We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavour ($N_{\mathrm{f}} =1$) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by numerical results obtained for the SU(2) gauge theory with two Dirac fermion flavours ($N_{\mathrm{f}} =2$) transforming in the adjoint representation, for which we perform numerical investigations at three values of the lattice spacing. The purpose of our study is to advance the characterisation of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate $γ_*$ decreasing significantly as one approaches the continuum limit for the $N_{\mathrm{f}} = 1$ theory towards a value consistent with $γ_* = 0.170(6)$, while for $N_{\mathrm{f}} = 2$ the anomalous dimension converges more rapidly with $β$ to a value of $γ_* = 0.291(9)$. A chiral perturbation theory analysis shows that the infrared behaviour of both theories is incompatible with the breaking of chiral symmetry.

Univariate marked Hawkes processes are used to model a range of real-world phenomena including earthquake aftershock sequences, contagious disease spread, content diffusion on social media platforms, and order book dynamics. This paper illustrates a fundamental connection between univariate marked Hawkes processes and multivariate Hawkes processes. Exploiting this connection renders a framework that can be built upon for expressive and flexible inference on diverse data. Specifically, multivariate unmarked Hawkes representations are introduced as a tool to parameterize univariate marked Hawkes processes. We show that such multivariate representations can asymptotically approximate a large class of univariate marked Hawkes processes, are stationary given the approximated process is stationary, and that resultant conditional intensity parameters are identifiable. A simulation study demonstrates the efficacy of this approach, and provides heuristic bounds for error induced by the relatively larger parameter space of multivariate Hawkes processes.

We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic quantum processes. This serves as a unifying framework for many models, including i.i.d., Markovian, periodic, and quasiperiodic models. We establish various characterizations of irreducibility, from which we recover a number of general ergodic theorems. We then analyze some specific examples, and, in particular, give a refinement of our theory in the i.i.d. case.

The resource theory with covariant Gibbs-preserving operations, also called enhanced thermal operations, is investigated. We prove that with the help of a correlated catalyst, the state convertibility for any coherent state is fully characterized by the free energy defined with the quantum relative entropy. We can extend this result to general resource theories in the form that imposing the covariant condition to a general resource theory does not change the state convertibility as long as the initial state is coherent and distillable. This means that the additional constraint from the law of energy conservation is irrelevant in the correlated-catalytic framework.

We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient method for the solution of linear, time-dependent problems: the Laplace transform (LT) and the model-order reduction (MOR) techniques, hence the name LT-MOR method. The application of the Laplace transform yields a time-independent problem parametrically depending on the Laplace variable. Following the two-phase paradigm of the reduced basis method, first in an offline stage we sample the Laplace parameter, compute the high-fidelity solution, and then resort to a Proper Orthogonal Decomposition (POD) to extract a basis of reduced dimension. Then, in an online phase, we project the time-dependent problem onto this basis and proceed to solve the evolution problem using any suitable time-stepping method. We prove exponential convergence of the reduced solution computed by the proposed method toward the high-fidelity one as the dimension of the reduced space increases. Finally, we present numerical experiments illustrating the performance of the method in terms of accuracy and, in particular, speed-up when compared to the full-order model.

Counterspeech has gained attention as a strategy to reduce hate speech on social media. Although previous studies suggest that counterspeech can reduce hate speech, little is known about its effects on participation in online hate communities. Relatedly, we lack an understanding about the degree of hostility in counterspeech. Hostile counterspeech may increase online conflict, potentially hardening the positions of hate adherents, and further eroding online environments. Here, we analyzed the effect of counterspeech on 16,513 newcomers across 104 hate subreddits (forums within Reddit.com). We devised an LLM-based counterspeech detection approach that outperforms specialized models trained on existing datasets, then examined the presence, and effects of, hostility. While counterspeech comments are less toxic than hate speech comments, they are almost twice as toxic as other discourse within hate subreddits. We then evaluated the effect of counterspeech on newcomer engagement in hate subreddits. We found that newcomers using hate speech who receive counterspeech are less likely to continue posting within these hate subreddits, rather than becoming galvanized. We speculate that, instead of constituting ardent hate adherents, readily-dissuaded newcomers may merely be toying with beliefs that are proscribed in other contexts. Although we found no association between the toxicity of counterspeech and its effects on user retention, consistent with prior research regarding the harmful effects of toxic speech, we found that toxic counterspeech increases the probability of continued hostility from hate users within the same discussion.

