In 1991, Rousseau gave a new proof of Gauss's quadratic reciprocity by comparing two distinct coset representations of the group $(\mathbb{Z}_{p}^{*} \times \mathbb{Z}_{q}^{*}) / U$ using the Chinese Remainder Theorem, without Gauss's Lemma. In this paper, we extend Rousseau's approach to $\mathbb{F}_{q}[t]$, providing a new, elementary proof of the reciprocity law for the $d$th power residue symbol, where $d$ is any divisor of $q-1$.

This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties of notable graphs such as the Petersen graph, Paley graphs, Hamming graphs, and the Hoffman-Singleton graph, with emphasis on their symmetry and combinatorial structure. Connections with permutation groups are also discussed. Computational examples using SageMath are included to illustrate key concepts and to compute automorphism groups and related invariants.

A Galileo sequence \((a_n)\) is a sequence of positive integers whose partial sums $S_n$ satisfy $S_{2n}=kS_n$ for some $k>1$. In this paper we prove that every polynomial Galileo sequence is given by first differences of the form \(a_n= C\left(n^d-(n-1)^d\right)\). We then show that every positive Galileo sequence has a binary-tree representation. Finally, for positive monotone integer-valued Galileo sequences, we prove power-law growth bounds, and give a continuous analog together with a characterization of all continuous solutions.

This paper presents an algebraic-geometric construction of the derivative developed initially within the class of polynomial functions without introducing limits at the initial stage. Tangency is characterized by an algebraic condition: the difference between a function and a linear approximation has a double root at a given point. On this basis, the derivative is defined as a functional correspondence assigning to each point the slope of the tangent. Within the class of polynomials, the existence, uniqueness, and fundamental rules of differentiation are established purely algebraically. The constructed model is then extended conceptually to elementary functions and connected to the linear decomposition of functions, from which the classical limit representation of the derivative naturally emerges. Thus, the limit appears not as a starting point but as an analytic expression of an already constructed concept.

This paper develops a physical framework for the prebiotic emergence of information and meaning. Building on Constructor Theory, we define information as a reproducible physical difference and meaning as a difference with stable functional consequences. Casimir-Lifshitz-coupled protocell clusters serve as a minimal model that exhibits reproducible attractors, ordered transitions, and autonomous task structures. We show that such clusters carry both informational states (e.g., distances, geometries, gradients) and meaningful states that regulate prebiotic tasks such as approach, exchange, or stabilization. This approach integrates physical mechanisms, computational mechanics, and early proto-semantic functions into a coherent account of information formation before biology.

We give a method for constructing an interactive art piece which illustrates two different definitions of the braid groups, along with their faithful action on the free group. The box also demonstrates how all motions of points in the plane can be realized by motions in a single T-shaped subspace of the plane. This helps students and those who are not specialists in algebraic topology to understand these important topological objects.

Let $μ_λ$ be the Bernoulli convolution measure with parameter $λ\in(0,1)$. We study the regularity of the function %We prove that $h=h_ϕ:λ\mapsto \int_{\mathbb{R}}ϕ(x)\,dμ_λ(x)$ for Hölder observables $ϕ$. We describe sufficient conditions for both smoothness and non smoothness of this function. In particular, we show that for almost every function with respect to certain Wiener like measures on $C[0,1]$, $h_ϕ$ exhibits a phase transition: it is almost nowhere differentiable for small $λ$ and it is almost everywhere differentiable for large $λ.$

Accurate reconstruction of localized extreme structures remains a critical bottleneck in the physics-informed modeling of electro-thermal-convective flows. Although conventional physics-informed neural networks effectively capture smooth global dynamics, they frequently suffer from numerical diffusion and distortion when attempting to resolve sharp charge boundary layers or abrupt multiphase interfaces. To address these limitations, we propose a Residual-Attention Physics-Informed Neural Network (RA-PINN) that embeds gated attention modulation within a residual feature framework to adaptively enhance local sensitivity to steep physical gradients. The proposed architecture is rigorously evaluated against standard and recurrent network baselines using canonical electrohydrodynamic scenarios, encompassing near-electrode exponential boundary layers and sharply concentrated charge fields. Quantitative analyses demonstrate that the RA-PINN significantly reduces localized errors and faithfully preserves critical interface topologies without compromising the global consistency dictated by the coupled governing equations. Ultimately, this methodology establishes a highly robust predictive framework for resolving complex interfacial and boundary layer phenomena in advanced fluid dynamics applications.

