Stellar rotation is a fundamental tracer of stellar magnetic evolution, age, and activity, with broad implications for Galactic archaeology and exoplanet characterization. The Transiting Exoplanet Survey Satellite (TESS) provides high-precision time-series photometry across the sky, enabling rotation measurements for an unprecedented number of stars. We present the TESS All-Sky Rotation Survey (TARS), an all-sky catalog of stellar variability periods for 1,046,317 stars with T < 16 and distances within 500 pc. We estimate that 93% of these periods are rotation periods. This catalog increases the number of rotation period measurements for stars with T < 16 within 100 pc by a factor of 2.3 and within 500 pc by 4.0. We also present a method to correct half-period aliases in TESS data and show that it reliably recovers periods as long as 25 days from a single TESS sector. TARS represents the largest homogeneous catalog of stellar rotation periods to date, providing a foundation for studies of stellar ages, young associations, and Galactic structure. We make the light curves used in our analysis available as a HLSP through MAST. Beyond the default TARS catalog, we provide code that allows users to generate rotation period catalogs with adjustable completeness and reliability thresholds. This code and all rotation period measurements are available through Zenodo.

The superconductor-insulator transition as a paradigm of quantum phase transitions has attracted tremendous interest over the past three decades. While the magnetic field and carrier density can be tuned to drive the transition, the role of disorder in the transition is not well understood due to the complicated interplay between superconductivity and electron localization. In this work, we controllably introduce disorder in a two-dimensional high-temperature superconductor by depositing iron clusters onto the superconducting monolayer Fe(Te,Se) crystalline film. The spectral evolution from superconducting gaps to insulating gaps with increasing disorder is detected by scanning tunneling spectroscopy measurements. When the disorder is strong, large U-shaped gaps are observed and attributed to the localization-enhanced Cooper pair correlation. Our observations provide the insight into the emergent phases of low-dimensional and high-temperature superconductors with disorder.

For window applications in hot climates, it is desirable to have windows with high visible transparency, while maintaining strong reflectance in both the ultraviolet and near infrared, to minimize unwanted heat gain. Given that more than 70% of incident solar energy is at wavelengths shorter than 1000 nm, achieving spectrally abrupt transitions from transparent to reflecting at the boundaries of the visible is essential. Such abrupt transitions at multiple wavelengths typically would require tens of dielectric layers, which is impractical for most window applications. Here, we propose and realize a structure comprising only eight planar layers that achieves sharp reflectance changes at ~390 and ~680 nm, resulting in high visible transmittance (>70%), and high near-infrared (>80%) and UV (>60%) reflectance, as well as high mid-infrared emissivity (>90%) for additional radiative cooling. We demonstrate that our engineered window reduces air temperature by up to 3.8 °C inside an enclosed box simulating a vehicle, compared to a box with a reference window.

If a computer could be assembled from superconducting components, the energy efficiency would far surpass that of conventional electronics. Historic research efforts towards this goal yielded pivotal breakthroughs in the development and discovery of scanning tunnelling microscopy and high temperature superconductivity. Although recent strides have been taken in advancing superconducting diode and switching technologies, harnessing read/writeable memory functionality in superconducting platforms has remained challenging. Here we show that bulk single crystal specimens of the triplet superconductor candidate uranium ditelluride (UTe$_2$) possess such properties. Upon applying a magnetic field to access an intermediate regime straddling two distinct superconducting phases, we find that direct current pulses can push the material in and out of a metastable state possessing an enhanced critical current $J_c$. This switching is controllable by the strength and duration of the stimuli, with the system `remembering' whether it is in the high or low $J_c$ state for extended periods. We interpret this to be due to competition between two distinct vortex species, which can be perturbatively pushed into a non-equilibrium high-disorder configuration with stronger pinning forces and thus higher $J_c$. Rather than requiring proximate magnetic or semiconducting interfaces, this memory functionality appears to be an intrinsic property of UTe$_2$ rooted in the superconducting order itself. Our findings underscore the rich complexity of quantum vortex matter, and demonstrate the viability of engineering a new class of superconducting memory elements with ultralow-power switching.