Most point process models for earthquakes currently in the literature assume the magnitude distribution is i.i.d. potentially hindering the ability of the model to describe the main features of data sets containing multiple earthquake mainshock aftershock sequences in succession. This study presents a novel multidimensional fractional Hawkes process model designed to capture magnitude dependent triggering behaviour by incorporating history dependence into the magnitude distribution. This is done by discretising the magnitude range into disjoint intervals and modelling events with magnitude in these ranges as the subprocesses of a mutually exciting Hawkes process using the Mittag-Leffler density as the kernel function. We demonstrate this model's use by applying it to two data sets, Japan and the Middle America Trench, both containing multiple mainshock aftershock sequences and compare it to the existing ETAS model by using information criteria, residual diagnostics and retrospective prediction performance. We find that for both data sets all metrics indicate that the multidimensional fractional Hawkes process performs favourably against the ETAS model. Furthermore, using the multidimensional fractional Hawkes process we are able to infer characteristics of the data sets that are consistent with results currently in the literature and that cannot be found by using the ETAS model.

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizontal displacement as well as renewal-process arguments.

Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic, the former linked to the flow of information, the latter to the structure of space-time. Leveraging a framework introduced in PRA, 106, 032204 (2022), which formally connects these two notions in general physical theories, we study their interplay. Here, information-theoretic causality is defined through a causal modelling approach. First, we improve the characterization of information-theoretic signalling as defined through so-called affects relations. Specifically, we provide conditions for identifying redundancies in different parts of such a relation, introducing techniques for causal inference in unfaithful causal models (where the observable data does not "faithfully" reflect the causal dependences). In particular, this demonstrates the possibility of causal inference using the absence of signalling between certain nodes. Second, we define an order-theoretic property called conicality, showing that it is satisfied for light cones in Minkowski space-times with $d>1$ spatial dimensions but violated for $d=1$. Finally, we study the embedding of information-theoretic causal models in space-time without violating relativistic principles such as no superluminal signalling (NSS). In general, we observe that constraints imposed by NSS in a space-time and those imposed by purely information-theoretic causal inference behave differently. We then prove a correspondence between conical space-times and faithful causal models: in both cases, there emerges a parallel between these two types of constraints. This indicates a connection between informational and geometric notions of causality, and offers new insights for studying the relations between the principles of NSS and no causal loops in different space-time geometries and theories of information processing.

This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point process model with temporal decay kernel being a Mittag-Leffler function. A maximum likelihood estimation scheme is developed and its consistency is checked. It is then compared to the ETAS model on three earthquake sequences in Southern California. The fractional Hawkes process performs favourably against the ETAS model. Additionally, two parameters in the fractional Hawkes process may have a fixed geophysical meaning dependent on the study zone and the stage of the seismic cycle the zone is in.

Let $L_0,L_1,L_2 \subset M$ be exact Lagrangian spheres in a Liouville domain $M$ with $2c_1(M)=0$. If $L_0,L_1,L_2$ form an $A_3$-configuration, we show that $\mathscr{L}(L_0)$ and $\mathscr{L}(L_2)$ endowed with the Hofer metric contain quasi-isometric embeddings of $(\mathbb{R}^\infty, \|\cdot\|_\infty)$, i.e. infinite-dimensional quasi-flats. A corollary of the proof presented here establishes that $\text{Ham}_c(M)$ itself contains an infinite-dimensional quasi-flat. We also show that for a Dehn twist $τ: M \to M$ along $L_1$ the boundary depth of $CF(τ^{2\ell}(L_0), L')$ is unbounded in $L' \in \mathscr{L}(L_2)$ for any $\ell \in \mathbb{N}_0$.