F-theory compactifications with a nontrivial Mordell-Weil group realize abelian gauge symmetry through rational sections, but their consistency is ultimately a statement about the quantum effective action. We show that compactification on a circle makes this statement concrete: the quantized, parity-odd Chern-Simons couplings of the resulting three-dimensional theory provide a one-loop exact and scheme-independent encoding of all local four-dimensional abelian anomalies, including the mixed gauge-gravitational terms, together with their Green-Schwarz cancellation. We determine these Chern-Simons couplings in two logically independent ways, first from flux-induced terms in the M-theory dual description, and second from an explicit one-loop integration over the complete massive spectrum, including Kaluza-Klein towers and Coulomb-branch states. The agreement fixes all normalizations and clarifies how large gauge transformations reorganize the spectrum. We then show compatibility with type IIB modular duality once the known ten-dimensional duality counterterm is included, and we present a fully explicit rank-two example over projective three-space.

Scenario pathways (e.g. for the energy transition) often use a single trajectory or a band. That is not sufficient when one needs to understand why outcomes differ and under what stress or uncertainty they arise. Doing so requires tracking disequilibrium along pathways, comparing runs across "worlds" or storylines, and surfacing outcomes that are unlikely under a central view but plausible when how factors interact is uncertain. Cross-Impact Balance (CIB) is a well-established method for generating pathways. This paper extends CIB to formalise and implement these dimensions in pathway runs, and defines four run types that respectively emphasise one-off shocks, extremes under alternative regimes, influence-structure uncertainty that widens over time, and exogenous shocks as a baseline for comparison. The approach is applied to a socio-technical decarbonisation pathway for illustration. Together, the extensions support stress-testing, comparison across storyline or regime assumptions, and exploration of rare or surprising futures, and help analysts distinguish results that are stable across those assumptions from those that depend on structural uncertainty about the influence table.

A credit rating of AAA asserts near-certainty of repayment. This paper asks whether the pre-crisis information environment could have supported that assertion for structured products. Bayes' theorem implies that any reliability target requires a minimum level of statistical discrimination between instruments that will repay and those that will not. At structured-finance base rates, a four-nines reliability target demands discrimination on the order of 10,000 to 1. A three-nines target demands 1,000 to 1. Nothing in the published credit-prediction literature provides an affirmative basis for believing that discrimination of this magnitude was achievable with the data available at rating time. Retrospectively, the realized system fell short of the four-nines benchmark by roughly 90,000-fold. The framework accommodates the historical feasibility of corporate AAA ratings, where high base rates and rich information produce low required discrimination. Illustrative calibrations for contemporary collateralized loan obligations suggest that material tension between the precision target and the information environment persists. The central implication is that the AAA precision claim itself likely exceeded what the available information could support.

The Parker-Sochacki (PS) method is investigated as an alternative to Runge-Kutta (RK) methods for solving the Lorentz equations of motion for a charged particle in a static magnetic field. Traditional methods, including fixed-time-step fourth-order RK, adaptive Dormand-Prince RK, and Gauss-Legendre Runge-Kutta (RKG), advance the solution by sampling derivative estimates at selected points to approximate the solution over a time increment. In contrast, the PS method uses a power series expansion in time that is specific to the system of equations, which is a fundamentally different approach. We assess the accuracy and long-term stability of the RK, RKG, and PS methods for three static magnetic fields: uniform, hyperbolic tangent, and dipole, with the RKG method included only for the dipole problem. The PS method results in a 4 to 13 orders-of-magnitude improvement in kinetic energy conservation over the RK methods. When the methods are compared at matched target kinetic energy error, the PS method was substantially faster than RK4, the method with the shortest runtime under identical fixed-time-step conditions. For the dipole field problem, the PS method had the lowest kinetic energy error and had runtimes 4 to 5 times shorter than RKG when using the same fixed time step for proton runs. The PS method was the only method in this study to maintain accuracy and stability for all problems for both protons and electrons; the RKG method failed on all electron runs in the dipole problem. We further show that, over sufficiently long integrations in inhomogeneous magnetic fields, the symplectic RKG may exhibit secular growth in energy error. Overall, these results indicate that the PS method provides a computationally efficient and highly accurate alternative to the symplectic RKG and standard RK methods.

These are notes for a graduate-level introductory course on singularity categories.

