Papers

This paper investigates the global well-posedness of strong solutions to a stress-diffusive Oldroyd-B system in two-dimensional smooth bounded domains in the zero Reynolds number (creeping flow) regime. The stress-diffusion term is kept explicit throughout the paper and is understood as the usual center-of-mass diffusion regularization of the Oldroyd-B constitutive equation. In the corresponding non-diffusive creeping-flow setting, the strongest available result is a Beale-Kato-Majda type breakdown criterion for the three-dimensional Cauchy problem due to Kupferman, Mangoubi and Titi [Commun. Math. Sci. 6 (2008)], and global well-posedness remains open even in two dimensions. We prove the global existence and uniqueness of strong solutions for arbitrarily large H1 initial polymeric stresses satisfying the natural non-negativity condition on the conformation tensor. The result covers the initial-boundary value problem on general smooth bounded domains and shows how the Stokes elliptic structure, the preservation of the non-negativity of the conformation tensor, and the stress diffusion combine to close large-data estimates at the H1 level. We also point out a regularity feature specific to the zero Reynolds number regime: the velocity field gains higher spatial regularity from the elliptic Stokes equation than the polymeric stress tensor.

The Bernstein problem for the affine maximal type equation \[ \sum_{i,j=1}^n f^{ij} w_{ij}=0,\qquad w\equiv \left[\det\left(\frac{\partial^2 f}{\partial x_i\partial x_j}\right)\right]^a,\quad x\in\Omega\subset\mathbb R^n, \] is a central problem in affine geometry. It originates from Chern's conjecture on entire locally convex graphs for the case $n=2$ and $a=-\frac{3}{4}$ in 1977. This conjecture was completely resolved by Trudinger and Wang in 2000, who moreover proposed a generalization to arbitrary dimension $n\ge2$ for $a=-\frac{n+1}{n+2}$ under the assumption of Euclidean completeness. Later, using real affine techniques, Li and Jia provided a new purely analytic proof of Chern's conjecture by establishing the Bernstein theorem for $n=2$ and $a\in(-\infty,-\frac{3}{4}]$. Despite considerable efforts over the past two decades, the higher-dimensional Chern's conjecture remains open. Recently, Du constructed explicit non-quadratic Euclidean complete solutions for $a\in[-\frac{n-1}{n},0)$. In this paper, from the perspective of submanifold theory and Calabi affine geometry, we investigate affine maximal type surfaces. It provides a geometric characterisation for Du's explicit Euclidean complete counterexamples—including Warren type, Trudinger-Wang type, and other solutions in dimension two. More importantly, we construct a new class of non-quadratic Euclidean complete affine maximal type hypersurfaces, which extends Du's parameter range, for all $n\ge 2$, to $a\in[-\frac{n}{n+1},\,0).$

We study nonlinear Dirac equations on the three-dimensional torus with subcritical Soler-type nonlinearities. The variational problem is strongly indefinite, while the non-coercive Soler potential prevents direct compactness. We recover the Palais–Smale condition by introducing a small coercive perturbation. Refined spectral estimates and a linking argument yield perturbed solutions with uniform energy bounds. Passing to the limit as the perturbation vanishes gives a nontrivial continuously differentiable periodic solution. This existence result holds for every spectral parameter in an explicit interval below the mass.

We introduce an accelerated gradient flow with an endogenous gradient-memory anchor and a nonlinear restoring–damping feedback. The anchor evolves from a weighted history of the gradients, while the nonlinear feedback is modulated by the squared coordinatewise displacement from the anchor. The resulting dynamics uses only first-order information from the objective function and does not involve explicit Hessian information. Under suitable assumptions, we establish global existence and uniqueness of strong solutions. A Lyapunov analysis yields the accelerated objective-value estimate $F(x(t))-F^\star=\mathcal{O}(t^{-2})$, with the nonlinear restoring–damping term contributing additional dissipation. Under similar assumptions, the primal trajectory converges strongly to a minimizer. When, in addition, the solution set $S$ is affine, the limit is identified explicitly as the Euclidean projection $P_S(z_0)$ of the initial anchor $z_0$ onto $S$. In particular, for rank-deficient least-squares problems, the dynamics selects the least-squares solution closest to $z_0$. We also establish a finite weighted dissipation estimate for the phase variable. Moreover, in coordinates where the nonlinear feedback is active, if the trajectory remains separated from the anchor over an interval, then the corresponding homogeneous phase dynamics acquires an additional polynomial decay factor. Numerical experiments illustrate the minimizer-selection, accelerated objective-value decay, and restoring–damping mechanisms.

