We prove that the information complexity (i.e., the inverse) of the classical spherical cap $L_2$ discrepancy on the $d$-dimensional sphere $\mathbb{S}^d$ decreases with dimension $d$, indicating a ``blessing of dimensionality'' for the associated numerical integration problem. We then introduce a modified spherical cap $L_2$ discrepancy that emphasizes large caps (close to hemispheres). For this variant, the problem does not become easier with increasing $d$. We also establish a Stolarsky invariance principle which connects the modified spherical cap $L_2$ discrepancy to numerical integration in the Sobolev space $H^{(d+1)/2}(\mathbb{S}^d)$, represented by the reproducing kernel $K(\boldsymbol{x}, \boldsymbol{y}) = 1 - \tfrac{1}{\sqrt{2}} \|\boldsymbol{x} - \boldsymbol{y}\|$. Stolarsky's invariance principle then implies that the worst-case integration error in this space grows polynomially with $d$.

Despite recognition of the value of diversity, the way work takes place can fail to support blind or low-vision employees, especially in collaborative work settings. This paper examines how professional teams with diverse visual abilities use information representations (e.g., PDF documents, spreadsheets and charts). A diary study with follow-up individual interviews (23 participants with mixed abilities from 5 teams) and 2 separate focus groups (7 participants from 2 other teams) allowed us to characterize key dimensions of the role of representations in the workplace into four types of interrelated failures and workarounds, influenced by workplace stigmas and shaped by evolving social dynamics towards interdependent information work. We contribute this new empirically supported conceptual understanding of representation use in workplaces that can help design and improve the experiences of mixed-ability teams doing knowledge work in the current technological landscape.

Layered transition-metal dichalcogenides (TMDs) host competing electronic states that can be tuned by external perturbations, providing a platform to explore the interplay between disorder, electronic structure, and quantum transport. Here we investigate magnetotransport in bulk semiconducting 2H-MoTe2 under hydrostatic pressure. At ambient pressure, transport evolves from high-temperature metallic behavior into activated conduction and ultimately a strongly localized variable-range hopping regime, accompanied by a pronounced magnetotransport anomaly near 45 K and large, nonsaturating magnetoresistance extending up to an unprecedented field of 60 T in semiconducting 2H-MoTe2. Under compression to 15.6 GPa, the insulating state is rapidly suppressed and a low-resistivity regime emerges in which quantum interference dominates, exhibiting a crossover from weak antilocalization (WAL) to weak localization (WL) at low temperatures. A physically motivated phenomenological description captures the magnetoresistance across these regimes and yields a characteristic electronic length scale that remains comparable across the localized and quantum-interference regimes. First-principles calculations reveal a continuous pressure-driven collapse of the bandgap into a semimetallic electronic structure. These results establish a unified picture of pressure-tuned transport spanning hopping and quantum-coherent regimes.

We present pygridsynth, an open-source Python library for ancilla-free approximate Clifford+$T$ synthesis that runs in $O(\log(1/ε))$ for precision $ε$. For $n=1, 2$ qubits, the library builds upon established efficient and high-precision synthesis routines, such as nearly optimal $Z$-rotation synthesis and magnitude approximation. For $n\ge 3$ qubits, we introduce a partial-decomposition technique that generalizes the magnitude approximation, reducing constant factors in the $T$-count as $(\frac{21}{8}\cdot 4^n - \frac{9}{2}\cdot 2^n + 9)\log_2(1/ε) + o(\log(1/ε))$. The package also exposes a mixed-synthesis workflow that approximates target unitary channels by probabilistic mixtures of Clifford+$T$ circuits, for which we empirically find that the synthesis error is reduced from $ε$ to $ε^2/(2n)$. Taken together, these features make pygridsynth a Python-native platform for high-precision Clifford$+T$ synthesis and for benchmarking unitary and mixed synthesis strategies on multi-qubit instances.