A central goal in the foundations of physics is to understand the structure of physical theories, such as quantum theory, from physical principles. This is often explored by considering various information-theoretic principles. Here, we initiate a similar approach considering relativistic causality principles. No superluminal causation (NSC) and no superluminal signalling (NSS) are distinct relativistic principles, requiring, respectively, that causal influence/the ability of agents to signal are within the future lightcone. After formalizing their distinction, we investigate how well theories constrained by NSC and NSS perform in a task that involves generating non-classical correlations. We find a spacetime configuration in which this task cannot be achieved in any theory (classical, quantum, or post-quantum) satisfying NSC. However, we show that theories violating NSC but satisfying NSS can perfectly achieve the task. We give a protocol that would, in a world allowing superluminal causation, enable its operational certification without violating NSS, in general spacetimes. In the case of $(1+1)$D Minkowski spacetime, the task remains achievable in a configuration where measurement outcomes occur arbitrarily earlier in time than the settings, allowing a new form of certifiable retrocausality without violating NSS. We illustrate our results by linking two different types of non-classical post-quantum resources: PR-boxes and jamming. Our work offers insights into the role of different relativistic causality principles in fundamental physics and paves the way for characterising the information-theoretic structure of theories obeying such principles.

We solve the problem of an interacting quantum dot embedded in a Josephson junction between two superconductors with finite charging energy described by the transmon (Cooper pair box) Hamiltonian. The approach is based on the flat-band approximation of the Richardson model, which reduces the Hilbert space to the point where exact diagonalisation is possible while retaining all states that are necessary to describe the low energy phenomena. The presented method accounts for the physics of the quantum dot, the Josephson effect and the Coulomb repulsion (charging energy) at the same level. In particular, it captures the quantum fluctuations of the superconducting phase as well as the coupling between the superconducting phase and the quantum dot (spin) degrees of freedom. The method can be directly applied for modelling Andreev spin qubits embedded in transmon circuits in all parameter regimes, for describing time-dependent processes, and for the calculation of transition matrix elements for microwave-driven transmon, spin-flip and mixed transitions that involve coupling to charge or current degree of freedom.

We report experimental measurements of the second-order coherence function $g^{(2)}(τ)$ of the light emitted by a laser-driven dense ensemble of $^{87}$Rb atoms. We observe a clear departure from the Siegert relation valid for Gaussian chaotic light. Measuring intensity and first-order coherence, we conclude that the violation is not due to the emergence of a coherent field. This indicates that the light obeys non-Gaussian statistics, stemming from non-Gaussian correlations in the atomic medium. More specifically, the steady-state of this driven-dissipative many-body system sustains high-order correlations in the absence of first-order coherence. These findings call for new theoretical and experimental explorations to uncover their origin and they open new perspectives for the realization of non-Gaussian states of light.

This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the unknown sparsity parameter in differentially private sparse linear regression (DP-SLR), eliminating the need for prior knowledge of model sparsity, which is a requisite in the existing literature. Next, we develop the DP debiased algorithm that enables privacy-preserving inference on a particular subset of regression parameters. Our proposed method enables privacy-preserving inference on the regression parameters by leveraging the inherent sparsity of high-dimensional linear regression models. Additionally, we address private feature selection by considering multiple testing in high-dimensional linear regression by introducing a DP multiple testing procedure that controls the false discovery rate (FDR). This allows for accurate and privacy-preserving identification of significant predictors in the regression model. Through extensive simulations and real data analyses, we demonstrate the effectiveness of our proposed methods in conducting inference for high-dimensional linear models while safeguarding privacy and controlling the FDR.