In this article, we develop vertical control theorems for fine Selmer groups associated with Galois representations and their deformations in $p$-adic families. We apply them to provide new evidence for Conjectures A and B of Coates–Sujatha and to obtain pseudonullity of the fine Selmer groups for cyclotomic characters, elliptic curves, classical cuspidal newforms, and Hida families of $p$-ordinary cuspidal newforms.

In this paper, we study metrically bounded Volterra-type operators $J_g$ and $I_g$ on the area Nevanlinna spaces $N_\alpha^p$, where $1\le p<\infty$ and $\alpha>-1$. Choe, Koo and Smith \cite{CKS} obtained partial characterizations of the corresponding symbol classes, but the exact characterization was still open. We establish a Littlewood–Paley type characterization of $N_\alpha^p$ and use it to resolve this problem affirmatively. More precisely, $J_g$ is metrically bounded on $N_\alpha^p$ if and only if $g$ belongs to the Bloch space $\mathcal B$, while $I_g$ is metrically bounded on $N_\alpha^p$ if and only if $g\in H^\infty$.

Let $G$ be the topological fundamental group of a nonsingular complex projective surface. Troncoso and Urzúa proved that the Chern slopes $c_1^2/c_2$ of minimal surfaces of general type $S$ with $\pi_1(S)\simeq G$ are dense in $[1,3]$, and left $[1/3,1)$ open. We prove that they are dense in $[1/2,3]$, an interval that cannot be enlarged without contradicting either a theorem of Mendes Lopes and Pardini or Reid's conjecture. We prove more: the slopes of such surfaces with $K_S$ ample are dense in $[1/2,2]$, the first case in which the conjecture of Troncoso and Urzúa on ample canonical classes is established. The tool is an exact ampleness criterion for their product construction, which shows in particular that their own surfaces never have ample canonical class, whatever the defining sections.

Gradient-flow models are characterized by an intrinsic energy-dissipation structure, and faithfully preserving this structure at the discrete level is important for stable and reliable long-time simulation. To this end, we develop a Conditioning-Aware Representation Enhancement with Scalar Auxiliary Variable (CARE-SAV) framework, which constructs a compact spatial approximation space from flexible candidate features and evolves the gradient-flow dynamics directly within this space. The resulting fully discrete scheme preserves the discrete energy-dissipation law while providing a flexible alternative to conventional prescribed spatial discretizations. Rigorous analysis establishes the approximation capability, solvability, stability and convergence of the proposed method. Numerical experiments on representative gradient-flow problems demonstrate its accuracy, robustness and computational efficiency. We believe that CARE-SAV could provide a simple, flexible, and computationally efficient paradigm for structure-preserving discretization of gradient-flow problems.

Points in the unit ball of $\mathbb R^d$ are processed sequentially. Each new point $p_i$ is connected to a state $x_{i-1}$ that summarizes earlier observations, after which $x_i=\gamma x_{i-1}+(1-\gamma)p_i$, with $0\leq\gamma\leq1$. The cost is the sum of the $\alpha$-powers of the connection lengths. This constant-gain rule interpolates between the input-order path and the star centered at the initial point. For independent uniform points, we establish the stationary insertion-length distribution and prove that it decreases in stochastic order as $\gamma$ increases. If $d+\alpha>2$, or if $(d,\alpha)=(1,1)$, the optimal constant parameter satisfies $1-\gamma_N^*=\Theta(N^{-1/2})$, with an explicit asymptotic constant and closed bounds. For $\alpha=1$, its leading expected tree length equals that of the center star and is eventually smaller than the expected lengths of both endpoint constructions. For $\alpha=2$, the optimizer is unique and characterized exactly. For the same $N$, choosing $1-\gamma_N$ as a fixed positive multiple of $N^{-1/2}$ gives a sharp two-term expansion of the expected uniform-input cost and a maximal adversarial mean cost of $1+O(N^{-1/2})$. For every fixed $0\leq\gamma<1$ and $0<\alpha\leq3$, the exact asymptotic adversarial value is $(2/(1+\gamma))^\alpha$. When $d\geq2$, exponential weighting is within a factor smaller than $1.161^\alpha$ of the best fixed nonnegative weighted rule with the same average look-back, for $0<\alpha\leq3$. Comparison with the running mean highlights its time-homogeneous update, stationary coefficient profile, and fixed effective memory.