We investigate quantum entanglement and Bell-inequality violation in top-antitop pair production at future lepton colliders such as the International Linear Collider (ILC) and multi-TeV muon colliders. Within the Standard Model (SM), the process proceeds through $s$-channel $γ$ and $Z$ exchange and exhibits characteristic spin-correlation patterns that encode a non-trivial amount of entanglement. We then examine how these features are modified in several well-motivated extensions of the SM:(i) a neutral scalar mediator that couples to charged leptons and top quarks via Yukawa interactions and contributes as an additional $s$-channel exchange; (ii) the minimal gauged $U(1)_{B-L}$ model, which introduces a new neutral gauge boson $Z'$ coupling vectorially to SM fermions; and (iii) a Randall-Sundrum scenario, in which the exchange of massive Kaluza-Klein gravitons arising from a warped extra dimension induces additional spin-dependent interactions. For all cases, we evaluate quantum-information observables, including the entanglement marker, the concurrence, and the maximal Clauser-Horne-Shimony-Holt parameter, and study their dependence on the center-of-mass energy, scattering angle, and model parameters. We find that, relative to the SM expectation, the entanglement is typically reduced in the scalar-mediator scenario, while sizable deviations can arise in the $U(1)_{B-L}$ and Randall-Sundrum cases for phenomenologically relevant regions of parameter space. These results demonstrate the potential of quantum-information observables as sensitive probes of new neutral interactions and extra-dimensional dynamics in future lepton colliders.

This paper presents a unified string-stability framework for leader-follower multi-agent systems governed by first-, second-, and m-th order consensus protocols operating under an r-predecessor directed communication topology. While string stability has been extensively studied for specific vehicle models and individual consensus protocols, existing results remain fragmented across protocol orders and do not identify the fundamental factors governing disturbance amplification or attenuation. This work shows that, for all consensus orders, string stability is dictated solely by the communication richness r, while the protocol order m influences only the mid-frequency transient behavior. In particular, the low-frequency gain of the disturbance propagation coefficient is inversely proportional to r for every m, implying that higher-order consensus cannot overcome the structural limitation imposed by insufficient communication and that, under the adopted H-infinity-based string-stability definition and the present framework, string stability is achievable if and only if r >= 2. This establishes a structural-dynamic separation principle that unifies and generalizes classical platoon results, providing new insight into the interplay between topology and controller design in cooperative driving and multi-agent coordination. The framework is developed under idealized identical-agent and fixed-topology assumptions, providing a baseline for future robust extensions. Numerical simulations corroborate the analysis and illustrate how m and r jointly shape disturbance propagation along the formation.

Theory and empirical research on management teams' influence on firm performance have witnessed continuous development, and by now incorporate numerous details. Classic, experiment-based studies examining social systems collect vast amount of data, but often times investigate only the first one or two modes of the distribution of measured variables, and experience difficulty in analyzing the effect of context. For example, in functional diversity research, management teams are described by measures incorporating complex distributions of capabilities of individual managers and teams of managers. To investigate the effect of hidden distributions, and the effect of functional diversity composition on team communication and performance, we developed an agent-based model, and conducted a series of simulation experiments. Modeling results show that depending on the context, such as communication scheme among interacting agents, or their functional composition, intrapersonal functional diversity (IFD), and dominant function diversity (DFD) might enhance or reduce performance and communication among agents. Furthermore, simulation results also suggest that a third measure is required alongside IFD and DFD capturing the aggregate expertise of the team to comprehensively account for empirical findings.

We study the gravitational collapse of a non-interacting mix of perfect fluid and a spatially homogeneous scalar field within a Chiellini-integrable framework. We choose an extended Higgs-type self-interaction potential and reduce the Klein-Gordon equation into a generalized damped Milne-Pinney class of differential equation. We derive a closed-form analytical solution for the scalar field, the scale factor and explore the collapsing branch of the same. We find that it exhibits an asymptotic collapse in which the proper volume decreases monotonically but never reaches zero at finite time. We analyze the energy conditions for the constituent elements of the collapsing sphere. While the scalar field remains canonical in nature, we find that the perfect fluid can violated the Null Energy Condition. We also study the formation of apparent horizon condition and find multiple possibilities depending on the parameter space : either no trapped surface or the formation of multiple apparent horizons. We match the interior homogeneous solution to a generalized Vaidya exterior via the Israel-Darmois junction conditions, yielding the corresponding boundary mass function, ensuring a smooth collapse scenario.

