1033 matching entries · Page 8 of 21
Chen, Nie and Xu’s cone-inclusion Lemmas 3.1 and 3.2 show that adjoining a linear factor preserves the required right-Noetherian structure and inclusion, while f−εf′ has a strengthened right-Noetherian property and inclusion. These lemmas feed a projective uniform numerical criterion for complex Hessian-type equations.
Liu and Qin prove a uniform index I for projective log-canonical foliated triples of dimension at most three with K_F+B numerically trivial and coefficients in a fixed rational DCC set, so I(K_F+B) is linearly trivial. Rethlas contributed the non-algebraically-integrable case split and Lie-theoretic route.
For the Thue–Morse target in Alexander’s binary avoiding population, the project gives an attained exact maximum matching-path length L(v) for every natural starting vertex v, including zero, through a seven-case formula based on the factorization of ⌊v/2⌋+1 and adjacent digit-parity bits. It also proves a finite digit recurrence.
Turturean’s write-up claims h(n)=(1/2+o(1))log* n and H(n)=(1+o(1))log* n for almost all n, so H(n)/h(n) tends to 2. A GPT-5.5 Pro subset-product successor lemma supports the composite-divisor lower bound.
OpenAI claims a group of type F∞ containing every finitely presented group. Its finitely generated subgroups, up to isomorphism, are exactly the finitely generated recursively presented groups.
For D(q)=q s q⁻¹ on n-cycles, Lefebvre-Naré’s October note claims depth p^(e−1) for odd prime powers p^e, depth 2^(e−1)−1 for powers of two, and the maximum prime-power depth for general n. The shorter proof uses a defect commutator and triangular Sylow-group filtration.
Qiu and Yan prove interior curvature bounds in every dimension n≥3 for smooth admissible graphs on B₃⁄₂ solving σ₂(κ[u])=1 with bounded height and gradient. The model-suggested compression inequality in Lemma 3.4 controls a two-surface Jacobi inequality; the model also supplied the auxiliary η in equation 62.
For rational-coefficient affine linear matrix pencils, a universal nonadaptive polynomial-size list of rational matrix evaluations detects nonsingularity over the free skew field. The paper also gives a rank-detecting list for rectangular rational pencils, with polynomial construction and output bounds in the dimensions and variable count.
Every regular language over a finite alphabet has a generalized regular expression over that same alphabet with at most three nested Kleene stars, allowing union, concatenation and complement.
For n=3, K=2 and d=4, Peng gives positive definite symmetric matrices arbitrarily close to the identity with ||W_SS|| > ||W_RS||, refuting the SS–RS half. For all n≥2, K≥1 and d≥1, the RS–GD half holds when (1−1/(4n²+1))I ≤ Aᵢ ≤ I.
The September OpenAI manuscript claims an infinite-dimensional finitely presented nonunital nil associative algebra over F₂ that is Jacobson radical but not nilpotent. Its unitization is finitely presented, algebraic and infinite-dimensional.
For any planar convex body K and 0<W<width(K), one plank of width W covers at least as much area of K as any finite family of planks whose total width is at most W. The assessed AI-associated result is this planar reduction.
For every nontrivial increasing graph property on n≥2 vertices invariant under relabeling and 0<ε<1/2, the probability width from ε to 1−ε is at most 2¹⁹ log(1/(2ε))/(log n)².
For smooth convex-concave objectives with a monotone K-Lipschitz gradient operator and a saddle point, the schedule αₜ=1/(K√(t+γ)), βₜ=γ/(t+γ), γ≥2, gives squared-gradient residual O(1/t) at the last iterate of anchored gradient descent-ascent.
The authors adapt a ChatGPT-supplied q-lift example against reciprocal flat-count convexity into matroids whose numbers of flats by rank are not unimodal. The final construction combines Larson’s graphic matroids with Whittle’s q-lift.
On every separable infinite-dimensional complex Hilbert space, the paper constructs a nonzero bounded norm-quasinilpotent operator S whose commutant has no nonzero proper closed invariant subspace. The operator S itself has ordinary invariant subspaces.
On every separable infinite-dimensional complex Hilbert space, the commutant of the constructed operator is a proper unital complex algebra, closed in the strong operator topology and transitive.
For every real p>4, Xiong constructs an equilateral set of 8m points in ℓₚ^(8m−2) for some power-of-two m, exceeding the proposed dimension-plus-one maximum.
A sparse set B that is not an asymptotic additive basis gives, for every A of Schnirelmann density 0<α<1 and every cutoff N, a shift b∈B for which A∪(A+b) covers at least (α+f(α))N of [1,N], with f(α)>0.
For nondecreasing F tending to infinity, an infinite-measure measurable set S of positive reals with no distinct-point integer quotient and |S∩(0,x)|≥F(x) eventually exists exactly when ∫₁∞ F(x)/x² dx is finite.
In the Boolean-output quantum random oracle model, every finite-round perfectly complete key-agreement protocol with quantum local operations, independent initial private states and classical communication admits a passive eavesdropper that recovers the key with certainty using O((q_A+q_B)^5) classical oracle queries. The eavesdropper may use unbounded computation.
For k≥4, the ordered three-summand count Fₖ(t) modulo 2ᵏ−1, with total binary weight below k, equals (k+23)3^(k−4) when the k-bit target has exactly two nonadjacent zero digits. The paper proves balancing only through carry mass five and does not classify global maximizers.
For every ε>0, there is an r such that integers 2^k+n with n having at most r prime factors have lower density at least 1−ε. The claim neither establishes a natural density nor fixes one r for all ε.
A connected normal complex projective variety has a universal cover biholomorphic to a semialgebraic open subset of a projective variety exactly when that cover is D×C^m×F, with D a bounded symmetric domain and F simply connected, normal and projective.