The relationship between the frame bounds of frames (Gabor) for the space $L^2(\mathbb{R})$ with several generators from the Weyl-Heisenberg group and the scalars linked to the sum of frames is examined in this paper. We give sufficient conditions for the finite sum of frames of the space $L^2(\mathbb{R})$ from the Weyl-Heisenberg group, with explicit frame bounds, in terms of frame bounds and scalars involved in the finite sum of frames, to be a frame for $L^2(\mathbb{R})$. It is shown that if a series of square roots of upper frame bounds of countably infinite frames from the Weyl-Heisenberg group is convergent and some lower frame bound majorizes the sum of all other frame bounds, then the infinite sum of frames for $L^2(\mathbb{R})$ space turns out to be a frame for the space $L^2(\mathbb{R})$. We show that the sum of frames from the Weyl-Heisenberg group and its dual frame always constitutes a frame. We provide sufficient conditions for the sum of images of frames under bounded linear operators acting on $L^2(\mathbb{R})$ in terms of lower bounds of their Hilbert adjoint operator to be a frame. The finite sum of frames where frames are perturbed by bounded sequences of scalars is also discussed. As an application of the results, we show that the frame bounds of sums of frames can increase the rate of approximation in the frame algorithm. Our results are true for all types of frames.

We investigate separability and entanglement of Rokhsar-Kivelson (RK) states and resonating valence-bond (RVB) states. These states play a prominent role in condensed matter physics, as they can describe quantum spin liquids and quantum critical states of matter, depending on their underlying lattices. For dimer RK states on arbitrary tileable graphs, we prove the exact separability of the reduced density matrix of $k$ disconnected subsystems, implying the absence of bipartite and multipartite entanglement between the subsystems. For more general RK states with local constraints, we argue separability in the thermodynamic limit, and show that any local RK state has zero logarithmic negativity, even if the density matrix is not exactly separable. In the case of adjacent subsystems, we find an exact expression for the logarithmic negativity in terms of partition functions of the underlying statistical model. For RVB states, we show separability for disconnected subsystems up to exponentially small terms in the distance $d$ between the subsystems, and that the logarithmic negativity is exponentially suppressed with $d$. We argue that separability does hold in the scaling limit, even for arbitrarily small ratio $d/L$, where $L$ is the characteristic size of the subsystems. Our results hold for arbitrary lattices, and encompass a large class of RK and RVB states, which include certain gapped quantum spin liquids and gapless quantum critical systems.

Central configurations are fundamental equilibrium solutions of the Newtonian $n$-body problem and play a key role in understanding the structure and dynamics of gravitational systems. However, the classification and enumeration of such configurations remain incomplete in the four-body case, particularly for symmetric configurations. In this work, we develop a framework for determining and classifying symmetric four-body Dziobek configurations. The method allows the explicit determination of the number of admissible configurations directly from the mass parameters, without requiring prior knowledge of their geometric structure. Combined with previously established semi-analytical relations, this approach provides a systematic characterization of symmetric configurations in terms of mass ratios. As a physically relevant application, we apply the framework to the Earth--Moon system and determine the possible symmetric four-body central configurations involving Earth- and Moon-mass bodies and an additional object of arbitrary mass. We identify both isolated configurations and continuous families of equilibrium solutions, extending the concept of libration points to the four-body problem. The presented semi-analytical approach contributes to the understanding of equilibrium structures in multi-body gravitational systems and provides a foundation for further studies in celestial mechanics, planetary dynamics, and spacecraft motion in complex gravitational environments.

