Mott physics - the interplay between itinerancy and localization of electrons - is undergoing a paradigm shift from the binary "bandwidth - filling" tuning framework to an intertwining of geometric, topological, and fractionalized degrees of freedom. Based on a series of breakthroughs in 2024 - 2025, this paper proposes five pioneering discoveries: (1) Prediction of the golden-ratio scaling of quantum metric fluctuations near the Mott critical point, supported by functional renormalization group arguments and DMRG numerical verification (phi = 0.618 +/- 0.005); (2) Establishment of a correspondence between the denominator q of fractional Chern insulator charge and the subgroup index of the quantum geometry group, predicting that allowed q values follow the Fibonacci sequence {2,3,5,8,13,...} with specific material realizations; (3) Proposal of the Provability Hierarchy Theorem, classifying critical states like strange metals as "true but unprovable" QMA hard problems, establishing a rigorous connection to the complexity of the Consistency of Local Density Matrices(CLDM) problem; (4) Prediction of interference oscillations in the nonlinear Hall conductance within the pseudo gap phase, induced by geometric phase differences, supported by tight-binding numerical simulations; (5) Unveiling the quantum geometric tensor as a unified descriptor of band geometry and topology. These findings provide an experimentally testable theoretical framework for understanding strongly correlated quantum materials.

We study curves on the product of two $K$-trivial surfaces. In the case of the product of two very general abelian surfaces $A_1\times A_2$, we prove that the minimal genus of a non-trivial curve on $A_1\times A_2$ is $6$.

Existing LLM agent frameworks lack formal semantics: there is no principled way to determine whether an agent configuration is well-formed or will terminate. We present $λ_A$, a typed lambda calculus for agent composition that extends the simply-typed lambda calculus with oracle calls, bounded fixpoints (the ReAct loop), probabilistic choice, and mutable environments. We prove type safety, termination of bounded fixpoints, and soundness of derived lint rules, with full Coq mechanization (1,519 lines, 42 theorems, 0 Admitted). As a practical application, we derive a lint tool that detects structural configuration errors directly from the operational semantics. An evaluation on 835 real-world GitHub agent configurations shows that 94.1% are structurally incomplete under $λ_A$, with YAML-only lint precision at 54%, rising to 96--100% under joint YAML+Python AST analysis on 175 samples. This gap quantifies, for the first time, the degree of semantic entanglement between declarative configuration and imperative code in the agent ecosystem. We further show that five mainstream paradigms (LangGraph, CrewAI, AutoGen, OpenAI SDK, Dify) embed as typed $λ_A$ fragments, establishing $λ_A$ as a unifying calculus for LLM agent composition.

Within the effective field theory approach to gravity, deviations from general relativity can be systematically described by higher-curvature operators. However, computing the resulting corrections to black hole quasinormal mode spectra remains challenging in the rapidly rotating regime, where perturbative expansions in the spin break down. We use recently constructed numerical rotating black hole solutions to compute quasinormal mode frequency corrections at leading order in the effective field theory. Focusing on scalar perturbations, we evaluate cubic-curvature corrections, which constitute the leading modifications. We employ a pseudo-spectral collocation method to solve the resulting perturbation equations on these backgrounds, enabling accurate computation across a broad parameter range. We obtain frequency corrections for fundamental modes with $l\le5$ for all $m$, and the first overtone of $2 \le l \le 5$ modes for all $m$ for spins up to $a=0.99M$, with relative errors below $10^{-4}$. We observe that corrections to certain modes grow significantly as the spin approaches the near-extremal regime.

The manipulation of light in periodic structures is fundamental to the development of discrete photonics and provides a versatile platform for controlling light propagation in integrated and quantum photonic systems. This work reports the experimental observation of discrete one-dimensional (1D) solitons in a photonic lattice, optically induced in warm rubidium vapor. The lattice is generated by the interference of two coupling laser fields intersecting at a small angle, which creates a spatially modulated 1D refractive index. When a probe beam is focused into a single lattice site, discrete diffraction is observed. By increasing the probe intensity, discrete solitons emerge as a result of the balance between discrete diffraction and self-focusing within the nonlinear atomic medium. Experimental results are supported by numerical simulations, in which the refractive index is modeled via optical Bloch equations for a multilevel atomic system driven by the coupling and probe fields in a $Λ$ configuration. These results, combined with the inherent controlability of gain and loss in atomic vapors, suggest that this platform provides a versatile foundation for exploring non-Hermitian nonlinear dynamics and parity-time-symmetric photonic lattices.

