The increasing demand for high-speed wireless connectivity and scalable quantum information processing has driven parallel advancements in millimeter-wave (MMW) communication transmitters and cryogenic qubit controllers. Despite serving different applications, both systems rely on the precise generation of radio frequency (RF) waveforms with stringent requirements on spectral purity, timing, and amplitude control. Recent architecture eliminates conventional methods by embedding digital signal generation and processing directly into the RF path, transforming digital bits into physical waveforms for either electromagnetic transmission or quantum state control. This article presents a unified analysis of direct-digital modulation techniques across both domains, showing the synergy and similarities between these two domains. The article also focuses on four core architectures: Cartesian I/Q, Polar, RF- Digital-to-Analog Converter (DAC), and harmonic/subharmonic modulation across both domains. We analyze their respective trade-offs in energy efficiency, signal integrity, waveform synthesis, error mitigations, and highlight how architectural innovations in one domain can accelerate progress in the other

Let $Q$ be a set of primes with relative density $δ$. We count integers in $[1,x]$ with prime factors all in $Q$ that also have a divisor in $(y,2y]$. We establish the order of magnitude for all $δ\in (0,1]$. This generalizes the case $δ= 1$ from the 2008 work of Ford. We also show that there is a phase transition at the critical point $δ= 1/\log 4$, for which we explicitly determine the behaviour.

Hobby has recently shown that almost all finite hyperfields of even order fail to be the quotient of a field. Using a probabilistic argument, we extend this result to all orders: a finite hyperfield is almost always non-quotient. This confirms a conjecture of Baker--Jin. We show that in almost every finite hyperfield the sum of any four or more nonzero elements contains 0. We also give a precise asymptotic for the number of finite hyperfields on a given finite abelian group.

Scientific visualization (SciVis) has become an essential means for exploring, understanding, and communicating complex scientific phenomena. However, the field still lacks a validated instrument assessing how well people read, understand, and interpret them. We present a scientific visualization literacy assessment test (SVLAT) that measures the general public's SciVis literacy. Covering a range of visualization forms and interpretation demands, SVLAT comprises 49 items grounded in 18 scientific visualizations and illustrations spanning eight visualization techniques and 11 tasks. Instrument development followed a staged, psychometrically grounded pipeline. We defined the construct and blueprint, followed by item generation, and expert review with five SciVis experts using the content validity ratio (mean CVR = 0.79). We subsequently administered a pilot test (30 participants) and a large-scale test tryout (485 participants) to evaluate the instrument's psychometric properties. For validation, we performed item analysis and refinement using both classical test theory (CTT) and item response theory (IRT) to examine item functioning and overall test quality. SVLAT demonstrates high reliability in the tryout sample (McDonald's omega_t = 0.82, Cronbach's alpha = 0.81). The assessment materials are available at https://osf.io/hr3nw/.

We present results from our ongoing campaign to follow up the satellite candidates from the Identifying Dwarfs of MC Analog GalaxiEs (ID-MAGE) survey. Previously, we published a list of 355 unresolved satellite candidates identified around 36~nearby LMC- and SMC-mass hosts (D$=$4$-$10~Mpc). We present the velocities of 83 satellite candidates from new Green Bank Telescope \hi\ observations, optical long-slit spectra, and the Dark Energy Survey Instrument Data Release 1. Based on their velocities, we identify six candidates as probable satellite galaxies ($6.5\times10^5\leq M_\star/M_\odot\leq1.5\times10^7$) and 77 as background galaxies. Our results underscore the ability of spectroscopic follow-up to effectively separate satellites from background galaxies. Using the refined sample, we update our previously derived estimates for the average satellite population per host and find 1.7$\pm$0.7 (1.0$\pm$0.3) satellites per LMC-mass (SMC-mass) host. Our current satellite sample includes 25 galaxies confirmed by distances or velocities. This set includes the complete satellite populations of three hosts (UGC~04422: zero satellites, UGC~08201: zero satellites, NGC~3432: four satellites), which we compare to simulations and known satellite systems from the literature. Our sample is nearly complete for the most massive satellites (M$_\star > 10^7~M_\odot$). We find these massive satellites have a quenched fraction of 10--25\%, placing them between the $<$5\% quenched fraction of isolated galaxies and the 40--70\% quenched fraction of MW-analog satellites with $10^7~M_\odot < $ M$_\star < 10^8~M_\odot$. This demonstrates the impact that low-mass galaxies have on the evolution of their satellites.

