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We present SpiderCat, a multiwavelength catalog of all publicly known compact binary millisecond pulsars (MSPs) in the Galactic field. These systems, colloquially known as "spiders," consist of neutron stars in tight orbits with low-mass companions, which are gradually ablated by the pulsar wind. SpiderCat includes both primary subclasses$-$redbacks and black widows$-$distinguished by companion mass, as well as candidates and peculiar systems such as transitional, huntsman and tidarren MSPs. As of this initial release, SpiderCat contains 111 entries: 30 redbacks, 50 black widows, two huntsmans, 23 redback candidates, five black widow candidates, and one huntsman candidate. In this paper, we compile and summarize key parameters for each system, including spin and orbital properties, and multiwavelength data from radio, optical, X-ray, and $γ$-ray observations. An interactive, publicly accessible web interface, at https://astro.phys.ntnu.no/SpiderCAT, enables exploration and visualization of the data. The rapid growth of the number of known spiders, accelerated by the Fermi Large Area Telescope survey and its ability to identify MSPs in $γ$-rays, has opened the door to population-lev

We introduce the canonical, parameter-free, and efficiently computable notion of peel neighborhoods in a finite metric space of strict negative type. Using a soft threshold to upper bound their radius or cardinality allows peel neighborhoods to be computed at scale, enabling useful microscopic descriptions of geometry and topology. As an example of their utility, peel neighborhoods enable efficient and performant estimates of local dimension and detections of singularities in samples from stratified manifolds.

Applications of metric magnitude often rely on numerically exact results in order to exploit a connection with information theory. We examine various approaches for scaling the dense linear algebra involved and identify hierarchical low-rank solvers as a preferred approach, with a clear path to scales of $10^5$ points on a single powerful workstation, and larger scales using our containerized CUDA-enabled C++/MPI pipeline.

We develop a scalable approach to computing the magnitude homology Euler characteristic for directed acyclic graphs based on decategorification. Along with motivating mathematical results and some simple controlled examples, we deploy the Euler characteristic in a proof of concept application to the dynamic analysis of multilayer perceptrons, recovering class-discriminative structure while holding simpler subgraph properties fixed.

We devise an algorithm to generate propositions that objectively instantiate graphs supporting coherence-driven inference. We also benchmark the ability of large language models (LLMs) to reconstruct coherence graphs from (a simple transformation of) propositions expressed in natural language, with promising results from a single prompt to reasoning-optimized LLMs. For example, o1/3/4-mini achieve perfect reconstruction half of the time on sparse graphs. Coherence-driven inference on consistency evaluations by LLMs may advance machine cognition capabilities.

Large language models (LLMs) can compile weighted graphs on natural language data to enable automatic coherence-driven inference (CDI) relevant to red and blue team operations in cybersecurity. This represents an early application of automatic CDI that holds near- to medium-term promise for decision-making in cybersecurity and eventually also for autonomous blue team operations.

We describe a unified and computationally tractable framework for finding outliers in, and maximum-diversity subsets of, finite metric spaces of strict negative type. Examples of such spaces include finite subsets of Euclidean space and finite subsets of a sphere without antipodal points. The latter accounts for state-of-the-art text embeddings, and we apply our framework in this context to sketch a hallucination mitigation strategy and separately to a class of path diversity optimization problems with a real-world example.

Inconsistencies are ubiquitous in law, administration, and jurisprudence. Though a cure is too much to hope for, we propose a technological remedy. Large language models (LLMs) can accurately extract propositions from arguments and compile them into natural data structures that enable coherence-driven inference (CDI) via combinatorial optimization. This neurosymbolic architecture naturally separates concerns and enables meaningful judgments about the coherence of arguments that can inform legislative and policy analysis and legal reasoning.

We demonstrate that large language models can produce reasonable numerical ratings of the logical consistency of claims. We also outline a mathematical approach based on sheaf theory for lifting such ratings to hypertexts such as laws, jurisprudence, and social media and evaluating their consistency globally. This approach is a promising avenue to increasing consistency in and of government, as well as to combating mis- and disinformation and related ills.

We examine (directed) greybox fuzzing from a geometrical perspective, viewing dissimilarities on inputs and on control flow graphs (with dynamical statistics) as primitive objects of interest. We prototype and evaluate GoExploreFuzz, a greybox fuzzer for time-intensive programs that incorporates this perspective. The results indicate useful capabilities for greybox fuzzing that have hitherto been underutilized, notably quantifying the diversity of paths and autonomously tuning the "bandwidth" of mutations.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

The Kuramoto-Sivashinsky equation was introduced as a simple 1-dimensional model of instabilities in flames, but it turned out to mathematically fascinating in its own right. One reason is that this equation is a simple model of Galilean-invariant chaos with an arrow of time. Starting from random initial conditions, manifestly time-asymmetric stripe-like patterns emerge. As we move forward in time, it appears that these stripes are born and merge, but do not die or split. We pose a precise conjecture to this effect, which requires a precise definition of 'stripes'.

We outline a geometrical correspondence between capacity and effective free energy minima of discrete memoryless channels. This correspondence informs the behavior of a timescale that is important in effective statistical physics.