Mapping parallel threads onto non-box-shaped domains is a known challenge in GPU computing; efficient mapping prevents performance penalties from unnecessary resource allocation. Currently, achieving this requires significant analytical human effort to manually derive bespoke mapping functions for each geometry. This work introduces a novel approach leveraging the symbolic reasoning of Large Language Models (LLMs) to automate this derivation entirely through in-context learning. Focusing on state-of-the-art open-weights models, we conducted a rigorous comparative analysis across spatial domains of increasing complexity. Our results demonstrate that modern local LLMs successfully infer exact O(1) and O(log N) mapping equations for complex 2D/3D dense domains and 2D fractals, vastly outperforming traditional symbolic regression methods. Crucially, we profile the energetic viability of this approach on high-performance infrastructure, distinguishing between the code-generation and execution phases. While one-time inference incurs a high energy penalty -- particularly for reasoning-focused models like DeepSeek-R1 -- this is a single upfront investment. Once integrated, the generated analytical kernels eliminate block waste entirely, yielding massive energy and time savings (e.g., up to 4833x speedup and 2890x energy reduction) during actual GPU workloads. Finally, we identify a current "reasoning ceiling" when these models face highly recursive 3D fractals (e.g., the Menger Sponge). This limitation benchmarks the present maturity of open-weight architectures, charting a viable path toward fully automated, energy-efficient GPU resource optimization.

Hot Neptunes in the sub-Jovian desert offer unique insights into planetary system evolution, retaining signatures of dynamical processes that shaped their present-day architectures. Many of these planets exhibit polar orbits, yet the mechanisms responsible for these misalignments between the stellar spin axis and planet orbit normal remain under debate. GJ 436 b stands among the very few hot Neptunes with both a polar and an eccentric orbit, thereby preserving dynamical signatures that may have otherwise been erased by tidal circularization. We investigate the unusual orbital architecture of GJ 436, exploring von Zeipel-Lidov-Kozai migration induced by a distant companion as a mechanism to explain the present-day orbit of GJ 436 b. Using $\sim$20 years of archival radial velocity measurements and astrometric data from the Hipparcos-Gaia Catalog of Accelerations, we constrain a potential companion to $a_{c}<5.4$ AU for $m_{c}>0.05$ $M_{Jup}$ and $a_{c}<64$ AU for $m_{c}>24$ $M_{Jup}$ in the GJ 436 system at the $2σ$ confidence level, providing the most stringent constraints to date. We further perform three-body hierarchical secular simulations to determine which companion configurations could reproduce GJ 436 b's present-day orbit within the observationally constrained parameter space. Our dynamical modeling favors sub-Jovian masses on orbits with $a_\mathrm{c} \gtrsim 6.8$ AU, suggesting a substellar perturber. These observational and dynamical constraints can guide future companion searches and illuminate formation mechanisms for hot Neptune desert planets on polar orbits.

This proceeding summarises recent studies on semileptonic and leptonic $B$ decays, which provide stringent tests of lepton flavour universality as well as key experimental inputs to ultimately increase the precision of inclusive $|V_{ub}|$ and $|V_{cb}|$ determinations. The presented analyses investigate electron-positron collision data recorded by the Belle and Belle II detectors at the $Υ(4S)$ resonance, comprising the complete Belle data set of 711 fb$^{-1}$ and 365 fb$^{-1}$ of Belle II data samples collected between 2019 - 2022.