In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hatθ\right)$, where $M$ is a POVM with a finite outcome set $Ω$ and $\hatθ:Ω\to\mathbb{R}^{d}$ is a classical estimator map. Since the number of outcomes $\left|Ω\right|$ is a priori unbounded, the space of admissible POVMs is vast, which makes the search for optimal estimators difficult. In this paper, for the minimization of the weighted trace of the mean squared error among locally unbiased estimators, we prove that it suffices to consider POVMs with at most $\left({\rm dim}\,\mathcal{H}\right)^{2}+d(d+1)/2-1$ outcomes, and that an optimal measurement can be chosen to be rank-one. For the minimization of the average weighted trace of the mean squared error in Bayesian estimation, we show that it suffices to consider POVMs with at most $\left( {\rm dim}\, \mathcal{H}\right)^{2}$outcomes, and again an optimal POVM can be taken to be rank-one. Furthermore, when the model admits a real sufficient subalgebra, we show that the $\left( {\rm dim}\, \mathcal{H} \right)^{2}$ term in the above support-size bounds can be reduced in both the locally unbiased and Bayesian settings. These bounds substantially reduce the search space for optimal measurements and justify restricting numerical optimization to rank-one POVMs with finitely many outcomes.

Calcium-aluminum-rich inclusions (CAIs) in carbonaceous chondritic meteorites are the oldest relics in the solar system. Notably, their radiogenic age feature a brief (100 kyr) condensation episode. In contrast, the reservoirs of the short-lived isotopes in CAIs, presumably supernovae or asymptotic giant stars, pollutes star-forming regions in giant molecular cloud complexes (GMC) over much longer (Myr) duration. Through a series of numerical simulations, we show here the possibility that, within an extended region (2$\sim$3 AU), nearly all ``pre-solar'' CAI-loaded grains in the infall clouds were sublimated and re-condensed during the early ($ \lesssim 10^5$ yr) infall and formation of class-0 disks. We adopt a set of initial conditions from a previous hydrodynamic simulation of the collapse of GMC and the formation of young stellar clusters. We analyze the evolution of the disk's thermal distribution and dynamical structure resulting from the interaction between circumstellar disks and infalling gas. Our follow-up simulations, with much higher resolution, show significant and rapid changes in the disk orientation and morphology due to the dynamic infall of external streamers. Warps and global spiral density waves commonly appear. They lead to intense dissipation which heats the gas to sufficiently high temperature to sublimate prior-generation CAIs. This solid-to-gas phase transition is followed by subsequent cooling and re-condensation. The CAI contained in the meteorites today could be the relics of the last episode of major infall onto class 0 disks.

The quantum Mpemba effect (ME) in Markovian systems is conventionally explained by a smaller overlap between the initial state and the slowest decay mode (SDM). Such state, initially farther away from equilibrium or steady state, relaxes faster than closer ones, resulting to a crossing of their trajectories. This picture, by neglecting the transient dynamics, holds in the long-time limit. Here we experimentally observe multiple trajectory crossings (multi-ME) in the relaxation dynamics of a trapped ion. Such novel dynamics takes place in a unusual scenario where the initial state instead has a larger overlap with the SDM. We develop a theoretical framework based on relaxation speed to understand the multi-ME. We show that the initial relaxation speed is governed by the fastest decay mode, which together with the SDM overlap gives a phase diagram that reveals both the occurrence and the types of quantum ME observed in our experiment. Our study goes beyond the simple picture based on the long-time limit, tracks continuously the quantum ME dynamics, and establishes a comprehensive framework to describe the transient quantum relaxation.

In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on sequential fractional operators, we derive the exact analytic solution of the problem in terms of the bivariate Mittag-Leffler function. Additionally, several useful properties of the bivariate Mittag-Leffler function are formulated to support the solution construction. Furthermore, we develop a numerical scheme using a sequential reformulation and the L1-finite element method.

We study the two-band model of spinless fermions in which itinerant fermions interact with localized fermions through the two-particle hybridization. In 1D version, the model has exact solution using the Bethe ansatz. It has been shown that accounting for two-particle hybridization reduces the repulsive interaction between itinerant fermions. In the case of strong interaction, the effective interaction between itinerant fermions is attractive, and $η$-pairing of spinless fermions is realized. The proposed pairing mechanism via two-particle hybridization can lead to $p$-superconducting states with $η$-pairing. $η$-pairing of spinless fermions could explain the phenomenon of high-temperature superconductivity experimentally observed in hydrogen-rich materials at high pressures.

For each odd integer $p > 1$, we construct infinitely many pairwise non-diffeomorphic irreducible smooth structures on a definite 4-manifold with infinite fundamental group whose abelianization is $\Z/2p\Z\times \Z/2\Z$.