Generative AI services like ChatGPT and Gemini are some of the fastest-growing consumer services. Individuals using such services must accept their terms of use before access, and conform to these terms for continued use of the service. Established literature has shown that despite their status as legally-binding agreements, terms of use are not actually well-understood, and may contain implications that are surprising for consumers. In this paper, we analyse the terms of 6 generative AI services from the perspective of an EU-based consumer. Our findings, based on a developed codebook which we provide in the paper, reiterate known issues regarding generative AI services such as the default use of user data for training and surface new concerns regarding responsibility, liability, and rights. All terms in our analysis contained language that explicitly discards assurances regarding the quality, availability and appropriateness of the service, regardless of whether the service is free or paid. The terms also make users solely responsible for outputs meeting norms dictated by the provider, despite no information or control being provided over the functioning of the model, and at the risk of account termination. The terms further restrict users in how outputs can be used while service providers utilise both user-provided inputs as well as user-liable outputs for a wide variety of purposes at their discretion. The implications of these practices are severe, as we find consumers suffer from lack of necessary information, significant imbalance of power, and have responsibilities they cannot materially fulfil without violating the terms. To remedy this situation, we make concrete recommendations for authorities and policymakers to urgently upgrade existing consumer protection mechanisms to tackle this growing issue.

This study introduces a novel experimental configuration using OH-PLIF imaging to directly determine the stretch factor ($I_0$) in laminar premixed hydrogen flames transitioning from a quasi-stable to a thermodiffusively unstable regime. A rod-anchored V-flame is stabilised in a laminar premixed reactant flow. Near the anchoring rod, the mildly strained flame remains quasi-stable, exhibiting a smooth surface and a well-defined inclination angle ($θ_{\mathrm{s}}$) to the main flow. This stable branch is associated with a burning rate $S_{\mathrm{s}}$. Farther downstream, the flame abruptly transitions to a regime dominated by thermodiffusive (TD) instabilities, characterised by cellular structures and a wrinkled surface. The distance between this transition and the anchor decreases with increasing equivalence ratio. This TD-unstable branch exhibits a larger mean flame-surface angle ($θ_{\mathrm{u}}$), enabling direct determination of the flame-speed increase, $S_{\mathrm{u}}/S_{\mathrm{s}}$. It is assumed that this ratio represents the normalised flame consumption speed, $S_{\mathrm{c}}/S_{\mathrm{L}}$. Determination of $I_0$ additionally requires the increase in flame-surface area caused by the thermodiffusive instabilities. Three complementary methods are therefore used to evaluate the surface area of the TD-unstable branch ($A$) relative to a smooth reference area ($A_0$), yielding consistent trends in $A/A_0$ over the investigated equivalence-ratio range. The resulting $I_0$ values, with the main uncertainty arising from $A$, decrease monotonically with increasing equivalence ratio, from about 1.1--1.3 at $ϕ=0.35$ to 0.8--0.9 at $ϕ=0.40$, consistent with theoretical predictions. Additional numerical simulations in a reduced two-dimensional representation reproduce the same transition behaviour and yield qualitatively consistent results.

Identifying a universal material constitutive law, that describes the mechanical response of rubber-like solids for all deformation fields and achievable extensions, is an outstanding challenge. Here, we propose to exploit the propagation of elastic waves and demonstrate that monitoring incremental guided wave propagation in an elastomer plate undergoing uniaxial extension reveals model sensitivities that are inaccessible in the corresponding static test. We measure the dispersion relations of the three zero-order guided modes, propagating parallel and perpendicular to the direction of imposed elongation. We compare them with predictions from the acoustoelastic theory, that also take into account material rheology, using parameters extracted from fitting the uniaxial stress-strain curve across three successive elongation regimes, following the methodical procedure of Destrade $\textit{et al.}$ (Proc. R. Soc. A 2017). We evidence that our approach lifts the degeneracy between hyperelastic models with different functional forms of the so-called $C_2$ term, which remain undistinguishable from static uniaxial tension stress-strain measurements alone. However, like their static counterpart, our dynamics measurements cannot distinguish between different generalized neo-Hookean models.