In this paper, we initiate the study of the Yang-Mills-Higgs-Schrödinger(YMHS) flow, i.e. the Hamiltonian flow of the Yang-Mills-Higgs functional defined on a symplectic fiber bundle. The YMHS flow provides a natural gauge-theoretic extension of the classical Schrödinger flow within the framework of symplectic reduction theory, and generalizes the Chern-Simons-Schrödinger equations to a non-Abelian gauge and non-linear fiber setting. We study its geometric structures and establish the local well-posedness of the corresponding Cauchy problem on compact Riemann surfaces.

Our main result is a computation of the full link Floer complex of the Borromean rings. The Borromean rings are well known to be an L-space link. We prove that the full link Floer complex is not a free-resolution of its homology, in contrast to the situation for L-space knots, plumbed L-space links, and two-component L-space links. We also describe the link involution of the Borromean rings, up to a minor ambiguity. The proof goes by way of studying some general techniques about $A_\infty$-deformations of L-space link Floer complexes. Our techniques give a simple criterion for when an L-space link must have formal link Floer complex, which reproves the existing formality results for one- and two-component L-space links.

Comparing correlation matrices across time or stress scenarios is critical in quantitative finance and multivariate statistics, yet sample estimation noise often obscures whether an observed distance reflects a true structural shift. We derive the asymptotic sampling distribution of the intrinsic off-log (log-Euclidean) distance between two independently estimated full-rank correlation matrices under the null hypothesis that their population correlation matrices coincide. Under general sampling with finite fourth moments, the scaled squared distance converges to a weighted sum of independent $\chi_1^2$ variables, with weights determined by the asymptotic covariance of the Generalized Fisher Transformation (GFT) coordinates. Under Gaussian sampling at independence, this simplifies to a parameter-free $4\chi_d^2$ law. To calibrate tail probabilities, we provide closed-form cumulant generating functions, Lugannani–Rice saddlepoint quantiles, and an explicit Chernoff envelope requiring no root-finding. The first moment of the limiting law establishes a simple rule of thumb for the baseline expected distance under the null hypothesis ($\operatorname E[d_{\mathrm{LE}}] \lesssim 2\sqrt{d/n}$ near independence), quantifying the average separation induced strictly by estimation error. We establish plug-in consistency, present an explicit Gaussian covariance factorization, compare the distance statistic with coordinate Wald tests, and characterize its local power.

We study the Cauchy problem for the defocusing mKdV equation with almost periodic initial data. If the initial data corresponds to a reflectionless Dirac operator which satisfies certain Craig-type conditions on the spectrum, we prove that the Cauchy problem has solution that is almost periodic in spacetime, and that this is the only solution which is locally bounded in a suitable sense. In particular, the result applies to small analytic quasiperiodic initial data with Diophantine frequencies.

Paradigmatic interaction models explain how collective behaviors can emerge in complex systems from interactions among the constituent agents. In bio-inspired swarms, however, interactions alone may not suffice to bring the population to a desired aggregate configuration within a prescribed time horizon, as needed in applications ranging from targeted therapy to collective transport and emergency evacuation. In the present work, we consider finite-horizon minimum-energy collective steering for inertial swarms that are subject to stochastic disturbances. We focus on the mean-field representations of these multi-agent systems driven by Cucker–Smale alignment or Morse attraction–repulsion interactions. Our objective is to steer the swarm between prescribed endpoint distributions using a state-feedback control, where the endpoint specifications can be full phase-space distributions (positions and velocities) or position marginals alone. Our formalism is rooted in the theory of Schrödinger bridges, which has inspired contemporary developments spanning statistical inference, biological modeling, stochastic control, and generative learning. Within the bridges framework, the uncontrolled interacting stochastic dynamics are viewed as a prior model, and the optimal control as the minimum-energy corrective drift needed to realize the prescribed distributions. We derive nonlinear, coupled necessary optimality systems with a time-symmetric structure reminiscent of classical Schrödinger bridges, and propose nested fixed-point schemes to numerically solve them. Numerical examples show that the obtained optimal control (corrective drift) can dynamically exploit or counteract the interaction forces, depending on whether the latter are favorable or adversarial to the steering task.