Why do some national music markets sustain a rich musical diversity whereas others converge on mostly formulaic output? The existing models of cultural consumption (superstar economics, rational addiction, Bayesian social learning) each capture part of the answer, but none can explain how exposure, social influence, institutional gatekeeping, and algorithmic curation interact to shape what listeners come to prefer. We address this gap by modeling musical taste as a learning process rather than a fixed parameter: a listener's evaluative disposition evolves with each encounter, shaped by the balance between the comfort of the familiar and the reward of the new. Drawing on the active inference framework from cognitive science, we formalize this as a sequential choice model in which preferences, information, and the consumption environment co-evolve, and show how the framework nests and extends key mechanisms from the three canonical economic models. An agent-based simulation generates four predictions: algorithmic curation suppresses consumption diversity beyond a sharp nonlinear threshold; institutional structure determines winner-take-all intensity through confirmatory cross-system contrasts; cultural capital buffers listeners against homogenization; and high-curation, high-conformity systems collapse supply-side dispersion relative to pluralistic ecosystems. We test the framework against four national music ecosystems (Italy's Festival di Sanremo, Brazil, South Korea, and the United Kingdom), identifying structural determinants of ecosystem vitality on both the supply and demand sides. The welfare implications are direct: because listeners' preferences adapt to impoverished environments through the very learning mechanisms the model describes, revealed preference analysis cannot reliably evaluate the outcomes of cultural markets.

The 2030 Agenda for Sustainable Development of the United Nations outlines 17 goals as global challenges for countries of the world to address in their development. However, the progress of countries towards these goals has been much slower than expected. In a previous study, we analyzed the data over two decades (2000--2022), using unsupervised machine learning techniques. Based on this study, we take into account three main factors to construct a mathematical model to simulate and predict the dynamical behavior of the SDGs. These factors are: (1) the distribution of amount of resources that each country uses to meet the goals, (2) the cooperation between countries, and (3) the correlations between the goals. In this work, we show that the model is capable of reproducing the real data and therefore could be used to simulate hypothetical scenarios that could help to improve actions towards optimal fulfillment of the goals.

Despite growing interest in AI education, most AIED initiatives remain narrowly targeted toward STEM-prepared students, limiting participation by non-STEM learners and adults seeking to engage with AI in public-interest, policy, or workforce contexts. This paper presents and evaluates an NSF-funded, innovative mixed-cohort AI education model that intentionally integrates non-STEM undergraduates and adult learners into a shared learning environment centered on ethical reasoning, socio-technical judgment, and applied AI literacy rather than technical proficiency alone. Drawing on mixed-methods data from course surveys, open-ended reflections, and educator reports, we examine learners' academic agency, confidence navigating AI concepts, critical engagement with ethical tradeoffs, and perceived expansion of postsecondary and career trajectories. Quantitative results indicate significant gains in confidence and perceived relevance of AI across cohorts' participants, while qualitative analyses reveal a consistent emphasis on responsibility, judgment, and contextual reasoning over technical mastery. Instructors and near-peer mentors corroborated high levels of engagement and productive challenge, particularly in dialogic and scenario-based learning activities. Our findings suggest that human-centered instructional supports, such as ethical scaffolding, mentorship, and structured discussion, are essential components of equitable AI education, especially in heterogeneous and non-traditional learner populations. We argue that ethical judgment should be treated as a core learning outcome in AIED alongside AI literacy, and we offer design implications for expanding access to AI education in policy-relevant and workforce-adjacent contexts.

When software is designed by people from diverse identities and experiences, it is more likely to be inclusive and address a broader range of user needs. However, for transgender and non-binary students in software engineering, the path to becoming such creators may be marked by unique challenges. While existing research explores gender minorities in professional software engineering, limited attention has been given to their educational journey, a key phase for ensuring equal opportunities and preventing exclusion in the tech workforce. This study aims to address this gap by investigating the experiences of transgender and non-binary students in software engineering, with a particular focus on their motivations for entering the field, the obstacles they encounter, and potential strategies for fostering greater inclusivity within their academic environments. Based on 13 semi-structured interviews with transgender and non-binary students across the globe, we found that gender identity plays an indirect role in their decision to pursue software engineering. Key factors include the appeal of remote work and a personal desire to create more inclusive technologies. Although the participants did not report direct discrimination within their universities, many described experiencing verbal insults, judgment, intolerance, and hostility, all of which negatively impacted their mental health. These challenges often stem from socio-cultural norms and a lack of representation. Despite these obstacles, the students remain committed to their choice of study but call for greater institutional support, structural changes, and increased representation. From these findings, we suggest concrete steps to support students, regardless of gender identity.