In 2007, Papanikolas established that if Carlitz logarithms of algebraic functions are linearly independent over the rational function field, then they are algebraically independent. The purpose of the present paper is to provide a new proof of this theorem using Mahler s method instead of the theory of t-motives. We revisit and extend the approach developed by Denis, which enabled him in 2006 to prove this result in the particular case of the logarithm of elements in Fq(theta) via a Mahler system.

We study soft emission in QED during scattering of Faddeev-Kulish dressed states. The incoming and outgoing charged particles are accompanied by coherent clouds of soft photons with energies below a characteristic infrared scale $E_d$. We focus on explicit processes that allow the dependence of the soft factors on the hard particles' momenta and total angular momenta to be displayed clearly. We argue that the dressings remove the infrared divergences in hard amplitudes order by order in perturbation theory, effectively regulating the contributions from virtual soft photons at the scale $E_d$. Essentially, the Faddeev-Kulish hard amplitudes become equivalent to the infrared-finite part of the corresponding Fock-basis amplitudes. Finally, tree-level soft-photon emission is found to be suppressed once the dressings are extended to subleading order in the soft-momentum expansion, as prescribed in recent work by Choi and Akhoury.

In the prototypical AdS$_5$/CFT$_4$ correspondence, the free energy of $\mathcal{N}=4$ SU$(N)$ super Yang-Mills theory is commonly reproduced from the Euclidean on-shell action of five-dimensional gauged supergravity -- a consistent truncation of Type IIB supergravity -- rather than computed directly in ten dimensions. A longstanding obstacle to the latter is that the conventional Type IIB pseudo-action evaluated on the $AdS_5\times S^5$ background vanishes identically, apparently precluding a first-principles holographic comparison. A recent proposal by Kurlyand and Tseytlin, based on the Pasti-Sorokin-Tonin formulation, resolves this issue for a special class of backgrounds including the $AdS_5\times S^5$ vacuum by introducing a topological term required for consistency, yielding a non-vanishing on-shell value in agreement with holography. In this work we extend this refinement to a broader class of Type IIB backgrounds by introducing a generalized topological correction under milder conditions, encompassing AdS geometries of generic dimension and non-vanishing 2-form potentials. We test the proposal on non-trivial solutions such as the Lunin-Maldacena background and the $AdS_4$ $S$-fold solution, and find agreement with the corresponding lower-dimensional gauged supergravity on-shell actions and thereby with the expected holographic observables. Our results place direct holographic comparisons within the ten-dimensional Type IIB framework on firmer ground.

Child sexual exploitation and abuse (CSEA) case data is inherently disturbing, fragmented across multiple organizations, jurisdictions, and agencies, with varying levels of detail and formatting, making cross-case analysis, pattern identification, and trend detection challenging. This paper presents CaseLinker, a modular system for ingesting, processing, analyzing, and visualizing CSEA case data. CaseLinker employs a hybrid deterministic information extraction approach combining regex-based extraction for structured data (demographics, platforms, evidence) with pattern-based semantic analysis for severity indicators and case topics, ensuring interpretability and auditability. The system extracts relevant case information, populates a comprehensive case schema, creates six interactive visualizations (Timeline, Severity Indicators, Case Visualization, Previous Perpetrator Status, Environment/Platforms, Organizations Involved), provides a platform for deeper automated and manual analysis, groups similar cases using weighted Jaccard similarity across multiple dimensions (platforms, demographics, topics, severity, investigation type), and provides automated triage and insights based on collected case data. CaseLinker is evaluated on 47 cases from publicly available AZICAC reports (2011-2014), demonstrating effective information extraction, case clustering, automated insights generation, and interactive visualization capabilities. CaseLinker addresses critical challenges in case analysis including fragmented data sources, cross-case pattern identification, and the emotional burden of repeatedly processing disturbing case material.

Structured light in the quantum regime has garnered considerable attention due to the opportunities it offers when mixing light's internal degrees of freedom, for high-dimensional and multi-dimensional quantum states of light. A popular example is to harness polarisation and spatial entangled photons with a shared topological invariant that is robust against numerous families of noisy quantum channels. Yet, producing such states with high purity and adaptability remains challenging. Here we introduce a compact, self-locking Mach-Zehnder interferometer that integrates digital spatial light modulators with static beam displacers to map spatial-mode entanglement from a parametric down-conversion source onto topological entanglement with high fidelity. The device also mimics the action of a reprogrammable controlled-unitary gate, digitally driven by the spatial light modulator. This approach is an enabling platform and provides a practical route to generating reliable, high-purity quantum-structured light with topological features, both at the single-photon level and as entangled states, a direction of growing topical interest.