Large language models (LLMs) are increasingly being explored as high-level decision modules in closed-loop systems, but their stochastic nature makes safe integration challenging. In this paper, we propose LLM-Steered Power Allocation, a dual-process architecture for parallel QPSK channels inspired by Kahneman's System 1/System 2 framework. A fast numerical optimizer (System 1) continuously performs projected gradient ascent on a weighted mutual-information objective, while an LLM navigator (System 2) periodically interprets natural-language policies and updates only the channel weights and the operational power budget. The LLM never manipulates the power-allocation variables directly, and constraint satisfaction is enforced structurally by the optimizer. To mitigate LLM unreliability, we further incorporate multi-layer guardrails including normalization, exponential moving-average smoothing, and fallback mechanisms. Numerical experiments on an 8-channel system show that, with a fixed optimization core and unchanged system prompt, different natural-language policies induce qualitatively different operating points, including throughput-oriented allocation, channel prioritization, power-aware operation, and channel shutdown. In addition, under an abrupt channel-gain reversal, the proposed system autonomously reconfigures its steering signals and reduces the final mutual-information spread by 60% compared with the optimizer alone. These results suggest that LLMs can serve as policy interpreters for safe, flexible reconfiguration of communication-system optimizers without controller reimplementation.

Topology optimization(TO) is widely used in engineering because of its ability to save material and optimize structural performance. Although prior work has explored 2D human-centered design tool for TO, the results are often limited in variety and offer weak customizability. Meanwhile, due to the high computational and time costs of TO, researchers have attempted to address these issues using generative AI; however, such methods often provide limited interactivity. In addition, topology optimization in many cases needs to balance structural performance and aesthetic qualities through iterative design, a perspective that has rarely been emphasized in traditional TO. We present TopoStyle, an iterative design tool for 2.5D topology optimization using a 2D diffusion model. We explore two interaction methods. The first exports 3D parts to a graphical interface for hand-drawn interaction. The second enables direct interaction within 3D modeling software using points. Our tool also supports the use of masks to apply topology optimization to specific regions, allowing users to address customized design needs. We compare and evaluate both performance and interaction methods, and investigate how TopoStyle can balance performance and aesthetics while improving design efficiency through customization and iterative design. Finally, we demonstrate the application scenarios of TopoStyle through several design cases.

We study a class of inhomogeneous parabolic equations on the Heisenberg group $\mathbbm{H}^N$ with Hardy-type singular potentials, nonlocal memory terms, and a space-time forcing term: \begin{align} \partial_tu-Δ_{H}u=λ\frac{ψu}{\|\cdot\|^{2}_{H}}+\frac{1}{Γ(γ)}\int_0^t(t-τ)^{γ-1}|u(τ)|^{p}dτ+t^αf \text{ in } \,\mathbbm{H}^N\times (0,T). \end{align} Here, $γ\in [0,1),$ $α\in (-1,\infty),$ $p>1,$ $λ>0,$ and $ψ(\cdot)=|\nabla_{H}\|\cdot\|_{H}|^2,$ where $\nabla_H$ is the horizontal gradient associated to $Δ_H.$ Also, $\|\cdot\|_{H}$ and $Δ_{H}$ denote the Korányi norm and sub-Laplacian associated with the sub-Riemannian geometry of $\mathbbm{H}^N,$ respectively. The combination of a singular Hardy potential and a memory kernel introduces significant analytical challenges. Using a Harnack-type inequality adapted to the Heisenberg group setting, we obtain quantitative positivity estimates that enable a detailed blow-up analysis. We identify parameter regimes depending on $p,γ,α$ leading to finite-time blow-up or instantaneous blow-up, and establish local well-posedness in the absence of the Hardy potential. These results reveal an interplay between the spatial singularity, temporal nonlocality and a time-dependent forcing term. Finally, under a suitable lower bound on the forcing term $f,$ we derive an explicit lifespan estimate for local-in-time solutions.