In this paper, we study special solutions of five autonomous integrable partial difference equations (P$Δ$Es). More precisely, we show that these P$Δ$Es admit special solutions that are described by non-autonomous ordinary difference equations arising from Bäcklund transformations of the third and sixth Painlevé equations and the Garnier system in two variables. This result provides a new perspective on the relationship between autonomous integrable P$Δ$Es and Painlevé-type dynamics.

We study fixed points of cellular automata with $N$ sites on random sparse graphs. In the large $N$ limit such models are known to exhibit phase transitions, from a ``frozen'' phase, where at most a finite number of sites fluctuate at long times, to a ``fluctuating'' phase where a finite fraction of sites fluctuate. We consider several models, calculating the first and second moments of the number of fixed points, and find that these moments remain finite in the large $N$ limit, except at the transitions where they become singular. The singularities can take several forms, including divergence of the mean or variance of the number of fixed points, on one or both sides of the transition. The type of singularity is related to properties of the mean field dynamics or dynamics of the distance between copies of the system. In configuration space, we find that fixed points are organized into clusters, each consisting of sets of fixed points that agree with one another except for on a finite number of sites. In the frozen phase there is only one cluster, while in the fluctuating phase there may be multiple clusters. If there are multiple clusters, the distance between fixed points in different clusters is extensive. We show that the differences within the clusters correspond to local changes near short cycles in the directed graph of connections whose influence is eventually limited. In the frozen phase, we calculate the full distribution of the number of fixed points.

While recent reductions of zero-sum partially observable stochastic games (zs-POSGs) to transition-independent stochastic games (TI-SGs) theoretically admit dynamic programming, practical solutions remain stifled by the inherent non-linearity and exponential complexity of the simultaneous minimax backup. In this work, we surmount this computational barrier by rigorously recasting the simultaneous interaction as a sequential decision process via the principle of separation. We introduce distinct sufficient statistics for valuation and execution, the sequential occupancy state and the private occupancy family, which reveal a latent geometry in the optimal value function. This structural insight allows us to linearise the backup operator, reducing the update complexity from exponential to polynomial while enabling the direct extraction of safe policies without heuristic bookkeeping. Experimental results demonstrate that algorithms leveraging this sequential framework significantly outperform state-of-the-art methods, effectively rendering previously intractable domains solvable.

The origin of the X-ray plateau phase observed in a large fraction of gamma-ray burst afterglows remains debated. We present a novel analytic framework for the hydrodynamics of ultra-relativistic, radially stratified outflows interacting with an external medium. By explicitly accounting for a continuous distribution of Lorentz factors within the ejecta, we derive analytic expressions describing the evolution of a long-lived, mildly relativistic reverse shock and determine its crossing time. Then, we compute the resulting synchrotron emission from both the forward and reverse shocks. The forward shock naturally produces a shallow, long-lasting X-ray decay consistent with the observed properties of X-ray plateaus, including the Dainotti relation, without requiring prolonged central-engine activity or an additional high-energy emission component. We further show that reproducing the observed plateau durations requires a broad distribution of ejecta Lorentz factors, extending down to $γ_\text{min}\sim70-100$, consistent with the ultra-relativistic outflow that powers the prompt $γ$-ray emission. The reverse shock generates a long-lived millimeter emission component that outshines the forward shock emission at these wavelengths. Both the plateau and reverse shock emission terminate smoothly once the slowest ejecta are processed, marking a transition to the standard Blandford-McKee self-similar evolution. Such stratified outflows are expected on physical grounds, as the ultra-relativistic ejecta responsible for the prompt $γ$-ray emission are unlikely to be launched with a single Lorentz factor. This model provides a unified picture in which the same outflow powers the prompt emission, the X-ray plateau, and the subsequent afterglow evolution.

Let $η$ be a fixed positive integer. Let $S$ be a subset of $\mathbb{Z}$, $\star:S\times S\to \mathbb{Z}$ be a binary function, and $ζ_η:\{ξ\in \mathbb{Z}:\gcd(ξ,η)=1\}\to \{0,1\}$ be a function. For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to S$ (where $|S|=n$) is called an arithmetic cordial labeling modulo $η$ under $\langle S,ζ_η,\star\rangle$ if the induced function $f_η^*:E(G)\to \{0,1\}$, defined by $f_η^*(uv)=0$ whenever $ζ_η(f(a)\star f(b))=0$ or $\gcd(f(a)\star f(b),η)\neq 1$, and $f_η^*(uv)=1$ whenever $ζ_η(f(a)\star f(b))=1$, satisfies the condition $|e_{f_η^*}(0)-e_{f_η^*}(1)|\leq 1$, where $e_{f_η^*}(i)$ is the number of edges with label $i$ ($i=0,1$). In this paper, we explore the arithmetic cordial labeling of some graphs under conditions imposed on the function $ζ_η$. The graphs included are star graphs, ladder graphs, alternate cycle snake graphs, join graphs, corona graphs, and tensor product graphs.