In this third study of the 'Resolving supermAssive Black hole Binaries In galacTic hydrodynamical Simulations' (RABBITS) series we develop and implement a geometrically thin relativistic accretion disc model, which self-consistently evolves the mass and spin vector of black holes via analytically modelling the structure of steady-state accretion discs. The model employs a suite of relativistic, local solutions where pressure is dominated by either gas or radiation, while opacity is primarily governed by either electron scattering or free-free absorption. These local solutions are piece-wisely combined to form the global structure of the accretion disc based on each solution's range of validity. By explicitly modelling the structure of accretion discs, the model mitigates the stochasticity inherent in Bondi-type prescriptions, resulting in an approach where every episode of black hole mass accretion is derived from first principles. For the first time, our model enables galaxy formation simulations to place constraints on accretion disc sizes and structures. In addition, flux and temperature radial profiles can be directly extracted from the simulation, enabling the generation of spectral energy distributions. Consequently, by incorporating the thermal structure and spacetime geometry around spinning black holes, our model more accurately captures the energetic output of quasars, overcoming critical limitations of classical approaches. Along with this manuscript, we make public a C version of the model appropriate to be used as a module in simulations, a Python version of the model that can be used independently to post-process any simulation and build mock accretion discs, and an updated version of the Relagn model that has the capability of producing SEDs by building an accretion disc for a given set of parameters and extracting its surface density, temperature, and opacity profiles.

We prove that every virtually free group $G$ has property (LR) of Long and Reid: each finitely generated subgroup of $G$ is a retract of a finite index subgroup. The main ingredient in the proof is a new embedding result stating that every countable virtually free group embeds in a double of a finite group. As a corollary, we show that any group commensurable with the direct product of a free group and a finitely generated abelian group has (LR). This applies to generalized Baumslag-Solitar groups of arbitrary rank $n \in \mathbb{N}$ with finite monodromy, which, in particular, include all non-cyclic one-relator groups with center.

Photomultiplier tubes (PMTs) are widely used as photon sensors for neutrino and dark matter detection. Accurate charge and time information extracted from PMT waveforms is crucial for event reconstruction. An algorithm based on deconvolution technology was proposed and applied to the reconstruction of PMT waveforms. This study further investigated the reliability of the deconvolution algorithm when handling a large charge dynamic range (0-200 photoelectrons), varying scintillation time profiles, and muon-induced large signals. Monte Carlo data confirmed that the deconvolution algorithm exhibits relatively stable reconstruction performance: the residual non-linearity of charge reconstruction is controlled to approximately 1\% over the range of 0 to 200 photoelectrons for various configurations of undershoots and scintillation time profiles, and the algorithm is capable of handling muon-induced large signals.

Current Large Language Models (LLMs) are gradually exploited in practically valuable agentic workflows such as Deep Research, E-commerce recommendation, and job recruitment. In these applications, LLMs need to select some optimal solutions from massive candidates, which we term as \textit{LLM-as-a-Recommender} paradigm. However, the reliability of using LLM agents for recommendations is underexplored. In this work, we introduce a \textbf{Bias} \textbf{Rec}ommendation \textbf{Bench}mark (\textbf{BiasRecBench}) to highlight the critical vulnerability of such agents to biases in high-value real-world tasks. The benchmark includes three practical domains: paper review, e-commerce, and job recruitment. We construct a \textsc{Bias Synthesis Pipeline with Calibrated Quality Margins} that 1) synthesizes evaluation data by controlling the quality gap between optimal and sub-optimal options to provide a calibrated testbed to elicit the vulnerability to biases; 2) injects contextual biases that are logical and suitable for option contexts. Extensive experiments on both SOTA (Gemini-{2.5,3}-pro, GPT-4o, DeepSeek-R1) and small-scale LLMs reveal that agents frequently succumb to injected biases despite having sufficient reasoning capabilities to identify the ground truth. These findings expose a significant reliability bottleneck in current agentic workflows, calling for specialized alignment strategies for LLM-as-a-Recommender. The complete code and evaluation datasets will be made publicly available shortly.