The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was proved by Y. She. For hyper-Kähler varieties, which are higher-dimensional analogs of K3 surfaces, Y. André proved the Shafarevich conjecture for hyper-Kähler varieties of a given dimension and admitting a very ample polarization of bounded degree. In this paper, we provide a unification of both results by proving the (unpolarized) Shafarevich conjecture for hyper-Kähler varieties in a given deformation type. We also discuss the cohomological generalization of the Shafarevich conjecture by replacing the good reduction condition by the unramifiedness of the cohomology, where our results are subject to a certain necessary assumption on the faithfulness of the action of the automorphism group on cohomology. In a similar fashion, generalizing a result of Orr and Skorobogatov on K3 surfaces, we prove the finiteness of geometric isomorphism classes of hyper-Kähler varieties of CM type in a given deformation type defined over a number field with bounded degree. A key to our approach to these results is a uniform Kuga--Satake map, inspired by She's work, and we study its arithmetic properties, which are of independent interest.

Background: Combinatorial optimization problems (COPs) are central to Logistics and Supply Chain decision making, yet their NP-hardness prevents exact optimal solutions in reasonable time. Methods: This work addresses that limitation by developing a novel ternary network flow linear programming (LP) model of the assignment problem (AP) polytope. The model is very large scale (with Θ(m^9) variables and Θ(m^8) constraints, where m is the number of assignments). Although not intended to compete with conventional two-dimensional formulations of the AP with respect to solution procedures, it enables hard COPs to be solved exactly as "strict" (integrality requirements-free) LPs through simple transformations of their cost functions. Illustrations are given for the quadratic assignment problem (QAP) and the traveling salesman problem (TSP). Results: Because the proposed LP model is polynomial-sized and there exist polynomial-time algorithms for solving LPs, it affirms "P = NP." A separable substructure of the model shows promise for practical-scale instances due to its suitability for large-scale optimization techniques such as dantzig-Wolfe Decomposition, Column Generation, and Lagrangian Relaxation. The formulation also has greater robutness relative to standard network flow models. Conclusiuons: Overall, tyhe approach provides a systematic , modeling-barrier-free framework for representing NP-complete problems as polynomial-sized LPs, with clear theoretical interest and practical potential for medium to lrage-scale Logistics and other COP-intensive applications.

We study the relationship between line bundles on tropical compactifications of a very affine variety $Y$ and toric b-divisors on the associated tropical variety ${\rm Trop}(Y)$. By focusing on numerical equivalence classes, we construct a natural injective map from the group of numerical tropical line bundles on $Y$ to the space of toric b-divisors modulo linear equivalence. Moreover, we show that this map restricts to a bijection between the tropical nef cone of $Y$ and the set of toric b-divisors that are b-Cartier and tropically nef. This provides a higher-dimensional generalization of Baker's specialization for curves and clarifies the birational nature of tropical line bundles. We also discuss the kernel of the map from line bundles to numerical tropical line bundles, which encodes the continuous moduli lost in tropicalization.

We show that a rank two finite group G admits a finite G-CW-complex X homotopy equivalent to a sphere, with rank one prime power isotropy, if and only if G does not p'-involve Qd(p) for any odd prime p. This follows from a more general theorem which allows us to construct a finite G-CW-complex by gluing together a given G-invariant family of representations defined on the Sylow subgroups of G.

Let G be a rank two finite group, and let $\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X with isotropy in $\cH$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear G-CW-complex examples.

We define a nontrivial version of the square principle $\Box_ω$, which we then show consistent by means of forcing with finite conditions. This paper has been withdrawn by the author due to the fact that the presented $\Box_ω$ can be constructed in ZFC, as shown by Lajos Soukup and Philip Welch. Note, that the forcing itself has not been found flawed.

We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position expectation values and uncertainties for arbitrary wave packets and field states, allowing us to identify quantum corrections to the corresponding classical motion. While the corrections to the position expectation value are weak and largely insensitive to the quantum state of the field, the wave packet broadening exhibits a pronounced dependence on the field state. In particular, the quantum uncertainty of the radiation is directly imprinted onto the spatial uncertainty of the particle. We illustrate these effects for Gaussian wave packets interacting with coherent, Fock, and squeezed states, including bright squeezed vacuum. The interaction with a finite-duration laser pulse is also analyzed as a multimode example. Our results provide a transparent analytic route toward understanding how quantum fluctuations of light influence electron dynamics in strong-field settings.

