New non-perturbative counterexamples to Min-Oo's Conjecture are created.
problem Min-Oo's Conjecture on positive curvature and mass.
method Quantitative Gromov-Lawson Schoen-Yau surgery.
result Construction of new non-perturbative counterexamples with more complex topology.
Counterexample disproves conjecture about 3-manifold modules.
problem Disproving a conjecture about 3-manifold modules.
method Provided a specific counterexample.
result Disproved Marché's conjecture about 3-manifold modules.
Counterexample disproves recent Penrose conjecture variant.
problem A variant of the Penrose conjecture.
method Provided a counterexample.
result The conjectured variant of the Penrose inequality is false.
Four counterexamples in surface homology.
problem Understanding surface homology and minimal homology bases.
method Presenting four specific counterexamples.
result Minimal homology bases can be challenging to work with.
After reconsidering the Dasbach-Hougardy counterexample to the Kauffman Conjecture on alternating knots, we reformulate the conjecture and consider Dasbach-Hougardy counterexample and similar counterexamples in the light of the reformulated conjecture.
If there are any 2-component counterexamples to the Generalized Property R Conjecture, a least genus component of all such counterexamples cannot be a fibered knot. Furthermore, the monodromy of a fibered component of any such counterexample has unexpected restrictions. The simplest plausible counterexample to the Gene…
Numerical study confirms Brennan's conjecture for a counterexample to Thurston's K=2 conjecture.
problem Thurston's K=2 conjecture and Brennan's conjecture in planar domains. method Numerical analysis of a specific counterexample to Thurston's conjecture.
result The counterexample does not contradict Brennan's conjecture.
Counterexample disproves HK-conjecture for flat manifolds of dimension 9 and higher.
problem Disproving the HK-conjecture for flat manifolds of various dimensions.
method Using flat manifolds of dimension 9 and higher, constructing counterexamples.
result Minimal dimension 9 is required for counterexamples, and higher dimensions are possible.
In this letter a generic counterexample to the strong cosmic censor conjecture is exhibited. More precisely---taking into account that the conjecture lacks any precise formulation yet---first we make sense of what one would mean by a "generic counterexample" by introducing the mathematically unambigous and logically st…
Counterexample shows Ito integrand needn't be locally square integrable.
problem Ito integrand's square integrability condition is not always met.
method Provided a counterexample to Ito's Lemma's integrability condition.
result Ito integrand needn't be locally square integrable.
The study finds infinitely many counterexamples to a generalized Double Soul Conjecture.
problem The Double Soul Conjecture for non-simply connected manifolds.
method Analysis of double disk bundles and counterexamples.
result Infinitely many counterexamples to the generalized Double Soul Conjecture.
Conjecture 1 of Stanley Chang: "Positive scalar curvature of totally nonspin manifolds" asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to this conjecture, based…
We present a novel framework for augmenting data sets for machine learning based on counterexamples. Counterexamples are misclassified examples that have important properties for retraining and improving the model. Key components of our framework include a counterexample generator, which produces data items that are mi…
Counterexample disproves conjectures about log canonical thresholds.
problem Conjectures about log canonical thresholds were disproved.
method Provided a counterexample to both conjectures.
result Conjectures about log canonical thresholds are false.
New method finds large counterexamples by selectively exploring triangulations.
problem Finding small counterexamples in 3-manifold triangulations. method Selective enumeration of triangulations using heuristics.
result Found counterexamples to three conjectures about vertex triangulations.
Researchers found counterexamples to a 2-jet determination theorem in higher codimension.
problem Counterexample construction to the 2-jet determination Chern-Moser Theorem in higher codimension.
method Constructed counterexamples of quadratic submanifolds with specific properties.
result Generated counterexamples to the 2-jet determination Chern-Moser Theorem in higher codimension.
Proves Girth Alternative for some HNN extensions, finds counterexamples.
problem Girth Alternative for HNN extensions of finitely generated groups.
method Proves Girth Alternative for a specific class of HNN extensions.
result Girth Alternative holds for some HNN extensions but fails in general.