AI coding agents make empirical specification search fast and cheap, but they also widen hidden researcher degrees of freedom. Building on an open-source agent-loop architecture, this paper adapts that framework to an empirical economics workflow and adds a post-search holdout evaluation. In a forecast-combination illustration, multiple independent agent runs outperform standard benchmarks in the original rolling evaluation, but not all continue to do so on a post-search holdout. Logged search and holdout evaluation together make adaptive specification search more transparent and help distinguish robust improvements from sample-specific discoveries.

Crystal field quartets with quadrupole degrees of freedom play a crucial role in hidden ordering systems, as exemplified by CeB$_6$. We present a novel magnetoacoustic resonance technique that combines acoustically induced strain fields with a linearly polarized high-frequency microwave field to probe quadrupoles inherent in the quartet hidden behind magnetic properties. This method offers the advantage of enabling quantum quadrupole resonance transitions for large excitation energy gaps within quartet sublevels under a strong magnetic field, which cannot be achieved by acoustic experiments alone. Formulating a simultaneous single-phonon-single-photon absorption transition process using Floquet theory, we demonstrate how the transition probabilities are affected by changing the propagation direction of a bulk acoustic wave. The key result is that distinct maxima in transition probabilities, attributed to specific propagation directions, indicate a characteristic of quadrupole physics and exhibit an abrupt change owing to an induced ordered moment. This photon-assisted magnetoacoustic resonance technique will promote a broader range of applications of acoustic experiments for the study of quadrupole physics.

We introduce a mesoscopic model of dynamic Tetra-PEG hydrogel networks based on a hybrid Dissipative Particle Dynamics/Monte Carlo (DPD/MC) approach. Polymer chains are described by Finite Extensible Nonlinear Elastic (FENE) potential, while reversible cross-links are modeled with Morse potential and Monte Carlo bond exchange governed by Bell's force-dependent kinetics. After systematic calibration against theory and experiments, the model reproduces the characteristic Maxwell-like viscoelastic response of these networks. In particular, the relaxation time follows the expected scaling, $τ_R \propto τ_b (p - p_{\text{gel}})$, and the simulated storage moduli agree with experimental rheology. The mesoscopic resolution allows for graph-based topological analysis, where Tetra-PEG molecules and cross-links are represented as nodes and edges, providing access to bond distributions, fraction of dangling chains, and size of percolating clusters that are challenging to measure experimentally. Comparison with permanent-network predictions further suggests that dynamic bond exchange can affect bond distributions and delay the formation of a system-spanning cluster. This model bridges macromolecular bond kinetics and macroscopic mechanical properties, providing a complementary tool for rational design of dynamic polymer networks.

The role of quantum entanglement in thermodynamical systems remains elusive. Does entanglement result in thermodynamic advantages or does it impose fundamental limitations? Here, we unambiguously quantify the amount of heat and work in a quantum system that is due to the presence of entanglement. This is achieved by constraining the system's non-equilibrium dynamics to separable states, thereby isolating the impact entanglement has on thermodynamic effects. Unlike thermodynamic entanglement measures, which signify a loose connection between entanglement and thermodynamic properties, imposing a constraint constitutes an active intervention into a system -- answering how much of a system's thermodynamics is caused by (not correlated with) its quantumness. We benchmark our theory by applying the constrained dynamics to several multipartite systems, including quantum batteries and quantum refrigerators.

Interstellar objects (ISOs) motivate a coupled mission-design and inference question relevant to spacecraft dynamics and control in extreme environments: if volatile-rich, rotating comet-like bodies were used for sustained deep-space navigation by exploiting pre-existing hyperbolic motion and in-situ propellant, what stability requirements arise under non-gravitational forcing, and what astrometric signatures might distinguish active stabilization from uncontrolled natural dynamics? We develop a stability-theoretic framework for trajectory tracking with jet-actuated correction, and show that high-speed transit geometry -- including debris-belt avoidance and encounter phasing -- tightly constrains feasible trajectories, making long-horizon tracking stability mission-critical. We model tracking residuals as the balance of disturbances and corrective action, and derive stability conditions across four levels: disturbance-energy stability, outer-loop contraction, actuator-memory stability, and rotation-mediated (Floquet) stability. The analysis implies residual diagnostics that can motivate empirical tests: under comparable forcing, effective stabilization is expected to strengthen short-horizon error correction, reduce event-conditioned persistence and variance clustering, regularize standardized innovations, and yield bounded post-shock recovery. More broadly, the framework provides a reference for deep-space guidance and control under nonlinear, multi-field disturbances and for planetary-defense concepts involving attitude shaping or impulsive kinetic impact.

