, making both classical quadratic comparison exponents sharp over real and complex spaces.
Under OVH or SETH, Saha, Xu and Ye prove n^(2−o(1)) lower bounds for exact Furthest Pair, Bichromatic Closest Pair, Maximum Inner Product and Hopcroft’s problem in every efficiently constructible superconstant dimension.
Matherne and Morales give a 12-vertex, 19-edge bipartite graph G3 whose chromatic symmetric function is reported Schur positive while its three-variable specialization omits lattice-point weight (7,4,1) between present weights (6,6,0) and (8,2,2).
For every ordinal ω<α<ω₁, Almeida’s compact-range Vietoris power K(α,ord), with its range-plus-finite-coordinate topology, is second-countable and Lindelöf but neither σ-compact nor Menger. The Lean theorem ordinal_full covers this interval by a delayed diagonal.
The September manuscript proves that every admissible integrable zero-temperature Parisi minimizer for the pure zero-field Sherrington–Kirkpatrick model, with covariance ξ(t)=t²/2, has full relative Stieltjes support on [0,1). It uses a rational coercive identity and strict curvature on constant intervals.
Fang, Lan and Ma identify affine binary-dihedral orbifold Gromov–Witten theory with involution-equivariant sign-sector recursion on a type-D logarithmic Toda curve, for stable descendants with n>0 and 2g−2+n>0 and free energies with g≥2 on the stated smooth chamber.
For smooth positive steady single-species Vlasov–Maxwell–Landau solutions on the three-torus with Coulomb collisions, Schwartz velocity decay and a polynomial score bound, the stated Lean theorem yields a spatially uniform Maxwellian at ion density, zero electric field and constant magnetic field.
Ananth, Ragavan and Sahai give efficient, perfectly correct, one-time private-key encryption of one bit using a random nonidentity phase-free n-qubit Pauli and a random eigenstate. After key disclosure, both separated receivers recover the bit with probability at most 1/2+O(2^(−n/2)) against information-theoretic attacks.
For compact connected smooth manifolds of dimension at least three, the manuscript claims that equal density-valued energy Dirichlet-to-Neumann forms measured on any nonempty proper relatively open boundary patch determine two smooth metrics up to a smooth diffeomorphism fixing that patch.
The manuscript claims that every connected smooth closed Einstein four-manifold with strictly positive sectional curvature is, up to positive scaling, round S⁴, Fubini–Study CP², or round RP⁴, without assuming orientability.
Hou and Liu prove pseudo-effectivity of the first Chern class for every coherent quotient of every positive tensor power of the logarithmic cotangent sheaf under their smooth proper integral complex Deligne–Mumford stack, normal-crossings divisor, and big-determinant subsheaf hypotheses.
For primes p≤x with equal weight, the normalized logarithms of the ordered prime factors of p−1, counted with multiplicity, converge in every fixed finite joint distribution to Poisson–Dirichlet(1). The manuscript also derives a fixed-threshold Dickman law for the largest factor.
For critical angles 0 and π/2 of multiplicity three, Yan gives αₙ=c(n+1)^(-3/20)(1+(-i)ⁿ), 0<c<1/2. It satisfies Lukic’s localized decomposition conditions but has weighted entropy −∞, refuting that direction of the unrestricted multipoint conjecture.
Pozsgay gives an open-boundary spin-chain Hamiltonian built from two compatible Ising-type algebras with a hidden free-fermion solution and, for generic couplings, no exponentially growing homogeneous spectral degeneracy.
Appendix B Proposition B.1 gives a convex polyhedral Gaussian partition with prescribed cell masses and projected barycenters when a centered finite-support X is convexly dominated by ρG for 0<ρ<1. The GPT proof is an alternative martingale-coupling step, not the paper’s main Talagrand theorem.
For every minimal homeomorphism h of an infinite compact metrizable space X, the manuscript claims rc(C(X)⋊ₕZ)=mdim(X,h)/2, including infinite values. The new part is the lower bound for every finite open cover.