We present a Total Lagrangian finite element framework for finite-deformation multibody dynamics. The framework combines a compact kinematic representation, a deformation-gradient-based formulation, an element-agnostic constitutive interface, and a systematic constraint-construction machinery for coupling deformable bodies through engineering joints. Within this setting, we derive the equations of motion for collections of deformable bodies and formulate their response in the presence of external loads, frictional contact forces, and constraint reaction forces. The framework accommodates field forces applied pointwise, over surfaces, or throughout volumes, and supports material models of practical interest, including Mooney-Rivlin, Neo-Hookean, and Kelvin-Voigt. A companion paper discusses the GPU-accelerated implementation of the framework outlined herein and reports on numerical experiments and benchmark results.

We study once-excited random walks on general trees, modeled by placing a single "cookie" at each vertex. Each cookie acts as a metaphorical reward that is consumed upon the first visit to the vertex where the cookie is placed. On that initial visit, the walk is in an excited state and behaves like a biased random walk. Once the cookie is consumed, the process reverts to a symmetric random walk on all subsequent visits. We consider a random environment in which the bias parameters are independent random variables. We prove that the process exhibits a sharp phase transition between transience and recurrence on general trees with polynomial growth, where the critical threshold is determined by the branching-ruin number of the tree.

We study invariant random fields of nonlinear multiplicative stochastic heat equations in the weak disorder regime. Under a natural second-moment condition, we show that positive invariant fields are in one-to-one correspondence with bounded positive harmonic functions of the underlying space. This implies that the space of invariant fields inherits the structure of the Martin boundary. We also show that whenever the deterministic heat flow converges to a bounded harmonic function, the stochastic evolution converges to the corresponding invariant field. The results apply to many settings with nontrivial Martin boundary, such as negatively curved manifolds and trees.

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of fluctuations about the laminar base flow with respect to forcing amplitude, we establish a rigorous correspondence between linear resolvent analysis and higher-order nonlinear interactions. At second order, quadratic interactions of unsteady oblique waves generate steady streamwise streaks via the lift-up mechanism. We demonstrate that the spatial structure of these streaks is captured by the second output singular function of the streamwise-constant resolvent operator. At higher orders, nonlinear coupling between oblique waves and induced streaks acts as structured forcing of the laminar linearized dynamics, yielding additional streak components whose relative phase governs reinforcement or attenuation of the leading-order streak response. Our analysis identifies a critical forcing amplitude marking the breakdown of the weakly nonlinear regime, beyond which direct numerical simulations exhibit sustained unsteadiness. We show that this breakdown coincides with the onset of secondary instability, revealing that the nonlinear interactions responsible for streak formation also drive the modal growth central to classical transition theory. The resulting framework provides a mechanistically transparent and computationally efficient description of transition that unifies non-modal amplification, streak formation, and modal instability within a single formulation derived directly from the Navier-Stokes equations.

GitHub Security Advisories (GHSA) have become a central component of open-source vulnerability disclosure and are widely used by developers and security tools. A distinctive feature of GHSA is that only a fraction of advisories are reviewed by GitHub, while the mechanisms associated with this review process remain poorly understood. In this paper, we conduct a large-scale empirical study of the GHSA review processes, analyzing over 288,000 advisories spanning 2019-2025. We characterize which advisories are more likely to be reviewed, quantify review delays, and identify two distinct review-latency regimes: a fast path dominated by GitHub Repository Advisories (GRAs) and a slow path dominated by NVD-first advisories. We further develop a queueing model that accounts for this dichotomy based on the structure of the advisory processing pipeline.