We use deep learning under Bayesian perspective to quantitatively extract the in-medium heavy quark (HQ) potential from bottomonium nuclear modification factors ($R_{AA}$) measured across multiple heavy ion collision systems at the Large Hadron Collider (LHC) and the Relativistic Heavy-Ion Collider (RHIC). The in-medium HQ potential, comprising both a real and imaginary part, is parameterized and incorporated into a time-dependent Schrödinger equation to model the wave function evolution of $b\bar{b}$ dipoles within a hydrodynamically evolving hot QCD medium. We construct Convolutional Neural Networks (CNNs) to capture the non-linear correspondence between the heavy quark potential $V(T,r)$ and the bottomonium $R_{AA}$ for Pb-Pb collisions at 5.02 TeV and 2.76 TeV, and Au-Au collisions at 200 GeV. Training datasets are generated by sampling the potential parameters and are further augmented using Principal Component Analysis (PCA) and Gaussian Process Regression (GPR). After validating the stability and correctness of the CNNs, we employ Stochastic Gradient Langevin Dynamics (SGLD) to perform a simultaneous Bayesian inverse extraction of the optimal potential parameters and their posterior distributions using experimental data of bottomonium $R_{AA}$ in both LHC and RHIC energies. Our joint multi-energy extraction suggests that, within the present parametrization and hydrodynamic background, the real part of the in-medium potential remains close to the vacuum Cornell form, corresponding to a relatively weak screened Debye mass across RHIC to LHC energies. By contrast, the imaginary part is more strongly constrained by the data and provides the dominant contribution to bottomonium suppression from RHIC to LHC energies.

Nowadays, several projects of future colliding beam experiments are being considered in the world. Among them are the CEPC (Circular Electron Positron Collider) in China and the FCC (Future Circular Collider) at CERN (Switzerland). To perform experiments on flavor physics in the energy range of the projects an excellent particle identification up to momenta of 30 GeV/c is required. Several concepts of RICH detectors based on aerogel were considered and evaluated with the help of GEANT4 simulation: FARICH (Focusing Aerogel RICH) based on multilayer aerogel with maximal refractive index of 1.008, RICH with Fresnel lens based on aerogel with refractive index of 1.008, RICH based on transparent aerogel fibers with refractive index of 1.008. The results of the simulation are presented. Some results of beam tests at the BINP performed to validate GEANT4 simulation are presented as well.

Quasars exhibit stochastic variability across wavelengths, typically well described by a Damped Random Walk (DRW). Occasionally, however, they undergo extreme luminosity changes--known as flares--that represent significant departures from this baseline behavior and provide valuable probes of accretion disc dynamics and the physics of supermassive black hole fueling. Although modern transient surveys have spurred growing interest in flare detection, no systematic search has yet been conducted within the legacy SDSS Stripe 82 dataset, which contains 9,258 spectroscopically confirmed quasars observed over a ~10-year baseline. The principal statistical challenge is distinguishing these rare events from the ever-present stochastic variability. To address this, we present FLARE (Flare detection via physics-informed Learning, Anomaly scoring, and Recognition Engine), a modular three-stage framework for detecting transient flares in quasar light curves. FLARE models baseline DRW behavior, applies statistical anomaly scoring to flag candidate events, and employs a recognition engine to verify detections. For the Stripe 82 implementation, we deploy two complementary baselines--a physics-informed probabilistic Gated Recurrent Unit (GRU) trained on simulated DRW light curves, and an iterative Ornstein-Uhlenbeck (OU) process fitted directly to observed data with outlier masking--followed by Extreme Value Theory (EVT) for anomaly scoring. We benchmark twelve open-weight and proprietary Vision Language Models (VLMs) as recognition engines for final candidate verification. Detection is performed on r-band light curves, with candidates cross-checked against g-band data to rule out instrumental artifacts. Applying this framework, we identify 51 quasars exhibiting distinct flaring activity.

The divergence of the electron density of states (DOS) plays an important role in enhancing many-body interactions and inducing various quantum phases in low-dimensional systems. However, such unique electronic structures remain experimentally elusive in three-dimensional (3D) systems, particularly those with strong spin-orbit coupling (SOC). Using angle-resolved photoemission spectroscopy and first-principles calculations for a Laves-phase superconductor CsBi$_2$, which features a Bi-pyrochlore 3D network with strong SOC, we identify two characteristic electronic structures with a large DOS. One is a dispersionless topological flat band with p-orbital character, locally formed around the U-K line, which enhances DOS near the Fermi level. The other involves type-I and type-II saddle points connected by a flat band, which cooperatively produce an enhancement in the DOS. Our findings suggest a novel mechanism for achieving a DOS enhancement and lay a foundation for exploring exotic phenomena driven by the interplay of multiple singularities with a large DOS, nontrivial topology, and strong SOC in 3D pyrochlores.