This paper introduces Orthogonal Art, a proposed artistic discipline that emerges in dialectical response to artificial intelligence rather than in service of it. Unlike AI-augmented creative practices, Orthogonal Art is structurally defined by occupying the generative and conceptual spaces that current AI systems cannot access. As a founding instantiation of this framework, the paper presents a novel artistic practice in which technical schematics serve as the primary medium. A significant secondary contribution is the pedagogical dimension of the work: by grounding artistic practice in schematic logic and algorithmic structure, the framework provides an accessible entry point into the advanced field of Augmented Machines systems, enabling cross-disciplinary literacy within Humanities at the intersection of art, engineering, and philosophy.

Democracy is not a single mechanism. It is a space of possible configurations -- a spectrum stretching from pure direct participation to full delegation of authority. The systems we live under today occupy a narrow band of that spectrum, chosen centuries ago under constraints that no longer apply, and rarely questioned since. Votiverse is a platform for exploring the rest of that space. It provides organizations, communities, and institutions of any size with a configurable governance engine. Participants can vote directly, delegate their vote to trusted individuals by topic, or operate under any hybrid arrangement their group defines. Delegations are revocable, topic-specific, and transitive. A direct vote always overrides a delegation. In this model, traditional representative democracy is not the norm -- it is an edge case: the configuration you get when delegation is forced, universal, non-specific, and irrevocable for a fixed term. Votiverse introduces two structural innovations. First, a governance awareness layer -- a built-in system that monitors the delegation network and delivers contextual, progressive-disclosure reporting to participants at the point of decision. Second, a prediction-tracking accountability layer. Proposals carry falsifiable predictions. Outcomes are recorded. Over time, the platform builds a collective memory of what was decided, what was promised, and what actually happened. Together, these layers transform voting from a momentary act into an ongoing process of collective learning. This paper formalizes the governance model, situates it within existing work on liquid democracy and participatory decision-making, addresses known failure modes, and describes the architecture of the platform. The core platform has been implemented and released as open-source software.

This article presents CRED-1, an open, reproducible domain-level credibility dataset combining two openly-licensed source lists (OpenSources.co and Iffy.news) with four computed enrichment signals: domain age (WHOIS/RDAP), web popularity (Tranco Top-1M), fact-check frequency (Google Fact Check Tools API), and threat intelligence (Google Safe Browsing API). The dataset covers 2,672 domains categorized as fake, unreliable, mixed, conspiracy, or satire, each assigned a composite credibility score between 0.0 and 1.0. CRED-1 is designed for on-device deployment in privacy-preserving browser extensions to enable client-side pre-bunking of misinformation at the content delivery stage. The entire pipeline is implemented in Python using only standard library modules and is fully reproducible from publicly available sources. The dataset and pipeline code are released under CC~BY~4.0 and archived on Zenodo.

Retrieval systems are increasingly used in biomedical and clinical natural language processing applications, yet practical guidance for researchers building such systems is limited. In this work, we provide such guidance through an empirical study of how retrieval pipeline design choices affect performance and efficiency at scale. In particular, we examine retrieval over a variety of existing, public biomedical text datasets, leveraging a variety of disparate types of queries, including exam-style questions, conversational medical queries, community-asked questions, and non-question formulations across various retrieval pipeline settings spanning corpus selection, chunk granularity, and vector index configuration. Retrieval results are judged using a robust, win-rate comparison assessment via an LLM-as-a-judge setting with human validation. Across these experiments, we identify several points of concrete guidance for reviewers, including the superiority of corpus aggregation for absolute retrieval quality, and the emergence of MedRAG/pubmed as the Pareto-optimal singleton corpus under graph-based (HNSW) indexing, appropriate chunking strategies, and FAISS indexing choices that offer the best trade-offs in speed and efficiency.

We construct models for the classifying spaces of coabelian subgroups of right-angled Coxeter groups as homotopy orbit spaces of real moment-angle complexes, generalizing well-known models for the classifying space of a right-angled Coxeter group and its commutator subgroup. This identifies the cohomology of these groups with the Borel equivariant cohomology of elementary abelian $2$-group actions on cubical subcomplexes of a cube $[-1,1]^m$. We then characterize equivariant formality for these actions, leading to a simple graph-theoretic criterion for when the cohomology of a coabelian subgroup is free as a module over the cohomology of the quotient by the commutator subgroup of the right-angled Coxeter group.