Exponential random graph models (ERGMs) describe dependence among network ties, but inference becomes difficult when the likelihood is intractable and candidate network statistics are strongly correlated. We introduce BERGM Elastic Net, an adaptive empirical-Bayes approach that combines lasso shrinkage with ridge stabilization in a Bayesian ERGM. A latent-variable formulation supports approximate exchange sampling, while empirical-Bayes updates adapt the amount of regularization to the observed network. We connect the proposed prior to elastic-net penalized likelihood and clarify the interpretation of thresholded reporting and coefficient grouping. The method is developed for over-specified network models containing many related structural and covariate effects.

The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Carlo algorithms. Under a suitable friction scaling, the underlying diffusion relaxes on a ballistic time scale, suggesting that these discretizations, suitably tuned, sample targets with condition number $\kappa$ in $O(\sqrt{\kappa})$ iterations. We prove that no fixed choice of step size and friction, based only on the curvature bounds and the dimension, achieves this acceleration: total variation mixing time lower bounds for OBABO show that ballistic cold-start mixing fails uniformly over the smooth strongly convex class, and the lower bounds extend, with the same orders, to BAOAB and the other four Strang splittings. The proof transfers non-acceleration from optimization to sampling. Eliminating velocity gives an exact noisy heavy-ball recursion, and by the non-acceleration theorem of Goujaud, Taylor and Dieuleveut, for every tuning either some Gaussian target has a mode with relaxation time at least of order $\kappa$, or an attracting cycle exists on a smooth potential; dilating such a potential as $U_R(x)=R^2U(x/R)$ preserves its curvature bounds and produces metastability for a number of steps exponential in $R^2$, from an initial state at Wasserstein distance $O(R)$ from equilibrium. Using contraction estimates of Leimkuhler, Paulin and Whalley and a Wasserstein-to-total-variation regularization estimate, we prove a complementary upper bound of $O(\kappa)$ steps, up to logarithmic factors, for a fixed-parameter OBABO tuning. Hence, among fixed-parameter OBABO tunings, the optimal condition-number dependence of cold-start total variation mixing over this class is linear, up to logarithmic factors. A direct Gaussian calculation also rules out fixed-parameter acceleration for the left-endpoint exponential integrator.

Modern medical research, such as dose-finding studies, seamless trials, and shared control designs, often involves comparing multiple treatments simultaneously. Despite its wide applications, most research focuses on continuous endpoints, leaving the inference for general outcome types in high demand. In this article, we propose a new inference method for conducting multiple-treatment comparisons involving endpoints within the generalized linear model (GLM) framework under covariate-adaptive randomization (CAR). First, we investigate the asymptotic properties of the standard Wald z-statistics (z-scores) in multi-arm trials, highlighting issues when the working model is misspecified, particularly through omitted covariates. Our theoretical findings reveal that these \textcolor{black}{z-scores} do not consistently converge to a standard multivariate normal distribution, leading to either conservative or inflated Type I error rates, depending on the specific GLM endpoint. Second, based on these theoretical results, we develop adjusted test statistics to correct the distributional problems. To appropriately control the family-wise Type I error rate inherent in multi-arm comparisons, we incorporate our adjusted statistics with Simes-type multiple-testing procedures. This robust inference method can effectively control Type I error while potentially improving power. Extensive simulation studies and a real-world application to a metastatic breast cancer trial confirm the effectiveness and practicality of our approach.

We develop a framework for PDE-constrained optimal control on Hilbert complexes and its structure-preserving discretization by finite element exterior calculus (FEEC), with emphasis on problems where nontrivial topology creates physically meaningful global modes. We separate the gauge-fixed local state from harmonic components representing global circulation or flux, and introduce finite-dimensional topological actuators whose reachable modes are determined jointly by domain topology and actuator rank. We establish well-posedness, weak optimality conditions, reachability results, and FEEC error estimates preserving the harmonic structure. Numerical experiments on contractible and multiply connected domains demonstrate circulation and cavity- flux control, rank-dependent reachability, mesh-independent optimization, and topology-induced singular convergence. We further extend the framework to time-dependent Maxwell control, where harmonic electric circulation and magnetic flux become dynamical states exhibiting explicit conservation and reachability properties.