We found an infinite family of counterexamples to Batson's conjecture.
problem Batson's conjecture about nonorientable 4-ball genus of torus knots is false.
method We identified an infinite family of counterexamples to Batson's conjecture.
result We found an infinite family of counterexamples to Batson's conjecture.
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
Study finds counterexamples to simple loop conjecture in higher dimensions.
problem Simple loop conjecture for surfaces to manifolds of dimensions at least four.
method Provided specific counterexamples for every g≥2 and n≥4. result No simple loop is contained in the kernel of the map for certain surfaces and manifolds.
The abstract explains counterexamples in 4-manifold topology.
problem Understanding the equivalence relations on 4-manifolds.
method Explains and provides counterexamples for various equivalence relations.
result Illustrates the failure of potential implications between equivalence relations.
The study finds counterexamples to curvature estimates for minimizing surfaces.
problem Curvature estimates for minimizing surfaces in metric convergence.
method Constructing sequences of smooth minimizing surfaces in metrics converging to Euclidean.
result Found counterexamples with diverging L2 norm of second fundamental form. It is well-known that intersection of continuous correspondences can lost the continuity property. Lechicki and Spakowski's theorem says that intersection of H-lsc functions remains H-lsc if the intersection is a bounded subset of a normed space and its interior is nonempty. Lechicki and Spakowski pointed to the import…
This paper disproves a conjecture about knot projections under specific homotopy conditions.
problem Reidemeister moves of types 1 and 3 are insufficient to describe all homotopies of circle immersions.
method Constructs counterexamples with minimal crossing numbers of 15 and higher, extending previous results.
result Obtains the first counterexample with a minimal crossing number of 15, extending to higher odd numbers.
Researchers find counterexamples to inverse problems for wave equations.
problem Inverse problems for wave equations on domains and Lorentzian manifolds.
method Constructing non-isometric Lorentzian metrics leading to same partial data measurements.
result Non-isometric Lorentzian metrics can produce identical partial data measurements.
For applications in computing, Bezier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R^3 and yields a smooth polynomial curve C embedded in R^3. It is of interest to understand when L and C have the same embeddings. One class of counterexamples is shown for L being unknotted, wh…
Counterexamples found for knot conjectures.
problem Knot conjectures regarding bounding Möbius bands in 4-ball.
method Examined torus knots T(2,5) and T(2,9) in 3D space.
result Found counterexamples to Allen's conjectures.
New counterexample shows curved surfaces can deform geodesics without diffeomorphism.
problem Can curved surfaces deform geodesics without changing their lengths?
method Constructs a perturbed surface with longer geodesics but no contracting diffeomorphism.
result No diffeomorphism can contract all tangent vectors on a surface with longer geodesics.
Counterexamples found for volume entropy conjecture in hyperbolic 3-manifolds.
problem Volume entropy conjecture in hyperbolic 3-manifolds.
method Construction of metrics with specific curvature properties.
result Found counterexamples to the volume entropy conjecture.
Counterexample found to estimate for skew-symmetric tensors.
problem Estimate for skew-symmetric tensors was claimed and used for classification results.
method Analysis of the estimate in arXiv:2103.15482.
result Counterexample disproves the estimate for skew-symmetric tensors.
Counterexamples to a conjecture on ribbon graph genus changes were found and proven.
problem A conjecture on genus changes in ribbon graphs was formulated and disproven.
method A family of counterexamples was found and proven.
result Essentially, the counterexamples found by Qi Yan and Xian'an Jin are the only ones.
The study finds flaws in methods used to estimate foreign exchange option prices.
problem Flaws in estimating foreign exchange option prices.
method Provided counterexamples of popular FX option interpolation methods.
result Popular FX option interpolation methods fail in certain scenarios.
Counterexample disproves log canonical Beauville--Bogomolov decomposition.
problem Disproving the log canonical Beauville--Bogomolov decomposition.
method Constructing a specific log canonical, K-trivial variety with non-birational fibers.
result Provides a counterexample to the Beauville--Bogomolov decomposition in the log canonical setting.