We study a non-relativistic realisation of two-dimensional de Sitter gravity both from its boundary and bulk description with the goal of learning about de Sitter space and paving the way for extending the holographic duality into a non-relativistic direction. On the boundary side, we analyse the Schwarzian-type boundary action associated with non-relativistic de Sitter gravity and evaluate its one-loop partition function in order to compute its quantum fluctuations. Rather than relying on the coadjoint-orbit construction, we derive the path integral measure directly from the action using the Ostrogradsky formalism. We find a temperature-dependent prefactor scaling as $T^2$, of which the power agrees with the counting of the four global symmetry generators present. On the bulk side, we construct the corresponding torsionless Newton-Cartan geometry and show that it satisfies the equations of motion of a non-relativistic JT-like action and uplift the geometry to a three-dimensional Lorentzian geometry.

The item cold-start problem poses a fundamental challenge for music recommendation: newly added tracks lack the interaction history that collaborative filtering (CF) requires. Existing approaches often address this problem by learning mappings from content features such as audio, text, and metadata to the CF latent space. However, previous works either omit artist information or treat it as just another input modality, missing the fundamental hierarchy of artists and items. Since most new tracks come from artists with previous history available, we frame cold-start track recommendation as 'semi-cold' by leveraging the rich collaborative signal that exists at the artist level. We show that artist-aware methods can more than double Recall and NDCG compared to content-only baselines, and propose ACARec, an attention-based architecture that generates CF embeddings for new tracks by attending over the artist's existing catalog. We show that our approach has notable advantages in predicting user preferences for new tracks, especially for new artist discovery and more accurate estimation of cold item popularity.

The direct pair-production of the $\tildeτ$, is one of the most interesting channels to search for SUSY in: the $\tildeτ$ is likely to be the lightest of the scalar leptons, and the signature of $\tildeτ$ pair production is one of the experimentally most difficult ones, making it the ``worst'' possible scenario for SUSY searches. The current limit on $\tildeτ$ production in the general MSSM comes from LEP. Limits obtained at LHC do extend to higher masses, but they are only valid under strong assumptions. Future $e^+e^-$ colliders will be powerful for SUSY searches, offering advantages with respect to previous $e^+e^-$ colliders as well as to hadron machines. In order to quantify their capabilities, the ``worst-case'' scenario for $\tildeτ$ searches has been studied, taking into account the effect of the $\tildeτ$ mixing on both $\tildeτ$ production cross section and on detection efficiency. To evaluate the latter, the ILD detector concept, originally developed for the International Linear Collider (ILC), and the ILC beam conditions at a centre-of-mass energy of $500$\,GeV have been used for detailed simulations, including for the first time the effect of bunch-crossings containing no hard $e^+e^-$ interaction, but only low-$\it{P_{T}}$ hadrons from $γγ$ interactions and $e^+e^-$ pairs from beamstrahlung. Still, the obtained exclusion and discovery reaches extend nearly up to the kinematic limit even in the worst-case scenario. This remains true also when the $\tildeτ$ and the lightest SUSY particle are quite close in mass. The results of the detailed study are extrapolated to centre-of-mass energies, integrated luminosities and beam polarisations of other proposed Higgs factory projects and discussed in view of their respective experimental environments, in particular addressing the case of FCCee.

Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new dynamic network model classes exploiting the Generalized Poisson distribution to capture both under- and overdispersion. We consider three different dynamic specifications: latent factor dynamics, autoregressive dynamics, and latent position dynamics, and study some theoretical properties of the random networks, showing the impact of the dispersion parameter on the random network's connectivity. After discussing the parameter identification strategy, we present a Bayesian inference procedure along with a posterior sampling algorithm. A numerical illustration demonstrates the effectiveness of the designed algorithm and provides estimates of the misspecification bias when unequal dispersion is neglected. Our new models are then applied to two relevant dynamic datasets considered in previous studies: a set of bike-sharing dynamic networks and a set of dynamic media networks. Our results highlight the importance of explicitly modeling overdispersion for both an accurate in-sample fit and out-of-sample performance.