This paper introduces and analyzes a novel algorithm—Truncated Fourier Filtering (TFF)—for the fast, high-order accurate evaluation of standard integrals and convolutions involving piecewise-smooth (possibly discontinuous) integrands over general $m$-dimensional domains ($m \ge 1$) employing an $m$-dimensional Cartesian grid. For an $N$-point discretization, the method runs at a computational cost of $\mathcal{O}(N)$ operations for standard integrals and $\mathcal{O}(N \log N)$ operations for convolutions, following, in either case, a one-time $\mathcal{O}(N \log N)$ precomputation step (not required in dimension $m = 1$). The core idea underlying TFF is to approximate the characteristic function of the integration domain by a truncated Fourier expansion of it over a suitably extended periodic domain, and to evaluate the resulting integrals via trapezoidal quadrature on a Cartesian grid with an appropriately chosen discretization size. Despite its conceptual simplicity, TFF attains high-order accuracy even for complex, possibly non-smooth or even non-Lipschitz geometries. A complete theoretical analysis is provided that establishes the superalgebraic convergence (i.e., convergence faster than any negative power of $N$) of the overall approach.

We determine the sharp constant in the nearest-neighbor Hardy inequality on $\Z^3$ with the Euclidean inverse-square weight. For every finitely supported function $u:\Z^3\to\C$, we prove \[ \sum_{x\in\Z^3}\sum_{j=1}^3 |u(x+e_j)-u(x)|^2 \geq \frac14\sum_{x\in\Z^3\setminus\{0\}} \frac{|u(x)|^2}{|x|^2}. \] The coefficient $1/4$ is sharp, and equality is not attained by a nonzero finitely supported function. The proof uses an explicit reciprocal edge field and an edgewise completion of squares, together with a concavity argument for the associated vertex weight.

We apply the $d$-invariants of Ozsváth-Szabó and a theorem due to Brendan Owens to determine the unknotting numbers of 194 alternating knots with 13 or fewer crossings.

We introduce the wavemap: a spatial portrait of noise effects that assigns each site a per-noise-level arrival delay l_\gamma (v) and cross-entropy loss L_\gamma(v). These observables are exact at the lightcone frontier, where bond dimension \chi is small and the simulation is most faithful. Eigenvalue analysis of the composed gate-plus-noise Pauli transfer matrices confirms that the studied noise is pure amplitude damping: the spatial propagation pattern is entirely determined by the gate, making the wavemap a model-free noise diagnostic. We apply the multi-product formula (MPF) to recover the noiseless Pauli weight field from the noisy samples, subject to the Lieb-Robinson causal constraint nMPF <= nnl . Fitting time-adaptive coefficients \alpha(t) over the frontier recovers up to 55% of the information loss relative to the best noisy sample, exploiting the fact that the frontier is where truncation error is smallest. On an IBM heavy-hex lattice with heterogeneous hardware noise the method identifies an information-starved regime, pointing to calibrated synthetic noise as the next required experiment.

System operators will probably allow virtual power plants (VPPs) to submit their feasible region (FR) for market clearing and dispatch. A VPP needs to determine its FR to submit as a whole based on the individual operation model of its internal distributed energy resources (DERs), which is an FR aggregation problem. Existing FR aggregation approaches rely on analytical methods, which have issues with generality and adaptability. In this paper, we propose a data-driven approach to approximate the energy-regulation FR of VPPs. It adopts the virtual battery model to approximate the aggregate FR of a VPP and determines the model parameters through inverse optimization based on generated multi-scenario operation data using the original operation model. Numerical tests verified the accuracy of the proposed method. We believe that our work helps to better leverage the flexibility of DERs.

Let $F\colon A\to\mathcal{P}(X)$ be a soft linear subspace of a linear space $X$ over $\mathbb{K}$. Its soft elements form the product $\prod_{t\in A}F(t)$. We use this representation to characterize selection spaces, decompose soft norms and soft linear operators into their sectionwise parts, and compare soft, uniform, and componentwise convergence. We also characterize completeness and continuity in the box, extended-supremum, and product settings. Neumann-series and fixed-point results are obtained as applications.

In this work, we study the Markov–Krein correspondence in both the univariate and multivariate settings. Our main result provides an explicit moment–moment formula expressing the multivariate moments of the inverse Markov–Krein transform in terms of the multivariate moments of the Markov-Krein transform via cyclic interval partitions. We also derive moment–cumulant relations involving classical, Boolean and free cumulants.

