1033 matching entries · Page 7 of 21
For every p between sqrt(2+sqrt(3)) and 2, every horizon T and every predetermined nonnegative gradient-descent stepsize schedule, Ma and Chen construct a smooth convex problem in dimension at most T+1 with last-iterate error at least c_p L R²/(T+1)^p.
For each fixed acyclic 0–1 matrix pattern P, Gishboliner and Li prove Ex(n,P)≤n^(1+O_P(1/log log n)), establishing the weak n^(1+o(1)) Pach–Tardos statement.
Buys, Polak and Zuiddam give Lean-formalized Shannon-capacity lower bounds for C7, C11, C13, C15, C19, C21 and C23 using seven explicit base tuples and Gao’s product lemma. Their C7 bound is 3.258805369885… and their C11 bound is 5.294502522149….
Xu and Wang exhibit a strongly convex rational quadratic program with A=B=I₂ and identity third block whose direct three-block ADMM has a bounded non-KKT orbit of minimal period 66. A separate Kimi search gives a locally attracting period-23 orbit in dimension three that can be converted to all-identity blocks.
Waldron proves a cone theorem for projective Q-factorial log-canonical fourfold pairs over eligible positive- and mixed-characteristic bases p>5, assuming log resolutions for the relevant pairs and numerical equivalence K_X+Δ≡_U M≥0.
For a plurisubharmonic weight on a product of polydiscs, Xia proves that the ambient multiplier ideal restricts to the fiber multiplier ideal outside a pluripolar parameter set. The paper also extends the result to holomorphic fibrations.
For every fixed sequence of T=n vectors in [−1,1]^n chosen before the algorithm runs, the model-generated proof gives O(√n) maximum online prefix discrepancy. The authors also prove longer-horizon and sparse-column extensions, including O(√n) for T up to exp(cn/log^(2+η)(en)) with the stated high probability.
For the stated deterministic grand-canonical three-dimensional hard-sphere gas with smooth spatially summable Gaussian-bounded initial density and gradient, exactly centered empirical fluctuations converge at every fixed finite set of times and tests to a Gaussian linear fluctuating Boltzmann field on each prescribed finite interval where the classical Boltzmann solution has uniform Gaussian velocity decay.
Pohoata constructs n incident point-line pairs in [0,1]² whose off-diagonal distances are at least n^(−2/3−ε) for every ε>0 and all sufficiently large n. With the previous upper bound, the maximum separation is n^(−2/3+o(1)).
An OpenAI manuscript claims a finitely presented integral Poincaré-duality group of dimension four with a finite oriented aspherical Poincaré complex, but no closed aspherical topological four-manifold model.
For every fixed ε>0, a deterministic polynomial-time algorithm on finite rational metric k-median instances with specified candidate facilities opens at most k facilities and attains factor 1+2/e+ε. Together with known P≠NP hardness, this gives infimum approximation factor 1+2/e.
For every subDL theorem A → B, GPT-5.6 Sol’s terminal-hierarchy argument claims that A and B share a variable with the same sign at the same relevant-arrow depth.
Gargava gives an exact rotated E8 lattice packing of B₂⁴ × B₂⁴ with density π⁴(1+1/√5)⁴/1024, about 9.67% above the product D4 packing. A separate determinant-preserving perturbation of the nine-dimensional densest lattice Λ9 has lower computed flat-torus height.
The tilted residue-class sieve gives Y(X)≫X log X/log₃ X for covering and maximal prime gaps G(T)≫log T log₂ T/log₄ T for all sufficiently large T.
For exact double covers of {0,1,2}^d by proper subboxes, Patrick White’s model-origin modular and line-rigidity argument gives f(4)≥19, f(5)≥33 and the unconditional bound f(6)≥60.
Every word-hyperbolic one-relator group is virtually compact special: a finite-index subgroup is the fundamental group of a finite nonpositively curved cube complex locally isometric to a Salvetti complex. With Kielak–Linton this yields virtual free-by-cyclic structure, allowing an infinite-rank free kernel.
Assuming the four stated characteristic conditions on the split connected semisimple group G over a finite field, every canonical unramified Arthur-filtration subspace on the full space of finitely supported automorphic functions is defined over Q and is independent of ℓ, including noncuspidal functions.