Krishtal and Pfander construct a bounded invertible normal operator T on ℓ²(N) and a vector g whose normalized orbit {Tᵏg/||Tᵏg||: k≥0} is a frame.
For an unknown d-dimensional state and m adaptively chosen observables 0≤A≤I, Chen, O’Donnell, Pelecanos and Wright give online expectation estimates within ε with success probability at least 9/10 using O(log(m)√log(d)/ε³) or O(√m/ε²) copies, respectively.
For simple separable unital infinite-dimensional nuclear C*-algebras, the companion manuscripts claim strict comparison implies Jiang–Su absorption, completing the unital Toms–Winter equivalence with finite nuclear dimension. A separate extended-functional theorem also treats nonunital algebras under its own assumptions.
The manuscript constructs two distinct uniformly positive bounded measurable scalar conductivities on the ball B(0,3) in R³. Both equal one near the boundary, differ on a set of positive measure and have the same full weak Dirichlet-to-Neumann operator.
For a simple separable unital infinite-dimensional nuclear stably finite C*-algebra with traces, real rank zero of the uniform tracial ultrapower of its uniform tracial completion implies a central projection halving every specified trace on every coefficient. This yields uniform property Gamma for each specified free ultrafilter.
For separable nuclear complex C*-algebras with no nonzero elementary ideal subquotients, the manuscript claims finite nuclear dimension, Jiang–Su stability and nuclear dimension at most one are equivalent. It separately claims dim_nuc(A₀⊗Z)≤1 for every separable nuclear A₀.
For every fixed power k≥1, sufficiently many variables give a lattice monomial in the Newton polytope of the k-th Vandermonde power with zero coefficient. The new step is an explicit even-power seed for k≥4; earlier cases and propagation complete the result.
Matherne and Morales give two 12-vertex claw-free line graphs whose chromatic symmetric functions have [s₃₃₃₃] coefficients −64 and −40. Either graph refutes Stanley’s claim that every claw-free graph is Schur-positive.
For every fixed degree d≥3 and energy strictly inside the Kesten–McKay bulk, the unfolded adjacency-eigenvalue point process of a uniform simple labelled d-regular graph converges at that fixed energy to the GOE bulk process along all admissible graph sizes, without extra conditioning.
A five-element coverage function with marginals (3/10, 7/20, 3/10, 7/20, 7/20) has ordinary concave closure 4 and pairwise-independent closure at most 479/160. Their ratio is at least 640/479, above the conjectured universal 4/3 bound.
An infinite-chromatic graph has the property that, for every nonnegative function f(m) tending to infinity, every m-vertex finite subgraph contains an independent set of size at least m/2−f(m). A stronger construction bounds local odd-cycle-transversal number by any prescribed unbounded integer profile.
Theorem 6.1 gives an explicit quantitative stable-phase-retrieval bound for the closed real L² span of independent centred normalized random variables under indexed two-sided L¹ bounds on all but at most one coordinate. Its proof uses a head–tail concentration versus diffusion argument and Sperner-type anticoncentration.
For a thermal attenuator with environment photon number ν=1, a rank-two input on six Fock levels has certified coherent information at least 4.7×10⁻⁴ qubits per channel use at transmissivity η=0.8, while all single-mode Gaussian inputs have at most zero. A larger witness is certified positive at η=0.7841.
A polynomial-time algorithm finds a planar embedding of minimum edge-outerplanarity for every finite loopless planar graph, including graphs with parallel edges. It reduces edge-peeling depth to minimum face-depth of an auxiliary planar graph.
For every n≥2, a two-colouring of the edges of the n-cube in which antipodal edges have opposite colours contains a monochromatic path from some vertex to its antipode.
Every closed connected oriented smooth manifold of dimension at least two with positive scalar curvature is rationally inessential, without spin or fundamental-group restrictions. The aspherical obstruction also covers nonorientable manifolds through the orientation double cover.