It is shown, using sutured manifold theory, that if there are any 2-component counterexamples to the Generalized Property R Conjecture, then any knot of least genus among components of such counterexamples is not a fibered knot. The general question of what fibered knots might appear as a component of such a counterexa…
Counterexample found for Stein property of certain solvable Lie groups.
problem Stein property of simply connected unimodular solvable Lie groups with left-invariant complex structures.
method Constructing a solvable Lie group with specific properties.
result A simply connected solvable Lie group with a left-invariant complex structure whose universal cover is not Stein.
A computational technique for calculating nullity vectors and kernel vectors, using the new Finsler package, is introduced. As an application, three interesting counterexamples are given. The first counterexample shows that the two distributions KerR and NR do not coincide. The second shows that the nul…
A counterexample disproves the unknotting number conjecture for a specific knot combination.
problem Disproving the unknotting number conjecture for a particular knot combination.
method Used Snappy to discover and verify a counterexample.
result A counterexample showing u(71#71)≤5 disproves the conjecture. COMET learns monotonic neural networks by incorporating counterexamples.
problem Enforcing monotonicity constraints in neural networks for real-world tasks.
method Counterexample-guided learning technique for ReLU neural networks.
result COMET achieves state-of-the-art results and improves model quality.
Abstract and counterexamples show limitations of cost-efficiency in incomplete markets.
problem Understanding cost-efficiency in incomplete financial markets.
method Simple 3-state model and expected utility maximization problem.
result Characterization of perfectly cost-efficient claims and its application to incomplete markets.
We show that the torus knot T4,9 bounds a smooth Möbius band in the 4-ball, giving a counterexample to Batson's non-orientable analogue of Milnor's conjecture on the smooth slice genera of torus knots.
Counterexamples to continuity of optimal transportation on Riemannian manifolds with everywhere positive sectional curvature are provided. These examples show that the condition A3w of Ma, Trudinger, & Wang is not guaranteed by positivity of sectional curvature.
A new formula detects differences between counterexamples and standard embeddings of circles.
problem Detecting differences between counterexamples and standard embeddings of circles.
method Introducing a Gauss diagram formula for two-component links.
result A desired function is found for the two-component case.
Clarifies the theory of the deconfounder by Imai and Jiang.
problem Theoretical requirements for the deconfounder algorithm.
method Clarifies the assumption of 'no unobserved single-cause confounders' using empirical studies.
result Imai and Jiang's clarification of the assumption does not hold for counterexamples proposed by Ogburn et al. (2020).
The study refines known counterexamples in 4D to satisfy certain inequalities.
problem Addressing counterexamples in Gromov's and Rosenberg's conjectures.
method Analyzing simply connected and non-simply connected four manifolds up to homeomorphism.
result Gromov's and Rosenberg's conjectures hold for simply connected four manifolds up to homeomorphism.
Compactness fails for curvature equations in high dimensions.
problem Compactness of solutions to curvature equations fails in high dimensions.
method Chen and Wu constructed a smooth counterexample.
result Compactness fails in dimensions not less than 35.
Paper proves weak unique continuation for harmonic functions on RCD spaces but finds counterexample for strong uniqueness.
problem Unique continuation of harmonic functions on RCD spaces, especially strong uniqueness.
method Establishes weak unique continuation theorem and provides counterexample for strong uniqueness.
result Found counterexample for strong unique continuation in RCD(K,N) spaces for N≥4 and K∈R.
Counterexample disproves Yashiro's theorem on surface knots.
problem Yashiro's theorem on pseudo-cycles of surface knots is not universally true.
method Provided a counterexample to Yashiro's theorem.
result Yashiro's theorem is disproven for pseudo-cycles of surface knots.
Counterexample disproves key index computation in Gromov's conjecture paper.
problem Disproving an index computation in Gromov's conjecture paper.
method Constructing a counterexample to an index computation.
result Counterexample disproves the main result of the paper.