For PR[S] on square-free integers S⊂[2,n], with edges where gcd exceeds one, the n=51 graph has an exact integer Rayleigh witness showing its largest adjacency eigenvalue exceeds its number of distinct degree values.
For globally generic cuspidal complex automorphic representations of split connected adjoint absolutely simple groups of types G₂, F₄, E₆, E₇ or E₈ over global function fields, every local component is tempered, including arbitrarily ramified places and without a characteristic restriction.
For the single-neuron modular-addition setting, Appendix A extends Memana’s human counterexample to selection-independent Clarke trajectories and dead-neuron examples under the specified ReLU, dead-zone smoothing and fixed-step full-batch gradient-descent dynamics.
Any positive n-divisor arithmetic progression of height H with log H=o(√n) has length at least (√(8/27)−o(1))n^(3/4)/√log n. This excludes the proposed arithmetic-progression bounds at (α,β)=(1/3,1/3), and whenever α<1/2 and β<3/8.
Every infinite-dimensional complex normed space has unit vectors separated by at least 1+ε for some ε>0 even after either vector is multiplied by any scalar of modulus one.
For every 1<p<∞, Lp(L1) has uniform primary factorization and is therefore primary. The proof includes a scalar-compression argument on its doubly cancellative product-Haar part.
GPT-5.5 Pro’s Proposition 2 expresses the rank-two partial-trace quadratic form q⁽²⁾₋₁/₂(C) as projection terms. Song and Chen then use a separate human-developed lemma to prove nonnegativity and two-copy nondistillability at the Werner threshold.
For every bounded operator T:X→Y with separable Y, T is strictly cosingular if and only if its adjoint T* is strictly singular.
Star Fleet's construction shows that for every odd n at least 201, every integer k at least n·2^n·ceil(49n/100)^n+2 is the count of a tiling of the unit n-cube by positive homothetic cubes. This gives c(n)=o(n^n) along odd dimensions and refutes the proposed universal lower bound c(n)≫n^n; it does not determine the best bounds for c(n) in all dimensions.
Shmalo's paper verifies Ding–Sun Condition 1.2, including curvature and endpoint clauses, and Huang Condition 1.3 for the zero-margin Ising perceptron. Combining these with prior conditional and universality theorems yields M_N/N→α★≈0.8330786 in probability for Gaussian and fixed standardized subgaussian disorder, including Bernoulli.
Kafidov claims that, for every nonnegative 16-by-16 matrix with total entry sum 16, the Dittert functional (product of row sums plus product of column sums minus permanent) is at most 2-16!/16^16, with equality only at the constant matrix. The new joint-deficit scaling lemma makes a near maximizer doubly superstochastic after a sharper dilation and excludes a boundary maximizer at dimension 16.
Fredslund-Hansen, Mozes and Weimann report that, for a connected undirected unweighted planar graph with a designated face whose facial walk has k edges, the number of distinct facial distance-difference patterns is O(k^2), matching the known Omega(k^2) lower bound. The model supplied the forbidden-configuration and fixed-cardinality insight and a short prefix-trie proof; the paper's separate diameter algorithm is human-developed downstream work.
Three explicit Hermitian self-dual MDS codes with parameters [12,6,7] over F25 and [18,9,10] over F121 and F169 establish AME(12,5), AME(18,11), and AME(18,13); one-party projection establishes AME(17,11) and AME(17,13). The two length-18 matrices come from nine-entry group-circulant kernels; the theorem asserts existence, not classification.
Dong and Jain report that, for a nonnegative n-by-n matrix whose bipartite support graph has girth at least even g>=4, Theorem 1.3 proves Bethe(A)<=per(A)<=2^(2n/g)Bethe(A); disjoint unions of g-cycles attain the upper bound when g divides 2n. The model-developed intermediate proof had a weaker exp(n Theta(log g/g)) factor; the exact model-origin step retained in the final sharp proof is not identified.
For every epsilon>0, the OpenAI-authored manuscript constructs unital norm-separable C*-algebras on a common separable Hilbert space, with common identity and Kadison-Kastler distance below epsilon, which share their von Neumann closure but are not conjugate by any unitary. It does not assert abstract nonisomorphism or a von Neumann counterexample.
The OpenAI manuscript claims that, for dimensions 3 through 9, every smooth locally uniformly convex affine-maximal graph complete in its induced Euclidean metric is an elliptic paraboloid. The manuscript also derives the affine-metric-complete immersed-hypersurface corollary. The companion smooth nonquadratic entire example in dimension 10 is a separate contribution and does not supply affine-metric completeness.