For the specified row-stochastic 4×4 matrices supported on a 4-cycle, every nonreal eigenvalue a+ib has 0≤a≤1, a+|b|≤1 and (b²+a²+a)²+2a²−b²≥0. Conversely, upper-half-plane points with b>0, 0≤a≤1, a+b<1 and the polynomial nonnegative occur; the stated boundary arcs are attained. This includes Ran and Teng’s Conjecture 20.
For all sufficiently large X, the largest consecutive prime gap below X is at least a constant times log X (log₂ X)² log₄ X/(log₃ X)². The argument uses a short-translates proposition and a weighted sieve.
For split connected semisimple groups over global function fields and every effective divisor, including arbitrary multiplicity, rational and ℓ-adic cuspidal-function spaces split into direct sums indexed by dual-group nilpotent orbits. The same orbit controls all unramified Hecke places.
A flat complex family made by substituting T=sE into Singh’s determinantal family has a klt-type special fiber and nearby fibers that are not of klt type. It gives a negative answer to Han and Jiang’s Problem 4.6.
The OpenAI manuscript claims that the nearest-neighbor Anderson operator on ℓ²(Z²), with independent site potentials uniform on [−h,h], has almost surely pure-point spectral type and a complete eigenbasis for every fixed h>0. It also identifies the spectrum as [−4−h,4+h].
Antonio and Pablo Acuaviva construct a unital complex Banach algebra not isomorphic to B(X)/K(X) for any Banach space X, using large simple algebras and separable-range operator obstructions.
If T:X→Y is weakly compact and Y is separable with the bounded approximation property, then T factors through a reflexive Banach space with a Schauder basis.
Dai and coauthors construct a locally finite 1-differential poset P for which the two-multichain quotient M_(P,2)(q)/F_P(q)² is nonrational over every characteristic-zero field. This refutes Stanley’s proposed rational-factor property already at k=2.
For each composition α=(α₁,…,α_k) of n, the number of alternating permutations of 2n with record composition α is ∏_j binom(2s_j−1,2α_j−1)E_(2α_j−1), where s_j=α₁+…+α_j and E_m is an Euler number. The paper also realizes these counts in a noncommutative symmetric-function lift.
Conditional on Conjecture 1.1 about large prime divisors, the authors construct an S*_m-decoding polynomial with the optimal k+1 nonzero terms for every fixed k, for suitable k-prime m and finite field. The construction gives the stated fixed-server PIR tradeoff; finite prime checks make it unconditional through 15 servers.
For a real degree-n trigonometric polynomial with 2n distinct zeros on a period, Tao’s Theorem 1.13(ii) gives an integral of its Lebesgue-type sum at least 8, with equality for a sinusoid. The bound follows by multiplying two factors in Lemma 1.14.
For every n-element Sidon set A of natural numbers, AlphaProof Nexus proves 16 I(A+A)+100n+16≥n², where I counts sums whose neighboring integers are both absent from A+A. Thus the minimum isolated-sum count grows at least quadratically, answering the finite-set form of Erdős Problem 152.
For every fixed-in-advance sequence of T Euclidean unit vectors in dimension d, Aden-Ali’s Gaussian triplet walk assigns signs in O(dT) time. With probability at least 1−δ, every prefix has ℓ∞ discrepancy at most sqrt(18 log(2T²/δ)).
Over any characteristic-zero field, Wang and Zhang prove Fröberg’s predicted generic Hilbert series for equal-degree forms in four variables when the degree is 5 or 7 and the generator count is any r≥1. Exact rank certificates cover the previously open middle ranges r=6–11 and r=6–21, respectively; propagation covers the remaining counts.
Liu and Pikhurko use a Ramanujan-graph spectral 3-graph gadget to build a smoothly decreasing sequence of Lagrangians. With their separate recursive and lifting constructions, they show that for every r≥3, Turán densities of possibly infinite forbidden r-graph families contain a terminal interval [1−δ_r,1].
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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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