We study the complexity of the Thouless-Anderson-Palmer (TAP) free energy for Ising spin glasses with a general mixed p-spin covariance, working with the generalized TAP functional of Chen, Panchenko, and Subag. We formulate three conjectures about the complexity (i.e. number of critical points). First, the annealed complexity is given by the Legendre transform of a variational functional constructed from the Parisi formula subject to a constraint on the overlap mass at zero, thereby establishing a precise link between the enumeration of TAP states and the large-deviation rate function of the partition function. Second, the quenched complexity is governed by the Legendre transform of a closely related functional in which the mass up to -- but not including -- the supremum of the support is constrained. Third, TAP states at any non-equilibrium free-energy level are organized into an ultrametric hierarchy, with ancestor states at other levels appearing only in subexponential number. Using a Kac-Rice computation combined with a supersymmetric ansatz, we establish a lower bound on the annealed complexity that matches the prediction of the first conjecture. We further extend the analysis to a conditional setting in which a hierarchical "skeleton" of ancestors is prescribed, providing additional evidence in support of the second and third conjectures.

We present high-sensitivity Very Long Baseline Interferometry (VLBI) observations of four ultraluminous X-ray sources (ULXs): Holmberg II X-1, IC 342 X-1, NGC 6946 X-1, and NGC 925 X-1. No compact emission was detected on milliarcsecond scales, with rms noise levels reaching approximately 5--20 $μ$Jy. The corresponding $5σ$ flux density upper limits reach $\sim 26\,μ\mathrm{Jy}$, implying radio luminosity limits $L_{\rm R} \lesssim 2 \times 10^{33}\,\mathrm{erg\,s^{-1}}$. This disfavors any persistently bright hard-state-like compact core at our sensitivity level. The previously reported VLBI core in Holmberg II X-1 exhibits significant long-term variability, broadly consistent with an overall decline over the past decades. This behavior is consistent with emission from optically-thin ejecta undergoing adiabatic expansion. The VLBI non-detections may reflect intrinsically weak/intermittent compact emission, and/or low--surface--brightness structure that is resolved out by VLBI, and/or absorption/propagation effects such as free--free absorption in dense, ionized winds.

The fragility of quantum metrological advantages under loss remains a major barrier to practical quantum sensing. For a two-photon-driven (TPD) Kerr resonator (TPD-Kerr model) subject to unavoidable single-photon loss (SPL), both the quantum Fisher information gain and squeezing level exhibit hard-to-track long-lived damped oscillations, restricting useful sensing and squeezing to extremely short time windows. We show that adding engineered two-photon loss (ETPL) -- forming a TPD-Kerr-ETPL hybrid model -- significantly mitigates these oscillations and converts the decay into a smooth, monotonic drop. This extends the high-sensitivity windows by over an order of magnitude. Moreover, we reveal a temporal hierarchy of quantum resources: the initial boost in metrological sensitivity arises from Gaussian squeezing, while sustained high-precision sensing stems from dissipatively stabilized non-Gaussian even-parity cat states. Crucially, only in models that include ETPL -- such as the TPD-Kerr-ETPL and TPD-ETPL systems -- does the dynamics actively mitigate SPL's detrimental effects, transforming damped oscillation into a smooth, easily trackable trajectory and enabling a prolonged, usable metrological window. Our approach transcends encoding-based or feedback-controlled schemes, offering a fully autonomous route to high-precision measurement without real-time feedback control. This establishes a general design principle: engineered loss, combined with appropriate driving, can actively preserve metrologically useful non-Gaussian quantum resources even in the presence of SPL -- paving the way toward robust, scalable quantum sensors in superconducting circuits, optomechanics, and trapped-ion platforms.

We employ the exact factorization of a multi-component wavefunction to analyze the dynamics of interacting photons, electrons and nuclei. We consider physical situations emerging in the regime of strong coupling between light excitations and molecular - electronic excitations, giving rise to the so-called molecular polaritons. Nonadiabatic molecular dynamics techniques, routinely used in the field of chemical physics, have been often employed to simulate photophysical and photochemical phenomena in the presence of molecular polaritons. In this work, we analyze the foundations of these techniques in the eye of the exact factorization and we assess their performance on illustrative model studies.