The OpenAI-authored manuscript constructs unital von Neumann algebra pairs on separable Hilbert spaces with one-sided near-inclusion gaps tending to zero, yet every unitary embedding the source into the target stays a fixed distance from the identity. Spatial embeddings do exist; this does not refute two-sided Kadison-Kastler stability.
Moffat’s Theorem 3.1 claims to bound any single-letter entropy certificate whose classes contain product laws by c<=1-h(1/sqrt(2))/sqrt(2)=0.383099... . Theorem 3.4 gives a refined c<=0.382885260... ceiling when the iid protocol has a singleton class and other classes admit component hiding. These are limits of specified certificate methods, not bounds on the true union-closed constant. The paper's c>=0.38284 construction remains conditional on numerical hypotheses and is separate.
Theorem 1.1 claims that for every fixed integer r ≥ 4, each finite K_r-free graph on n vertices with average degree d ≥ 2 has an independent set of size at least c_r n log(d)/d, with c_r > 0 independent of n and d. It removes a log-log denominator in the fixed-clique-size average-degree bound; the paper does not optimize c_r or give an efficient algorithm.
Theorem 1 proves that the one-sided Airy factor g has v(x) = -(log g)''(x) > 0 and v(x) ≥ 4x. Since Chernoff's density f is proportional to g(x)g(-x), its curvature κ(x) exceeds 4|x| and has a positive global infimum. This proves strong log-concavity of the density of argmax_t{W(t)-t²}.
The complement of a 243-vertex ternary Golay Cayley graph has domination number and one-guard-moves eternal domination number both 3, below its vertex clique-cover number.
For k≥1 and δ,ε>0, Theorem 1.14 extracts an ε-tight uniform (k,δ)-ladder from a (t,2δ+ε)-tree at some depth t≤(1/ε)^(O(k/ε²)), avoiding a multicolored Ramsey step.
For independent W(q,r) contamination and the stated Hölder-smooth clean and contaminated densities in p dimensions, revised Theorem 4.1 gives the squared-loss pointwise minimax rate max{n^(−2s/(2s+p)), ε^(2s/(s+1+p/r))}. A smoothed kernel estimator attains the upper bound.
One bounded continuous stable radial pair potential in three dimensions has |φ(r)|≤C r^(−3−1/32) for r≥1 and finite canonical free energy. At one common βc in [7/8,9/8], the free energy has a strict inverse-temperature derivative jump for every density in an open interval around 5p/3.
For a projective four-dimensional log canonical pair with rational boundary over an algebraically closed characteristic-zero field, every program permitted by Definition 1.1 has finitely many birational steps for every choice of negative extremal ray.
If a smooth connected rationally connected projective complex manifold has a specified holomorphic splitting TX=E₁⊕E₂ into positive-rank subbundles, both summands are integrable.
Appendix A gives a Yoshinaga half-space-criterion proof of the two local arrangement obstructions used in genus-one differential-strata non-asphericity.
Appendix A proves that choosing one element from each of n sets of size k yields at least binomial(k+n−1,n) distinct multisets, using a multiset-shadow coupling. This establishes the edgeless-graph case of the unlabeled list-color conjecture.
For type-D ASEP with step initial data and fixed q, the standardized current of each species converges to the GUE Tracy–Widom F₂ law. Theorem 8.1 uses exact autonomy of each projected current and the known single-species step-ASEP limit.
A flat projective family over an open subset of the complex affine line has reduced Cohen–Macaulay fibers and smooth generic fiber, yet h¹(O) is 1 at the special fiber and 0 elsewhere.
An explicit 2×2 disk-domain example meets the stated Lorist–Schwenninger Lemma 1 hypotheses with ‖T‖>1 and Re⟨E₁Tx,x⟩<0. It rules out a proposed one-step positivity shortcut.
For circle-valued maps, Theorems 1.3–1.4 give degree inequalities with constants of order p−1 as p approaches 1 and order δ as δ approaches 0. The latter covers continuous maps for 0<δ≤√3.
Niedbala Giraudin gives an explicit irreducible degree-five Carlitz–Wieferich prime over F_(19³), refuting the proposed odd-characteristic rule that its degree must be divisible by the characteristic.
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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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