We establish interior regularity and optimal growth estimates for sign-changing minimizers of the $p-$singular or $p-$degenerate quasilinear Alt--Phillips functional throughout the full range of $1<p<\infty$ and of the nonlinearity power $0<γ<p$. In addition, we obtain local finite perimeter and density estimates, from which we deduce the local $(N-1)$-rectifiability of the reduced and two-phase free boundaries and the local finiteness of their $(N-1)$-dimensional Hausdorff measure for a restricted range of $γ$.

Partial Information Decomposition (PID) represents multivariate mutual information via antichain-lattice that aims to specify which source groups can recover which informational components of a target. For three or more sources, widely desired PID axioms become mutually incompatible. This is often treated as an axiomatic tuning issue. This paper argues that the obstruction is representational, rooted in the antichain indexing itself, so that purely axiomatic adjustments within an antichain-lattice structure cannot resolve it in general. We first introduce System Information Decomposition (SID) for the special target-free three-variable setting, obtaining a self-consistent entropy decomposition with an operational redundancy definition. More fundamentally, we then show that for general multivariate PID, there is no universal rule that recovers the decomposed mutual information from the antichain-indexed information atoms. In particular, two systems can share identical atoms regardless of any axioms while having different mutual information. These results reveal the limits of antichain-lattice and motivate relation-based foundations for multivariate information measures.

Black hole spacetimes provide a natural setting for quantum systems in curved spacetime, where effects such as Hawking radiation arise from event horizons. In this work, we investigate the impact of the Hawking effect on quantum imaginarity in Schwarzschild spacetime, focusing on nonlocal advantage of quantum imaginarity (NAQI) and assisted imaginarity distillation. For NAQI, it is significantly affected by Hawking radiation, exhibiting a pronounced difference between physically accessible and inaccessible regions. It is suppressed in the physically accessible region with increasing Hawking temperature and may vanish, while remaining absent in the physically inaccessible region across the parameter regime. For assisted imaginarity distillation, the Hawking effect modifies the assisted fidelity in a state-dependent manner. In the physically accessible region, the fidelity generally decreases with increasing temperature, indicating reduced distillation capability, whereas the physically inaccessible region exhibits the opposite monotonic trend, indicating enhanced distillation capability. These results highlight distinct operational behaviors of physically accessible and inaccessible regions under relativistic effects, providing insight into quantum imaginarity in curved spacetime.

We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of distributions, and then specialise our results to tempering sequences. We use our results to derive the complexity of SMC samplers with respect to the parameters of the problem, such as $T$, the number of target distributions, in the general case, or $d$, the dimension of the ambient space, in the tempering case. We use these bounds to derive practical recommendations for the implementation of SMC samplers for end users.

Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix multiplication based on an adaptive configuration of Hadamard tests. By leveraging Quantum Random Access Memory (QRAM) for state preparation, we demonstrate that the complexity of computing the inner product of two vectors can be reduced to $O(\log N)$. We introduce an "Adaptive Stacking" framework that allows the algorithm to dynamically reconfigure its execution pattern from sequential horizontal stacking to massive vertical parallelism based on available qubit resources. This flexibility enables a tunable time-complexity range, theoretically reaching $O(N^2)$ on fault-tolerant systems while maintaining compatibility with near-term hardware. We validate the numerical stability of our approach through a Quantum Machine Learning (QML) simulation, achieving 96% accuracy on the MNIST handwritten digit dataset. Our results suggest that adaptive quantum MatMul provides a viable path toward super-classical efficiency in high-dimensional linear algebra operations.