We investigate higher-rank transmissions for multi-connected Extended Reality (XR) devices enabled through tethering group (TGr), in which a nearby tethering User Equipment (UE) cooperates with an XR UE via a short-range tethering link (TL). In contrast to prior studies that are limited to rank-1 transmission and ideal tethering assumptions, we analyze TGr performance under higher-rank point-to-multipoint (PTM) transmission and realistic TL delays. Conventional single Outer Loop Link Adaptation (OLLA) offset results in inaccurate throughput prediction across ranks, leading to suboptimal rank selection. To address this limitation, we propose a multi-offset Outer Loop Link Adaptation (MO-OLLA) framework that introduces rank-dependent signal-to-interference-plus-noise ratio (SINR) correction to improve Link Adaptation (LA) accuracy. Furthermore, a Wireless Fidelity (WiFi) based delay model is incorporated to characterize the impact of practical TL constraints including limited bandwidth and achievable throughput on XR capacity and cellular resource utilization, providing the first such analysis for higher-rank multi-connected XR device. System-level simulations demonstrate that MO-OLLA provides up to 20% performance improvement over conventional OLLA for multi-connected XR UEs. Moreover, TGrs effectively exploit higher-rank transmission, achieving XR capacity gains of 180-200% over single-link XR UEs under ideal TL conditions. Critically, the gains of the TGr remain at 165-180% under realistic high-throughput TLs relative to single-link XR UEs, confirming the practical viability of TGr based cooperation for XR capacity enhancements within existing cellular resources.

In this paper we study boundedness and detailed spectral properties for the Cesàro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Cesàro-Hardy operators and their dual operators through subordination with $C_0$-semigroups $T(t)$ and $S(t)$ respectively. The spectral properties of the semigroup's infinitesimal generators are transferred to the Cesàro-Hardy operators using functional calculus methods. Furthermore, some implications for the Invariant Subspace Problem are explored by demonstrating the universality of certain translations related to the semigroup $T(t)$, and providing results on the invariant subspaces of these operators.

The discovery of higher-order topological insulator (HOTI) has established a new paradigm for understanding symmetry-constrained boundary electronic states. Here, based on first-principles calculations, we demonstrate the emergence of HOTI phase in organic lattices of two-dimensional azulenoid-kekulene-type carbon allotropes, namely AKC-[3,3] and AKC-[6,0]. Enabled by the $C_6$ rotational symmetry, the nontrivial bulk topology is confirmed through the topological invariant and fractionally quantized corner charge, giving $\{[M^{(I)}_{2}],[K^{(3)}_{2}]\}$ = $\{0,2\}$ and $Q_{\mathrm{corner}} = e/3$, respectively, accompanied by the emergence of exotic corner states in nanoflakes. Notably, the structural modifications are explored, revealing that in the derived structure PAK-[6,0], whose corner-localized states are preserved, highlighting the robustness of the higher-order topological phase. These findings highlight azulenoid-kekulene-based carbon allotropes as a promising platform to explore the interplay between structural design, crystalline symmetry, and higher-order topological boundary responses in two dimensional carbon systems.

Datalog is a declarative logic-programming language used for complex analytic reasoning workloads such as program analysis and graph analytics. Datalog's popularity is due to its unique price-point, marrying logic-defined specification with the potential for massive data parallelism. While traditional engines are CPU-based, the memory-bound nature of Datalog has led to increasing interest in leveraging GPUs. These engines beat CPU-based engines by operationalizing iterated relational joins via SIMT-friendly join algorithms. Unfortunately, all existing GPU Datalog engines are built on binary joins, which are inadequate for the complex multi-way queries arising in production systems such as DOOP and ddisasm. For these queries, binary decomposition can incur the AGM bound asymptotic blowup in time and space, leading to OOM failures regardless of join order. Worst-Case Optimal Joins (WCOJ) avoid this blowup, but their attribute-at-a-time intersections map poorly to SIMT hardware under key skew, causing severe load imbalance across Streaming Multiprocessors (SMs). We present SRDatalog, the first GPU Datalog engine based on WCOJ. SRDatalog uses flat columnar storage and two-phase deterministic memory allocation to avoid the OOM failures of binary joins and the index-rebuild overheads of static WCOJ systems. To mitigate skew and hide hardware stalls, SRDatalog further employs root-level histogram-guided load balancing, structural helper-relation splitting, and stream-aligned rule multiplexing. On real-world program-analysis workloads, SRDatalog achieves geometric-mean speedups of 21x to 47x.