Current multi-tonne-scale dark matter (DM) detectors are largely incapable of detecting light dark matter from the Galactic halo due to the energy threshold limitations of their recoil measurements. However, primordial black holes (PBHs) can evaporate via Hawking radiation to particles whose energies are set by the black hole temperature. Consequently, weakly interacting light dark matter (or dark radiation) particles produced in this manner can reach the Earth with sufficient flux and kinetic energy above the experimental thresholds. This opens up a novel avenue to probe the light dark sector in terrestrial experiments. In this work, we explore this possibility by considering fermionic DM produced through PBH evaporation and investigating its electron recoil signatures in direct detection experiments. We analyze both energy independent (constant) and energy dependent (scalar and vector mediated) DM-electron interactions, highlighting the strong dependence of the recoil spectra on the underlying Lorentz structure of the interaction. In addition, we also account for the attenuation effects due to the loss of kinetic energy while DM traverses through Earth's crust, which can significantly modify the incoming DM flux. Incorporating these effects carefully, we place constraints on light DM using the electron recoil data from XENONnT, LZ, and PandaX-4T. Finally, we also discuss the detection prospects of such dark matter in current and future generation neutrino detectors, such as Super-Kamiokande and Hyper-Kamiokande.

Community detection is a critical tool for understanding the mesoscopic structure of large-scale networks. However, when applied to aggregated or coarse-grained social networks, disjoint community partitions cannot capture the diverse composition of community memberships within aggregated nodes. While existing mixed membership methods alleviate this issue, they may detect communities that are highly sensitive to the aggregation resolution, not reliably reflecting the community structure of the underlying individual-level network. This paper presents the Link Fraction Mixed Membership (LFMM) method, which computes the mixed memberships of nodes in aggregated networks. Unlike existing mixed membership methods, LFMM is consistent under aggregation. Specifically, we show that it conserves community membership sums at different scales. The method is utilized to study a population-scale social network of the Netherlands, aggregated at different resolutions. Experiments reveal variation in community membership across different geographical regions and evolution over the last decade. In particular, we show how our method identifies large urban hubs that act as the melting pots of diverse, spatially remote communities.

It is shown that integration of a thin film superconducting strip with current-carrying control wires enables one to engineer a profile of supercurrent density $J(x)$ with no current crowding at the edges of a strip wider than the magnetic Pearl length $Λ$. Moreover, $J(x)$ in a strip can be tuned by control wires to produce an inverted $J(x)$ profile with dips at the edges to mitigate current crowding at lithographic defects and block premature penetration of vortices. These conclusions are corroborated by calculations of $J(x)$ in a thin strip coupled inductively with side control wires or in bilayer strip structures by solving the London and Ginzburg Landau equations in the thin film Pearl limit. Thermally-activated penetration of vortices from the edges and unbinding of vortex-antivortex pairs in inverted $J(x)$ profiles are evaluated. It is shown that these structures can be used to develop single-photon strip detectors much wider than $Λ$. Such detectors can be tuned {\it in situ} by varying current in control wires to reach the ultimate photon sensitivity limited by unbinding of vortex-antivortex pairs. The structures considered here exhibit a non-reciprocal current response and behave as superconducting diodes. They can also be used to study the physics of vortex matter in thin films not masked by penetration of vortices from the edges.

Accurately monitoring cognitive load in real time is critical for Brain-Computer Interfaces (BCIs) that adapt to user engagement and support personalized learning. Electroencephalography (EEG) offers a non-invasive, cost-effective modality for capturing neural activity, though traditional methods often struggle with cross-subject variability and task-specific preprocessing. We propose leveraging Brain Foundation Models (BFMs), large pre-trained neural networks, to extract generalizable EEG features for cognitive load estimation. We adapt BFMs for long-term EEG monitoring and show that fine-tuning a small subset of layers yields improved accuracy over the state-of-the-art. Despite their scale, BFMs allow for real-time inference with a longer context window. To address often-overlooked interpretability challenges, we apply Partition SHAP (SHapley Additive exPlanations) to quantify feature importance. Our findings reveal consistent emphasis on prefrontal regions linked to cognitive control, while longitudinal trends suggest learning progression. These results position BFMs as efficient and interpretable tools for continuous cognitive load monitoring in real-world BCIs.