In an effective-field-theory framework for gravity, black-hole quasinormal mode spectra acquire corrections in quadratic-curvature, scalar-tensor extensions of general relativity. Previous calculations of such corrections were limited to moderate spins, since the corresponding background solutions relied on expansions in the spin parameter. Using recently constructed numerical black-hole solutions valid for large spin, we compute the leading-order deviations from general relativity in the scalar quasinormal mode spectrum of rotating black holes in scalar Gauss-Bonnet and dynamical Chern-Simons gravity. We solve the resulting perturbation equations with pseudo-spectral collocation methods, allowing us to determine the quasinormal-mode corrections for dimensionless spins up to $a/M=0.99$, with accuracy better than $\lesssim 10^{-3}$ for the $l=m=0$ mode and $\lesssim 10^{-6}$ for higher multipoles. For spins $a/M>0.9$, the corrections to certain modes can increase by orders of magnitude.

Sequential recommender systems have achieved steady gains in offline accuracy, yet it remains unclear how close current models are to the intrinsic accuracy limit imposed by the data. A reliable, model-agnostic estimate of this ceiling would enable principled difficulty assessment and headroom estimation before costly model development. Existing predictability analyses typically combine entropy estimation with Fano's inequality inversion; however, in recommendation they are hindered by sensitivity to candidate-space specification and distortion from Fano-based scaling in low-predictability regimes. We develop an entropy-induced, training-free approach for quantifying accuracy limits in sequential recommendation, yielding a candidate-size-agnostic estimate. Experiments on controlled synthetic generators and diverse real-world benchmarks show that the estimator tracks oracle-controlled difficulty more faithfully than baselines, remains insensitive to candidate-set size, and achieves high rank consistency with best-achieved offline accuracy across state-of-the-art sequential recommenders (Spearman rho up to 0.914). It also supports user-group diagnostics by stratifying users by novelty preference, long-tail exposure, and activity, revealing systematic predictability differences. Furthermore, predictability can guide training data selection: training sets constructed from high-predictability users yield strong downstream performance under reduced data budgets. Overall, the proposed estimator provides a practical reference for assessing attainable accuracy limits, supporting user-group diagnostics, and informing data-centric decisions in sequential recommendation.

Let $G$ be a finite group and let $\Irr(G)$ denote the set of irreducible complex characters of $G$. For a normal subgroup $N \trianglelefteq G$ and $χ\in \Irr(G)$, we say that $χ$ is \emph{fully ramified} over $N$ if $χ(g)=0$ for all $g \in G \setminus N$. A group $G$ is said to be of \emph{central type} if there exists $χ\in \Irr(G)$ that is fully ramified over $Z(G)$. Motivated by this notion, an irreducible character $χ\in \Irr(G)$ is called of \emph{central type} if $χ$ vanishes on $G \setminus Z(χ)$, where \[ Z(χ)=\{\, g \in G : |χ(g)|=χ(1) \,\} \] is the center of $χ$. Groups in which every irreducible character is of central type are called \emph{GVZ-groups}. Furthermore, a group $G$ is said to be \emph{nested} if for all $χ,ψ\in \Irr(G)$, either $Z(χ)\subseteq Z(ψ)$ or $Z(ψ)\subseteq Z(χ)$. It is known that a GVZ-group is nilpotent. In this article, we classify all GVZ and nested GVZ $p$-groups of order at most $p^6$, where $p$ is an odd prime.

We consider the constrained stabilization problem of second-order systems evolving on the n-sphere. We propose a control strategy with a constraint proximity-based dynamic damping mechanism that ensures safe and almost global asymptotic stabilization of the target point in the presence of star-shaped constraints on the n-sphere. It is also shown that the proposed approach can be used to deal with the constrained rigid-body attitude stabilization. The effectiveness of the proposed approach is demonstrated through simulation results on the 2-sphere in the presence of star-shaped constraint sets.