Interstellar comets arrive with key ingredients for deep-space platforms already in place: volatile inventories convertible to propellant, natural rotation providing continuous attitude variation, and hyperbolic trajectories that carry them through the inner Solar System and back out to interstellar space. Rather than constructing spacecraft from scratch, we ask what \emph{minimal modification} is required to steer such a body along a controlled trajectory. The answer is surprisingly modest. By relaxing full six-degree-of-freedom control to forward-cone steering -- sufficient for practical navigation -- we show that \emph{four thrusters suffice}: one primary jet and three secondary jets at $120^\circ$ intervals. The secondary jets synthesize continuous in-plane steering, while the primary jet provides low-bandwidth attitude shaping: as the body rotates, the primary-jet torque direction sweeps predictably over a cycle, enabling out-of-plane steering via phase-scheduled firing. We formalize reachability under bounded-curvature constraints, characterize the rotation-mediated steering envelope, discuss enabling requirements including non-solar power at large heliocentric distances, and identify operational regimes and observable signatures implied by active trajectory control. The setting of a nutating axis is briefly considered and conjectured to preserve core results. The findings contribute to the broader effort of understanding the dynamics and control of small-body missions and offer a reference architecture relevant to long-horizon deep-space exploration and to potential planetary-defense concepts.

Antiferromagnets offer an attractive platform for spintronics due to their absence of net magnetization and ultrafast spin dynamics, yet their intrinsically spin-compensated electronic structure has traditionally limited their active role in spin transport. Here we identify a minimal, correlation-driven route to spin-polarized charge transport in collinear antiferromagnets. Using the doped antiferromagnetic Hubbard model within dynamical mean-field theory, we show that electronic correlations generate strong spin-dependent scattering upon doping away from half filling, while a uniform magnetic field lifts the residual symmetries that enforce spin-degenerate transport. Only the combined breaking of particle--hole symmetry by doping and of the antiferromagnetic sublattice equivalence by the applied magnetic field converts these dynamical asymmetries into a finite spin polarization of the charge current. Our results establish electronic correlations as an active ingredient for antiferromagnetic spintronics and reveal a correlated analogue of the symmetry-breaking mechanism underlying altermagnetic spin-polarized transport in structurally conventional, collinear antiferromagnets.

Recent debates over the changing correlation between Indian summer monsoon rainfall (ISMR) and the El Nino-Southern Oscillation (ENSO) have raised inconclusive claims about the stability of the ENSO-Monsoon relationship (EMR) and ISMR predictability. Here we show that this apparent instability arises because traditional Pacific-based ENSO indices incompletely represent ENSO's global influence and are affected by climate noise, making their correlation with ISMR unreliable. We introduce a Global-ENSO framework using the depth of the 20-degree Celsius isotherm (Dp), a subsurface predictor integrating contributions from all three tropical ocean basins and maximizing ISMR teleconnections. Contrary to previous findings, ISMR shows a strong and stable correlation (0.8) with Dp at 18-month lead during the historical period. This predictability emerges from lagged synchronization between ISMR and Dp, where ISMR evolves as a delayed realization of the Dp dynamics. Our findings suggest that true EMR is stable and ISMR robustly predictable, providing clarity amid ongoing controversies.

Let $V$ be a locally finite, connected and weighted graph. We study non-existence results of non-trivial, non-negative solutions of the system $$ \begin{cases} u_{t t}-Δu \geq h_1|v|^p & \text { in } V \times(0, \infty), v_{t t}-Δv \geq h_2|u|^q & \text { in } V \times(0, \infty), u=u_0;\;v=v_0 & \text { in } V \times\{0\}, u_t=u_1;\;v_t=v_1 & \text { in } V \times\{0\}, \end{cases}$$ where $p,q>1$, $h_1, h_2$ are positive potentials. Under some volume growth condition of a ball, we prove that the system has no non-trivial non-negative solutions. In particular, our result is a natural extension of that in [\textit{D.~D.~Monticelli, F.~Punzo, and J.~Somaglia. Nonexistence results for the semilinear wave equation on graphs. arXiv.2506.08697, 2025.}] from a single inequality to a system.