We provide the first investigation of the solar production of symmetrons, a well-motivated class of screened scalar fields with density dependent couplings to the Standard Model, and their subsequent absorption in underground direct detection experiments. We compute the flux of symmetrons produced through photon conversion in the magnetic field of the solar tachocline, and constrain the resulting luminosity to not exceed 3% of the observed solar output. Even under the conservative assumption that production occurs only in the tachocline, this criterion yields robust astrophysical bounds on previously uncharted regions of symmetron parameter space, and predicts a keV-scale symmetron spectrum at Earth. We then derive the corresponding absorption signal in liquid xenon detectors, where symmetrons can interact with electrons through both conformal and disformal couplings. Using binned data from XENONnT, we obtain new direct-detection limits that are complementary to the solar luminosity constraint, further tightening the viable symmetron parameter space. Our results demonstrate that the Sun provides a testable, previously unexploited, source of symmetrons, and highlight that the interplay of astrophysical and laboratory searches offers a powerful strategy for probing screened scalar theories.

We show the existence of self-similar solutions with constant finite mass to the time-fractional Porous-Medium Equation for all spatial dimensions $d \ge 1$ and all exponents $m>m_c=(d-2)_+/d$. This range is optimal. We find two types of solution depending on the exponent: compactly supported solutions in the slow-diffusion range $m > 1$ and positive solutions with heavy tails in the sub-critical fast-diffusion range $m_c < m < 1$. The self-similar solutions in the linear case $m=1$ were already known explicitly obtained by the Fourier transform, and we discuss their properties in our settings and the limit $m \to 1$.

Quasi-projective dimension of modules over associative rings is generalized in this paper to the one of complexes of modules. Basic properties of this dimension are established, including a comparison result with projective dimension and a derived Auslander-Buchsbaum formula for complexes of finite quasi-projective dimension. Several sufficient conditions are provided for a commutative noetherian local ring to be a complete intersection under the assumption that each finitely generated module has finite quasi-projective dimension. This provides some positive answers to an open question on quasi-projective dimension proposed by Gheibi-Jorgensen-Takahashi. Moreover, the behavior of quasi-projective dimension under taking the quotient of a commutative ring modulo a regular sequence is investigated, and some partial results toward the change-of-rings question on quasi-projective dimension are given.

Enabling observability in software systems brings many benefits. It can, for example, ease the identification of issues or the implementation of improvements. It is especially critical to be able to observe sustainability-related dimensions of systems to know and mitigate their impact. However, adding observability to a system, especially related to software sustainability, requires technical knowledge that may not be available in every project that would benefit from it. In this work, we propose an architectural blueprint along with its deployment code that can be used to facilitate the addition of observability in software systems. As a special case, it includes measuring the energy consumption of software. This toolkit provides support in defining which components are necessary for a given use case and for structuring their deployment. Moreover, we exemplify the addition of observability in two different use cases.

Data errors are widespread in real-world databases and severely impact downstream applications, such as machine learning pipelines or business analytics reports. Causes of such errors are manifold and can arise during both the design phase and the operational phase of a database. Some error types, such as missing values, duplicate tuples, or constraint violations, are widely recognized; others, such as disguised missing values or word transpositions, remain underexplored. Existing attempts to define and classify errors in data offer valuable but limited taxonomies, mostly informal and not covering the full range of error types. With the rise of AI, practitioners must increasingly detect and correct statistical errors such as bias and outliers, which are rarely considered within existing error taxonomies. This catalog presents a comprehensive list of 35 distinct error types, including both data errors (e.g., missing values, duplicate tuples) and error indicators (e.g., outliers, bias) for tabular data, classified into three non-overlapping categories: missing, incorrect, and redundant. For each error type, we provide a formal definition and practical example, and resolve terminological inconsistencies across related work. Our catalog enables researchers and practitioners to address various error types and systematically implement error-specific detection and cleaning strategies in data quality tools.