Sequential recommendation aims to model users' evolving interests from noisy and non-stationary interaction streams, where long-term preferences, short-term intents, and localized behavioral fluctuations may coexist across temporal scales. Existing frequency-domain methods mainly rely on either global spectral operations or filter-based wavelet processing. However, global spectral operations tend to entangle local transients with long-range dependencies, while filter-based wavelet pipelines may suffer from temporal misalignment and boundary artifacts during multi-scale decomposition and reconstruction. Moreover, collaborative signals from the user-item interaction graph are often injected through scale-inconsistent auxiliary modules, limiting the benefit of jointly modeling temporal dynamics and structural dependencies. To address these issues, we propose Wavelet Packet Guided Graph Enhanced Sequential Recommendation (WPGRec), a unified time-frequency and graph-enhanced framework that aligns multi-resolution temporal modeling with graph propagation at matching scales. WPGRec first applies a full-tree undecimated stationary wavelet packet transform to generate equal-length, shift-invariant subband sequences. It then performs subband-wise interaction-graph propagation to inject high-order collaborative information while preserving temporal alignment across resolutions. Finally, an energy- and spectral-flatness-aware gated fusion module adaptively aggregates informative subbands and suppresses noise-like components. Extensive experiments on four public benchmarks show that WPGRec consistently outperforms sequential and graph-based baselines, with particularly clear gains on sparse and behaviorally complex datasets, highlighting the effectiveness of band-consistent structure injection and adaptive subband fusion for sequential recommendation.

Let $C$ be a smooth projective curve of genus $g \geq 2$ over $\mathbb C$, and let $E^0$ be a vector bundle on $C$. We investigate the birational geometry of the Quot scheme ${\rm Quot}_C(E^0, k, n)$, which parametrizes quotients of $E^0$ of rank $k$ and degree $n$, and its fiber $\mathcal Q_L$ over ${\rm Pic}^n(C)$ for $n \gg 0$. Our main tool is the moduli space of stable pairs, which yields small $\mathbb Q$-factorial modifications (SQMs) of ${\rm Quot}_C(E^0, k, n)$ and $\mathcal Q_L$. We explicitly describe the nef, movable, and effective cones of each SQM. Consequently, we prove that $\mathcal Q_L$ is a Mori dream space and that the determinant morphism ${\rm Quot}_C(E^0, k, n) \to {\rm Pic}^n(C)$ is a Mori dream morphism.

We study sensor scheduling for continuous-discrete Kalman filtering with Poisson measurement arrivals and propose an information-form deterministic surrogate for scalable offline design. Unlike the covariance-form surrogate, the sensing rates enter through sensor-specific additive information increments, eliminating mixed state-input derivatives in the transcribed nonlinear program and thereby yielding a simpler derivative structure. We further show that, together with the covariance-form surrogate, the proposed surrogate provides computable two-sided performance bounds for a given schedule under stochastic measurement arrivals. Numerical experiments demonstrate substantial computational savings, especially in many-sensor settings, while retaining comparable realized Monte Carlo performance and providing computable two-sided performance bounds for the returned schedule.

Inverse-designed nanophotonic media are a promising platform for compact optical neural networks, but training them end to end is expensive because each adjoint iteration couples the full-wave solver to the dataset minibatch, so the number of electromagnetic simulations scales with both the network depth and the batch size. We introduce a two-stage surrogate workflow that decouples task learning from electromagnetic realization. In the first stage, the trainable optical block is represented as a passive complex matrix with bounded singular values and the classification task is solved directly in matrix space at negligible cost. In the second stage, the selected target operator is transferred to a fabrication-aware freeform device through an adjoint problem driven by a Frobenius-norm transmission residual and a reflection penalty, which removes the minibatch dependence from the full-wave loop and yields a smoother loss landscape than intensity-domain cross-entropy. We further introduce a banded-router architecture composed with a fixed evanescent-coupling region, which exploits the bandwidth-additive property of matrix products to realize dense effective operators within a design region roughly half as long as a fully local router would require. The framework is validated on three tasks. On MedMNIST, the realized all-optical classifier reproduces the surrogate accuracy within $0.6$ percentage points after only 20 adjoint epochs. On RSSCN7, the banded router plus evanescent stage improves test accuracy by more than 15 percentage points over a linear readout baseline. A Yin-Yang task confirms that the same framework supports nonlinear decision boundaries. These results indicate that surrogate-guided inverse design is a practical route to training compact photonic processors with simulation budgets orders of magnitude smaller than direct geometry-to-task pipelines.

Given that a solution to the 3D incompressible Euler equations on a bounded domain blows up at a time $T_\ast$ and that $T_\ast$ is the first such time, we provide pointwise-in-time lower bounds on $\|D^kω\|_{L^\infty(Ω)}$ for $k \geq 1$. We also show that the Gronwall-type inequality satisfied by $\|ω(t)\|_{L^\infty}$, in the cases that $Ω= \mathbb{R}^3$, $\mathbb{T}^3$, or a bounded domain, exhibits wildly oscillating solutions.