We present the cosmological analysis of the one-dimensional Lyman-$α$ flux power spectrum from the first data release of the Dark Energy Spectroscopic Instrument (DESI). We capture the dependence of the signal on cosmology and intergalactic medium physics using an emulator trained on a cosmological suite of hydrodynamical simulations, and we correct its predictions for the impact of astrophysical contaminants and systematics, many of these not considered in previous analyses. We employ this framework to constrain the amplitude and logarithmic slope of the linear matter power spectrum at $k_\star=0.009\,\mathrm{km^{-1}s}$ and redshift $z=3$, obtaining $Δ^2_\star=0.379\pm0.032$ and $n_\star=-2.309\pm0.019$. The robustness of these constraints is validated through the analysis of mocks and a large number of alternative data analysis variations, with cosmological parameters kept blinded throughout the validation process. We then combine our results with constraints from DESI BAO and temperature, polarization, and lensing measurements from Planck, ACT, and SPT-3G to set constraints on $Λ$CDM extensions. While our measurements do not significantly tighten the limits on the sum of neutrino masses from the combination of these probes, they sharpen the constraints on the effective number of relativistic species, $N_\mathrm{eff}=3.02\pm0.10$, the running of the spectral index, $α_\mathrm{s}=0.0014\pm0.0041$, and the running of the running, $β_\mathrm{s}=-0.0006\pm0.0048$, by a factor of 1.18, 1.27, and 1.90, respectively. We conclude by outlining the improvements needed to fully reach the level of confidence implied by these uncertainties.

We develop an information-theoretic analysis of Quantum-Memory-Free (QMF) Quantum Secure Direct Communication (QSDC) under collective attacks as an alternative to the use of a conventional Quantum Key Distribution (QKD) protocol in conjunction with one-time pads. Our main contributions are: 1) a QMF-QSDC protocol that only relies on universal hashing of coded sequences without wiretap coding; 2) a set of privacy amplification theorems for extracting secrecy from coded classical sequences against quantum side-information. These tools open the way to the design of effective QMF-QSDC protocols.

Understanding how water wets graphene is critical for predicting and controlling its behaviour in nanofluidic, sensing, and energy applications. A key measure of wetting is the contact angle made by a liquid droplet against the surface, yet experimental measurements for graphene span a wide range, with no consensus for free-standing graphene. Here, we use a machine learning potential with ab initio accuracy to provide an atomistic first-principles prediction for this unsolved problem, finding a weakly hydrophilic contact angle of $72.1 \pm 1.5 °$. More importantly, we unveil that graphene's wetting properties are highly sensitive to mechanical strain: tensile strain makes graphene significantly less hydrophilic, while compressive strain induces coherent ripples around the droplet, resulting in pronounced anisotropic wetting and contact angle hysteresis. We show that there is a strong coupling between the three-phase contact line and the intrinsic thermal ripples of free-standing graphene, which contributes to this strain sensitivity. Our results demonstrate that the wettability of 2D membranes are governed not only by their chemistry but also by their dynamic morphology, introducing a new class of wetting behaviour unique to atomically thin materials that offers an additional explanation for variability in experimental measurements. These findings reveal that mechanical strain may be a practical route to controlling wetting in 2D nanomaterials-based technologies, with promising consequences for nanofluidic and nano-filtration applications.

We designed, fabricated, and characterized the properties of a silicon-based vacuum window suitable for millimeter-wave astrophysical applications. The window, which has a diameter of 124 mm, optically active diameter of 68 mm, and thickness of about 4 mm, gives an average transmittance and reflectance of 99% and 1%, respectively, a fractional bandwidth of 67%. Absorptive loss is below the detection limit of our measurement. The anti-reflection coating is made with laser ablated sub-wavelength structures (SWS), and the measured transmittance and reflectance values agree with modeling based on the measured SWS shapes. The window has been integrated into DESHIMA v2.0, an astrophysics instrument that took year-long observations with the Atacama Submillimeter Telescope Experiment.

Autonomous systems increasingly require moral judgment capabilities, yet whether these capabilities scale predictably with model size remains unexplored. We systematically evaluate 75 large language model configurations (0.27B--1000B parameters) using the Moral Machine framework, measuring alignment with human preferences in life-death dilemmas. We observe a consistent power-law relationship with distance from human preferences ($D$) decreasing as $D \propto S^{-0.10\pm0.01}$ ($R^2=0.50$, $p<0.001$) where $S$ is model size. Mixed-effects models confirm this relationship persists after controlling for model family and reasoning capabilities. Extended reasoning models show significantly better alignment, with this effect being more pronounced in smaller models (size$\times$reasoning interaction: $p = 0.024$). The relationship holds across diverse architectures, while variance decreases at larger scales, indicating systematic emergence of more reliable moral judgment with computational scale. These findings extend scaling law research to value-based judgments and provide empirical foundations for artificial intelligence governance.