There are noncongruent simply connected strictly convex Euclidean plane domains with real-analytic boundaries and identical Steklov spectra, including multiplicities. Such pairs can approach a disk smoothly.
The diagonal cubic X³+Y³+Z³+ζ₃T³=0 over Q₂(ζ₃) has trivial R-equivalence. Gemini 3 Deep Think supplied rigorous methods for the gap-closing Lemmas 3.4–3.5 in the human-led proof.
A centrally symmetric simplicial six-dimensional polytope with 48 vertices has an antipodal boundary quotient that triangulates real projective five-space on 24 vertices.
For a reduced isolated complex hypersurface germ of dimension at least two, or an irreducible curve germ, weighted homogeneity after coordinate change is equivalent to a logarithmic holomorphic vector field transverse in the real-Euclidean sense to every sufficiently small link in those same coordinates. An invertible ambient linear part is a third equivalent condition.
For every k, there is a finite group with a minimal generating set of involutions whose Cayley graph has chromatic number at least k.
Some computably enumerable truth-table degree contains no computably enumerable irreducible many-one degree. Cintioli derives the example using Degtev’s c.e. semirecursive set with rigid complement and the fact that its simple-set representatives cannot be irreducible cylinders.
The Schubitope in R¹⁴ from columns {8,…,14} and {12,13,14}, equivalently Δ(7,14)+Δ(3,14), has Ehrhart quadratic coefficient −687323/79200. It is therefore not Ehrhart positive.
Bhatt and Ma construct a five-dimensional finitely generated flat normal domain over Z or any field with a codimension-one prime J for which H²_J has infinitely many minimal primes. The characteristic-two case uses a separate construction; a cone gives a six-dimensional normal local example.
For the largest measure M(R) of a measurable subset of a radius-R planar disk with no positive integer distance between distinct points, M(R)≤C√R. Together with Sárközy’s earlier lower construction, this yields M(R)=R^(1/2+o(1)).
For n independent standard Gaussian points in R^d, a positive semidefinite S with x_iᵀSx_i=d for every i exists with high probability when limsup n/d²<1/4 and fails to exist with high probability when liminf n/d²>1/4.
For every n≥2, g₄(n)=3: any A⊆{1,…,2n} with at least n+3 elements contains all six pairwise sums of four distinct integers, and the constant cannot be lowered. The four integers need not be positive or members of A.
For k≥1, a primitive set A of integers with at least k prime factors, and any set Q of odd primes, the sum f(A(Q)) is at most f(Nₖ(Q)), where f sums 1/(a log a).
For a differentiable convex function with a minimizer, trajectories of the r=3 Nesterov ODE converge to a minimizer. Jang and Ryu adapt this argument to show that both iterates xₖ and yₖ of standard finite-dimensional Nesterov accelerated gradient converge to one minimizer for an L-smooth convex function under the stated growing tₖ schedule.
In Korsky’s upper-bound argument for north-east lattice paths with no k collinear visited vertices, the mediant of Farey neighbors raises the uniform density-increment product from 1/[8(k−1)²] to 1/[4(k−1)²]. It gives log A(k)≤(2/e+o(1))(k−1)².
For every primitive set A contained in [x,∞), x≥2, the sum f(A)=Σₐ∈A 1/(a log a) is at most 1+O(1/log x).
If A has positive upper doubly logarithmic density Δ, then A contains an infinite strictly increasing divisibility chain whose upper count through x, divided by log log x, is at least Δ.
An explicit reduced planar convex body of thickness 1, with support-function parameters m=15/16 and ε=13/20, has area 0.7862156027…>π/4. It refutes Lassak’s proposed bound area(R)≤(π/4)Δ(R)² for all reduced planar bodies.
A specified connected graph with 33 vertices and 36 edges has domination polynomial divisible by x+4. Its exact factorization includes x¹¹(x+2)(x+4)(x²+3x+1), so −4 is an integer domination root.
Theorem 1.2 gives a marked profinite presentation of the absolute Galois group of Q₂ with four generators, a tame relation, an explicit wild-word relation, and a pro-2 condition on the normal subgroup generated by the wild generators.
For an integral domain k, the commutative ring R=k[X₁,X₂,…]/(Xᵢ(1−Xⱼ):i<j) has exactly the pure ideals 0, I=(x₁,x₂,…), and R. Thus 0 is purely-prime but not purely-maximal.
A diagonal transfer-layer family gives an upper bound for the cubic-lattice dimer constant. Its (m,n)=(5,5), p=2 exact finite computation yields ℓ₃≤0.452130.
For every n≥3, the even-degree Poincaré polynomial of the moduli space of stable n-pointed genus-zero curves is real-rooted. For n≥4, its n−3 roots are simple and negative and strictly interlace those for consecutive n.
AxiomProver proved in Lean that an integral x_n forces the squarefree kernel K_n to divide 1+m² with |m|≥√(K_n−1), that large exceptional x_n lie near a π/2 lattice point, and that the exceptional set has O(log N) members through N. Ono combines these with his asymptotic lower bound for K_n to show nonintegrality for almost all n.
For any number of indivisible goods and agents with nonnegative additive valuations, an allocation exists with bundle sizes differing by at most one, envy-free up to one good, and no balanced fractional reallocation that Pareto improves it.
For the released fixed four-terminal planar acyclic gadget with coordinatewise positive cost-difference scenarios, the normalized additive upper arc-deviation supremum is (299−41√41)/32 with one scenario, 17/8 with two, 3 with three, and 4 with at least four. The two-scenario value is not attained under scenario-wise cost non-increase.
There are constants C>0 and 1≤β<4/3 such that every finite n-point planar set has at most Cn^β unordered unit-distance pairs.
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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