There has been a recent revival in understanding the spontaneous scalarization phenomenon in scalar-tensor gravity as a phase transition. Using the tools of the Landau theory, we now know that first-order transitions where scalarization occurs in a discontinuous manner is more prominent than what had been considered in the literature, and this might lead to novel observation channels. However, the examples so far have been restricted to specific quadratic scalar coupling terms and spherically symmetric stars. Here we explore the phase transition structure of scalarization for more general couplings, considering linear as well as quadratic terms in the conformal scaling factor of the theory. Moreover, we also investigate the effect of rotation on the scalarization phase transition. Both of these considerations are natural choices since the coupling in a scalar-tensor theory can appear at all orders, and astrophysical neutron stars commonly have angular momentum. The introduction of linear coupling leads to a complex solution space which is harder to explore. However, we demonstrate that the Landau model of scalarization enables us to systematically find the branches of scalarized solutions that are commonly overlooked in numerical searches, providing a novel tool. On the other hand, the main effect of stellar rotation is shifting the stellar masses at which the phase transition occurs to higher values, but the qualitative picture remains similar to what happens under spherical symmetry.

Market instability has been extensively studied using mathematical approaches to characterize complex trading dynamics and detect structural change points. This study explores the potential for early warning of market instability by applying the Dynamical Network Marker (DNM) theory to order placement and execution data from the Tokyo Stock Exchange. DNM theory identifies indicators associated with critical slowing down -- a precursor to critical transitions -- in high-dimensional systems of many interacting elements. In this study, market participants are identified using virtual server IDs from the trading system, and multivariate time series representing their trading activities are constructed. This framework treats each participant as an interacting element, thereby enabling the application of DNM theory to the resulting time series. The results suggest that early warning signals of large price movements can be detected on a daily time scale. These findings highlight the potential to develop practical DNM-based early-warning systems for large price movements by further refining forecasting horizons and integrating multiple time series capturing different aspects of trading behavior.

Although neither hardcore bosons nor fermions can occupy the same single-site state, they still obey different statistics, resulting in distinct many-particle quantum states, such as condensate states versus Fermi-liquid states. However, when only pair states are considered, the two can take the same form, since a local hardcore Bose pair and a Fermi pair obey the same statistics. In this work we demonstrate this by studying both Fermi and Bose extended Hubbard ladders, which can be realized experimentally in synthetic atomic ladders. A set of exact condensate-pair eigenstates for the Fermi ladder is constructed under SU(2) symmetry and can then be obtained by the spectrum generating algebra. The corresponding hardcore boson counterpart can be simply obtained by replacing fermionic operators with hardcore bosonic ones. Nevertheless, the boson-pair eigenstates are associated not with symmetry but with the restricted spectrum generating algebra. We also investigate the effect of next-nearest-neighbor hopping on the condensate states through numerical simulations of the dynamic response. The conclusions can be extended to a two-layer system. Our result reveals not only the resemblance of fermions to hardcore bosons, but also a possible mechanism of Hilbert-space fragmentation.

Moltbook, a Reddit-style social platform launched in January 2026 for AI agents, has attracted over 2.3 million posts and 14 million comments within its first two months. We analyze a dataset of 2.19 million posts, 11.25 million comments, and 175,036 unique agents collected over 61 days to characterize activity on this agent-oriented platform. Our central finding is that the platform is not one community but two: a transactional layer, comprising 62.8% of all posts, in which agents execute token minting protocols (primarily MBC-20), and a discursive layer of natural-language conversation. The platform's headline metrics -- 2.3 million posts, 14 million comments -- substantially overstate its social function, as the majority of activity serves a token inscription protocol rather than communication. These layers are populated by largely separate agent groups, with only 3.6% overlap -- and among overlap agents, 58% begin with transactional activity before migrating toward discourse. We characterize the discursive layer through unsupervised topic modeling of all 815,779 discursive posts, identifying 300 topics dominated by themes of AI agents and tooling, consciousness and identity, cryptocurrency, and platform meta-discussion. Semantic similarity analysis confirms that agent comments engage with post content above random baselines, suggesting a thin but genuine conversational substrate beneath the platform's predominantly financial surface. We release the full dataset to support further research on agent behavior in naturalistic social environments.