We prove thirteen results concerning three aspects of magnitude theory. The first four concern small-scale magnitude and microscopic weightings. We identify the derivative of the magnitude function at the origin with maximal energy, allowing the value $+\infty$, and construct finite spaces for which small-scale magnitude diverges or for which the one-point property and finite concentration do not produce a microscopic weighting. A fifth result disproves the conjectured monotonicity of magnitude by giving a fourteen-point metric space of strict negative type whose magnitude function decreases. The remaining eight results concern continuity and dimension. Magnitude is Hausdorff-continuous at finite subsets of finite-dimensional positive definite normed spaces, but need not be continuous on compact subsets, even under convexity, geodesicity, bounded tractability, or simultaneous Hausdorff and Lipschitz convergence. The same constructions disprove an $\ell_1$-intrinsic-volume formula and two tractability conjectures. Finally, we construct a countable compact space of negative type whose Minkowski dimension is zero and whose lower and upper magnitude dimensions are both infinite.

We study estimation of the von Neumann entropy of a $d$-dimensional quantum state from independent outcomes of a fixed rank-one measurement. Let $\kappa_\nu\in[1,d+1]$ denote the normalized trace-zero frame spread; $\kappa_\nu=1$ for exact complex projective $2$-designs. For any fixed rank-one measurement and $n\le c_2d^2/\kappa_\nu$, the minimax mean-squared error is at least $c_1\log^2\{d^2/(\kappa_\nu n)\}$. For bounded frame spread and every fixed $0<a<2$, the minimax risk is of order $\log^2 d$ throughout $n\lesssim d^{2-a}$; hence fixed uniform accuracy requires $\Omega(d^2)$ observations. Existing tomography bounds give bounded risk from $O(d^3\log^3 d)$ observations for finite equal-weight exact designs and the Haar covariant measurement, while the intermediate minimax regime remains open. The results concern a fixed measurement repeated independently across copies; adaptive and collective protocols, and protocols that reuse common randomness across copies, are not covered.

The paper "Algebraic derivations and radicals of automorphism groups of algebras" continues both the well-known line of description of algebraic derivations of semiprime associative algebras in terms of inner derivations of their symmetric Martindale rings of quotients, and results on the coincidence of the prime and weakly solvable radicals of subgroups of multiplicative groups of PI-rings using the example of automorphism groups of algebras associated with their algebraic derivations.

Conditional aggregation operators evaluate profiles relative to admissible contexts whose active sources, criteria, or rules may vary. For a fixed context, such an operator is indeed an ordinary monotone functional on the restricted profile. The nontrivial structure appears at the family level, where local functionals on different profile spaces must be compared and possibly represented by one global rule. We develop a fibered representation theory for families of conditional aggregation operators. After separating fiberwise properties from cross-context compatibility, we characterize global representability without assuming that the full universe is itself an admissible context. Such a family is generated by a monotone global functional if and only if its local values respect the pointwise order after canonical zero extension; when this holds, explicit least and greatest global generators are available. This yields a hierarchy whose inclusions can be strict between arbitrary, zero-extension-consistent, and globally representable families. For finite systems, we then establish an extremal extension theorem for partial capacities and derive an exact overlap criterion for gluing local capacities into global ones. Finally, calibrated representation-preserving integral schemes unify the Choquet, Sugeno, and Shilkret cases: zero-extension consistency is equivalent to projective compatibility of local set functions, while overlap-compatible local capacities yield sharp lower and upper fuzzy-integral scores. Evidence-fusion and multi-criteria applications interpret these results as robustness under inactive sources, context-dependent interaction, and structural uncertainty under incomplete cross-context information.

We solve the three-dimensional symplectization question for several examples. These include small Seifert fibered $L$-spaces, a family of Whitehead-link surgery $L$-spaces, $S^1\times S^2$, certain surgeries on the figure-eight knot, explicit families of Brieskorn spheres, and arbitrary finite connected sums mixing these manifolds. In particular, the result covers the Weeks manifold and infinitely many hyperbolic $L$-spaces. The main symplectic step is to construct Liouville cobordisms in both directions from a symplectomorphism of symplectizations. The resulting preservation of strong fillability and of the vanishing of the monopole Floer contact invariant, together with the comparison with the Heegaard Floer contact invariant, connected-sum formulas, and classification results for tight contact structures, proves the stated rigidity results.