This paper, based on the interdisciplinary frontiers of quantum electrodynamics, causal set theory, and the AdS/CFT holographic duality, integrates Keppler's zero point field resonance theory, the discrete causal structure and horizon thermodynamics within causal set theory, and the latest advancements in holographic superconductivity models. For the first time, we establish a unified dynamical framework for macroscopic coherent states in quantum materials. We demonstrate that: (1) The quantum vacuum can form macroscopic coherent states with specific molecular electronic states in materials through resonant coupling, corresponding to a new mechanism for superconducting pairing; (2) The partial order relations and strongly connected components in causal set theory characterize the nonlocal correlation topology among quantum systems, with black hole event horizons exhibiting a blocking effect on such correlations; (3) Holographic duality treats the electronic structure of materials as a projection of a higher dimensional gravitational system onto the boundary, where the coherence length of the projection kernel satisfies a universal scaling law. Based on this, we deduce three groundbreaking discoveries: High Temperature Superconducting Pairing Mechanism Induced by Zero Point Field Resonance, Superconducting Synergy and Horizon Blocking in Causal Structure Networks, and Quantum Material Phase Transition Control Driven by Holographic Projection. Each discovery is translated into explicit experimental protocols and falsifiable conditions, and is compared and analyzed against mainstream experimental observations in the field of high temperature superconductivity, opening a computable and testable new direction for understanding emergent phenomena in quantum materials.

We introduce and study the filtration on the space of automorphic functions (in the everywhere unramified situation for the function field case) obtained by transferring the filtration on the spectral side of the classical Langlands conjecture, induced by coherent singular support. We propose a number of conjectures that tie this filtration (which, by design, arises from the notion of cohomological support) to a filtration on the space of C-valued automorphic functions that arises by considering the analytic spectrum of Hecke operators.

A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent positions evolve according to a vector autoregressive process that accounts for lagged and contemporaneous dependence across nodes and features, a characteristic neglected in the LSM literature. A Bayesian approach is used to address two of the primary sources of inference intractability in dynamic LSMs: latent feature estimation and the choice of latent space dimension. We employ an efficient auxiliary-mixture sampler that performs data augmentation and supports conditionally conjugate prior distributions. A point-process representation of the network weights and the finite-dimensional distribution of the latent processes are used to derive a multi-move sampler in which each feature trajectory is drawn in a single block, without recursions. This sampling strategy is new to the network literature and can significantly reduce computational time while improving chain mixing. To avoid trans-dimensional samplers, a Laplace approximation of the partial marginal likelihood is used to design a partially collapsed Gibbs sampler. Overall, our procedure is general, as it can be easily adapted to static and dynamic settings, as well as to other discrete or continuous weight distributions.

This paper presents a classification of locally $2$-homogeneous designs, extending Kantor's classification of 2-transitive symmetric designs (1985).

This paper introduces the Animal Welfare and Policy Risk Index (AWPRI), a composite risk index covering 25 countries over the period 2004-2022 (N=475 country-year observations). The AWPRI is constructed from 15 variables organised across three equal-weighted conceptual layers: Current Welfare State (L1), Policy Trajectory (L2), and AI Amplification Risk (L3). Variables are normalised to [0, 1] using min-max scaling, with higher values denoting greater policy risk. The index is validated through k-means cluster analysis (k=4; silhouette coefficient=0.447), principal component analysis (PCA) of the 15-variable cross-section, and sensitivity analysis under +/- 10 percentage-point layer weight perturbation (mean Spearman \r{ho}=0.993, minimum 0.979; mean Adjusted Rand Index (ARI)=0.684, range 0.477-1.000). Our Hausman specification test favours random-effects (RE) panel estimation (H=2.55, p=0.467). We use a difference-in-differences (DiD) design to exploit the 2019 AI governance risk classification divergence and find that countries identified as high-AI-governance-risk carry AWPRI scores 0.080 points higher than their low-risk counterparts, after controlling for country and year fixed effects (\b{eta}=0.080, SE=0.005, p<0.001). The L3 layer records the highest mean score in the 2022 cross-section (0.552, SD=0.175), significantly exceeding both L1 (Wilcoxon W=102,651, p<0.001) and L2 (W=99,295, p<0.001). China (0.802), Vietnam (0.612), and Thailand (0.586) record the highest composite risk scores in 2022; the United Kingdom (0.308) the lowest. AutoRegressive Integrated Moving Average (ARIMA)-based projections indicate that Thailand, Brazil, and Argentina face AWPRI risk deterioration by 2030. The AWPRI and its interactive visualisation are publicly accessible at https://awpri.aiinsocietyhub.com/.