In the series of papers Motivic GUT Part I: Grand Unified Theory of Topological Order, Motivic GUT Part II: Grand Unified Theory of Symmetry-Protected Topological Order, and Motivic GUT Part III: Grand Unified Theory of Symmetry-Enriched Topological Order, we propose a unified framework for gapped topological phases based on the Grothendieck-Kitaev-Lurie motivic yoga. In the spirit of Grothendieck's rising sea, we argue that the classification problem can only be properly addressed after identifying the correct higher-categorical ambient space in which its full richness appears. In this first part, we propose a unified definition of gapped topological order in spatial dimension $d$ in terms of unitary fusion $(\infty,d)$-categorical data, considered up to Morita equivalence. For $d=2$, this framework recovers unitary modular tensor categories. For $d>2$, it naturally leads to genuinely higher-categorical structures. This suggests a Copernican turn in the theory of topological phases: many existing classification schemes should be reinterpreted as lower-categorical shadow realizations of intrinsically $\infty$-categorical objects.

We report on a beam test of a Silicon Photo-Multiplier (SiPM)-on-tile Zero Degree Calorimeter (ZDC) prototype developed for the future Electron-Ion Collider (EIC). The detector implements the staggered scintillator-tile geometry envisioned for the final detector and includes 370 instrumented channels, corresponding to O(10%) of the full ZDC. The detector was tested using a 5.3 GeV positron beam at Jefferson Laboratory. We measure the energy response, shower shape, and spatial reconstruction performance of the detector and compare these results with simulation. These studies provide key input for the optimization of the final ePIC ZDC design.

Optical chirality density is widely used as a scalar measure of the chiral properties of electromagnetic fields and their interaction with matter. However, in anisotropic and structured media, a single scalar quantity is generally insufficient to capture the full complexity of chiral field-matter coupling. In this work, we go beyond the conventional optical chirality density and introduce a set of tensor measures of electromagnetic chirality based on the Lipkin formalism. These tensor quantities provide a richer and more physically transparent description of chiral electromagnetic fields, particularly in an anisotropic environment. The physical meaning of individual tensor components is discussed, and their role in characterizing different aspects of electromagnetic chirality is clarified. The proposed approach reveals multiple, complementary measures of field chirality that naturally emerge in anisotropic cases and are directly relevant to the interaction of structured electromagnetic fields with matter.

We present a new constraint on the effective number of relativistic species in the early universe, $N_{\rm eff}$, by combining recent primordial helium abundance measurements from the Large Binocular Telescope $Y_p$ Project with primordial deuterium abundance data, cosmic microwave background (CMB) observations from $\it{Planck}$, the Atacama Cosmology Telescope, and the South Pole Telescope, and baryon acoustic oscillation (BAO) data from the Dark Energy Spectroscopic Instrument, yielding $N_{\rm eff}=2.990\pm0.070$ (68% C.L.). This is the tightest constraint on $N_{\rm eff}$ to date, and is in excellent agreement with the standard model prediction of $N_{\rm eff}=3.044$. Furthermore, we constrain excess contributions to $N_{\rm eff}$ beyond the three neutrino species, finding $ΔN_{\rm eff}<0.107$ (95% C.L.). This bound nearly approaches the minimum contribution to $ΔN_{\rm eff}$ from a light spin-3/2 particle that decoupled at any time after inflation ended. Our baseline analysis does not include large-scale $\it{Planck}$ polarization information, enabling a fully consistent combination of state-of-the-art CMB and BAO measurements. As a byproduct, we show that current $N_{\rm eff}$ bounds are essentially insensitive to the inclusion or exclusion of optical depth constraints inferred from large-scale CMB polarization data, making $N_{\rm eff}$ highly robust in this regard. Our constraints place stringent limits on light particles in the early Universe and on a broad range of models aimed at increasing the CMB-inferred value of the Hubble constant.