Transition metal dichalcogenides (TMDs) and other van der Waals (vdW) semiconductors enable transfer-printed, lattice-mismatch-free stacking of many photovoltaic junctions, motivating a re-examination of multijunction detailed-balance limits under realistic material and optical constraints. Here, we develop a unified thermodynamic framework for a multijunction photovoltaic device, which can define a clear set of device-window constraints, optical boundary conditions, and luminescence/entropy penalties and therefore define how closely any realistic multijunction photovoltaic device can approach multicolor limit. By applying it to a conservative TMD bandgap window (1.0-2.1~eV), we show that the accessible bandgap window imposes a large-junction number (N) efficiency limit: under full concentration, unconstrained ladders approach 84.5% at N=50, whereas the TMD window plateaus near 63.4%. This efficiency plateau is set by photons outside the bandgaps, so radiative quality and optics dominate beyond N=5 junctions for realistic transfer-printed device stacks. We identify an experimentally achievable N=5 ladder Eg~(2.10,1.78,1.50,1.24, 1.00)eV and map each rung to candidate vdW/TMD absorbers. Using reciprocity and luminescence thermodynamics, we quantify penalties from finite external radiative efficiency, two-sided emission, and luminescent coupling, and introduce the upward-emitted luminescence power as an indicator of entropy-loss proxy. Incorporating excitonic absorptance and nanophotonic thickness bounds yields practical thickness and light-management targets for transfer-printed stacks. Finally, inserting an idealized nonreciprocal multijunction model into the reciprocity-optimized ladders provides conservative efficiency advantage estimates, which are consistent with negligible benefit for single junctions but measurable efficiency gains for multijunction TMD devices.

A suite of classifiers was developed to distinguish experimentally synthesized zeolites from computationally predicted zeolite-like structures. Using convolutional neural networks applied to 3D volumetric grids, these classifiers achieve accuracies more than an order of magnitude higher than previous approaches based on geometric filters or other machine learning methods. The best-performing model differentiates among hypothetical zeolites and those that can be synthesized as silicates, as aluminophosphates, or as both. This four-class classifier attains a false negative rate of 3.4% and a false positive rate of 0.4%, misidentifying only 1,207 of over 330,000 hypothetical structures--even though the hypothetical structures exhibit similar formation energies as real zeolites and chemically reasonable bond lengths and angles. We hypothesize that the ZeoNet representation captures essential structural features correlated with synthetic feasibility. In the absence of comprehensive physics-based criteria for synthesizability, the small subset of misclassified hypothetical structures likely represents promising candidates for future experimental synthesis.

Background: Open source software (OSS) libraries are critical components of modern software systems, yet their metadata-particularly links to source code repositories and donation platforms-is often incomplete, outdated, or inconsistent. Such deficiencies hinder dependency monitoring, security assessment, and the sustainability of OSS projects. Aims: This study aims to explain notable metadata practices in PyPI libraries, focusing on platform dominance, outdated links, and missing references to repositories and donation platforms. As this investigation relies on large-scale qualitative survey data, we further evaluate the robustness and quality of the LLM-based topic modeling approach used to derive the findings. Method: We conducted two surveys targeting PyPI authors and maintainers, collecting 1,776 open-ended responses. To analyze these responses, we developed a LLM-based topic modeling pipeline using LLaMA 3.3 70B, including preprocessing, topic extraction, and topic merging. Robustness was assessed across 30 repeated runs using Jaccard and cosine similarity, while topic quality was evaluated by 23 experts using a structured assessment framework and Randolph's Kappa. Results: The findings reveal that missing or outdated repository links are primarily associated with oversight, lack of awareness, or perceived irrelevance, while platform dominance is driven by ideological, technical, and organizational factors. Donation platform links are often omitted due to skepticism, limited perceived benefit, or lack of knowledge, and are preferentially placed on GitHub for visibility reasons. The topic modeling approach demonstrated high robustness (up to 88% lexical and 92% semantic similarity) and produced high-quality topics, with approximately 77-78% meeting all evaluation criteria and moderate inter-rater agreement.