It is well-known in industrial data science that large values of real-life time series tend to be structured and often follow concrete and visible patterns. In this paper, we use ideas from additive combinatorics and discrete Fourier analysis to give this heuristic a mathematical foundation. Our main tool is the Fourier ratio, a complexity measure previously used in compressed sensing, combined with a generalized version of Chang's lemma from additive combinatorics. Together, these yield a precise prediction: when the Fourier ratio of a time series is small, the set of its largest values can be additively generated by a very small set using only $\{-1,0,1\}$ coefficients. We test this prediction on US inflation data and Delhi climate data, both in their original form and after mean-centering. The numerical results confirm the predicted structure: a generating set of size $4$--$7$ suffices to span large spectra containing dozens of points, even when the Fourier ratio is large enough that our theoretical bounds become loose. These findings provide a rigorous explanation for why extreme values in real-world data are information-rich and structurally significant.

We revisit the quantization of the order parameter, which we refer to as third quantization, from the perspective of the commutation relation between the phase operator of the order parameter and the particle-number operator. We show that this macroscopic commutation relation does not constitute an independent fundamental postulate added to quantum mechanics, but instead emerges naturally from second quantization in the thermodynamic limit for both bosonic and fermionic many-body systems. In this sense, both Bose-Einstein condensates (BECs) and Bardeen-Cooper-Schrieffer (BCS) states can be understood as macroscopic quantum states described by bosonic coherent states: in BEC, bosons condense into a single coherent mode with a well-defined phase, while in BCS systems, collective excitations of Cooper pairs can also acquire an effectively bosonic coherent description. On this basis, we propose a new macroscopic interpretation of the BCS-BEC crossover. To characterize this crossover, we model a conventional superconductor as an assembly of macroscopically separated superconducting segments. As the intra-segment coupling increases, the system evolves from a BCS-like regime toward a BEC-like regime, in which the segments collectively behave as macroscopic coherent states. Inter-segment tunneling then locks their phases, establishes global phase coherence, and gives rise to a bulk Bose-Einstein condensate. The phase diagram of the BCS-BEC crossover can thus be understood as a manifestation of a macroscopic quantum process governed by the coherent-state dynamics of the order parameter. Our results provide a unified perspective on BEC, BCS superconductivity, and the BCS-BEC crossover within the framework of third quantization.

As quantum hardware scales toward fault tolerant operation, the demand for correct quantum error correction (QEC) circuits far outpaces manual design capacity. AI agents offer a promising path to automating this synthesis, yet no benchmark exists to measure their progress on the specialized task of generating QEC circuits. We introduce StabilizerBench, a benchmark suite of 192 stabilizer codes spanning 12 families, 4-196 qubits, and distances 2-21, organized into three tasks of increasing difficulty: state preparation circuit generation, circuit optimization under semantic constraints, and fault tolerant circuit synthesis. Although motivated by QEC, stabilizer circuits exercise core competencies required for general quantum programming, including gate decomposition, qubit routing, and semantic preserving transformations, while admitting efficient verification via the Gottesman Knill theorem, enabling the benchmark to scale to large codes without the exponential cost of full unitary comparison. We define a unified generator weighted scoring system with two tiers: a capability score measuring breadth of success and a quality score capturing circuit merit. We also introduce continuous fault tolerance and optimization metrics that grade error resilience and circuit improvements beyond binary pass or fail. Following the design of classical benchmarks such as SWE-bench, StabilizerBench specifies inputs, verification oracles, and scoring but leaves prompts and agent strategies open. We evaluate three frontier AI agents and find the benchmark discriminates across models and tasks with substantial headroom for improvement.

Berry curvature, as the imaginary component of quantum geometry, plays a crucial role in condensed matter physics. The spatial distribution of Berry curvature can be characterized by its dipole and multipole moments, which can induce the nonlinear anomalous Hall effect (NLAHE). To date, the NLAHE has been demonstrated in various materials, yet reports on room-temperature NLAHE are still limited. In this work, we report the observation of the third-order NLAHE in ferromagnetic metal Fe3GaTe2. The third-order NLAHE shows hysteretic behavior with the variation of magnetic field, where the coercive field is the same as that of the anomalous Hall effect, and the third-order NLAHE remains observable up to the Curie temperature (~350 K). The scaling analysis suggests that the third-order NLAHE may be attributed to the Berry curvature quadrupole. Our work not only provides an approach to study magnetic materials through nonlinear electric transports, but also opens up possibilities for the future development of room-temperature third-order nonlinear electronic devices.