Symbolic systems operate over precise identities: variables denote specific objects, pointers target precise memory locations, and database keys refer to singular records. Neural embeddings generalize by compressing away semantic detail, but this compression creates collision ambiguity: multiple distinct entities can share the same representation value. Exact identity recovery requires additional information precisely when representation fibers have size greater than one. The residual cost is controlled by a single combinatorial object: the collision-fiber geometry of the representation map $π$. Let $A_π=\max_u |π^{-1}(u)|$ be the largest collision fiber. The finite laws include a tight fixed-length converse $L \ge \log_2 A_π$, an exact finite-block scaling law, a pointwise adaptive budget $\lceil \log_2 |π^{-1}(u)|\rceil$, and an exact fiberwise rate-distortion law for arbitrary finite sources via recoverable-mass decomposition across representation fibers. The uniform single-block formula $D^\star(L)=\max(0,1-2^L/a)$ appears as a closed-form special case when all mass lies on one collision block, where $a = A_π$ is the collision block size. The same fiber geometry determines query complexity and canonical structure for distinguishing families. Because this residual ambiguity is structural rather than representation-specific, symbolic identity mechanisms (handles, keys, pointers, nominal tags) are the necessary system-level complement to any non-injective semantic representation. All main results are machine-checked in Lean 4.

Using data on shootings in U.S.\ K--12 schools from 1981 to 2022, we estimate the effect of temperature on school shootings and assess climate-change impacts. We find that days with maximum temperatures above 90$^{\circ}$F increase school shooting incidence by approximately 90\% relative to days with maximum temperatures below 70$^{\circ}$F. The response is concentrated in interpersonal incidents and in non-class periods, such as before school, dismissal, after school, and lunch: shootings during these periods more than triple on days with maximum temperatures above 90$^{\circ}$F, while shootings during class time show no detectable temperature response. The estimated effects are positive for both indoor and outdoor shootings and are larger for shootings involving fatalities or injuries than for shootings involving only minor or no injuries. Applying the estimated dose-response to future warming, we estimate that interpersonal school shootings increase by 6\% by mid-century (2051--2060) under moderate emissions (SSP2--4.5) and 8\% under high emissions (SSP5--8.5), or about 12 and 16 additional incidents per decade. The present discounted value of mid-century social costs is \$599 million under SSP2--4.5 and \$799 million under SSP5--8.5, driven primarily by lost lifetime earnings among exposed students. The results suggest that climate damages in schools may include rare but high-cost safety events, not only heat stress and learning losses.

Background: Open Source Software (OSS) libraries form the backbone of modern software systems, yet their long-term sustainability often depends on maintainers being reachable for support, coordination, and security reporting. Aims: In this paper, we empirically analyze the availability of contact information, specifically e-mail addresses, across 754,413 Python libraries on the Python Package Index (PyPI) and their associated GitHub repositories. Method: We examine where maintainers provide this information, assess its validity, and explore coverage across individual libraries and their dependency chains. Results: Our findings show that 79.1% of libraries include at least one valid e-mail address, with PyPI serving as the primary source (76.5%). When analyzing dependency chains, we observe that up to 97.7% of direct and 97.5% of transitive dependencies provide valid contact information. At the same time, we identify over 793,000 invalid entries, primarily due to missing fields. Conclusions: Our results indicate strong maintainer reachability, while highlighting opportunities for improvement, such as offering clearer guidance to maintainers during the packaging process and introducing opt-in validation mechanisms for existing e-mail addresses.

We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is represented by a stationary phase-field that represents a smooth indicator function. The fluid equations are approximated by a porous media approach and are time-dependent. In the latter aspect, the considered problem formulation extends earlier work. We prove that if the time horizon tends to infinity, minima of the time-dependent problem converge towards minima of the corresponding stationary problem. To do so, a convergence rate with respect to the time horizon, of the values of the objective functional, is analytically derived. This allowed us to prove that the solution to the time-dependent problem converges to a phase-field, as the time horizon goes to infinity, which is proven to be a minimizer for the stationary problem. We validate our results by numerical investigation.