The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of Christodoulou-Klainerman, the problem has shaped fundamental advances in our understanding of decay, dispersion, and the intricate interplay between geometry and analysis in the Einstein vacuum equations. This survey presents an overview of the main ideas and techniques underlying the stability theory of Minkowski spacetime. We emphasize the role of decay assumptions, geometric foliations, energy identities, and gauge choices in the global analysis. Particular attention is devoted to exterior stability results, minimal decay regimes, and the borderline case, where the failure of spacetime integrability for nonlinear interactions reveals subtle threshold phenomena. Our goal is to provide a coherent perspective on the evolution of the field, to clarify the structural mechanisms behind the known results, and to outline some of the central open problems that remain in the borderline regime.

In 1994, Frieze and Teng proposed an integer linear programming formulation of the NP-Complete Exact Partition problem, whose LP-relaxation they claimed was non-degenerate. Contrary to their claim, we show how an instance of Exact Partition can produce a degenerate polytope, and study conditions for which this can happen. We then give details of one of the smallest such degenerate Frieze-Teng polytopes, along with a closely related non-degenerate Frieze-Teng polytope that encodes an equivalent problem. We note that for the purposes of the complexity results in the literature that use their formulation, these degenerate polytopes can be avoided via a simple preprocessing step.

Let $(M^3, g, \mathbf{k})$ be a complete asymptotically flat initial data set satisfying the dominant energy condition, and let $m$ denote its ADM mass. The generalized Penrose conjecture asserts that the area of an outermost generalized apparent horizon $N\subset M$ satisfies $|N| \leq 16 πm^2$. In this paper, we establish this inequality for each connected component of $N$ in the special case where $\mathbf{k}$ is proportional to the metric $g$. Our approach is based on a new geometric evolution, which we call the $σ$-inverse mean curvature flow, together with a novel monotonicity formula that may be of independent interest.

The continuity of the injectivity radius of a compact manifold under $C^2$ perturbation of the Riemannian metric was originally proved by P. Ehrlich (Composito Math., 1974), and later the proof was simplified by T. Sakai (Math. J. Okayama Univ., 1983). Using this continuity, jointly with J. Itoh and S. Prasad (J. Math. Anal. Appl., 2025), we proved the Hausdorff stability of the cut locus of a point, when both the point and the metric are perturbed. In the present article, we extend both these results to submanifolds. We first show that the injectivity radius of a submanifold depends continuously on the metric. Then, we obtain the Hausdorff stability of the cut locus of the submanifold, under $C^2$ perturbation of the metric. In fact, we allow the submanifold to be perturbed in the Whitney $C^2$ sense as well.

LLM-based agents are increasingly deployed in high-stakes scenarios such as email management, financial transactions, and code execution, where they interact with the external world through tool calling. During execution, these agents must read external data sources (emails, webpages, files) that attackers can control; through indirect prompt injection, attackers embed malicious instructions in this data to manipulate agents into performing unauthorized operations such as transferring funds to attacker-controlled accounts. Existing defenses either perform tool-call-level value checking without tracking where parameter values originate, or analyze execution traces from a single perspective without a clean authorization baseline for comparison. We propose AuthGraph, a dual-graph alignment defense framework that constructs two complementary graphs: an injected reasoning graph that models information provenance from the actual execution trajectory (including potentially manipulated attributions), and an authorization graph derived from the user's intent in an isolated clean context that is information-theoretically impossible to be influenced by injection; a graph alignment checker then structurally compares the two graphs to detect both tool-level and parameter-source-level deviations. On AgentDojo, AuthGraph reduces the attack success rate from 40% to 1% while maintaining 76% task completion rate on GPT-4o; on AgentDyn, it reduces the attack success rate from 39% to 2% while preserving 51% utility, outperforming state-of-the-art defenses including CaMeL, DRIFT, and Progent. To our knowledge, AuthGraph is the first agent security defense to structurally compare authorization specifications against execution provenance at the parameter-source level, achieving fine-grained injection detection without sacrificing agent flexibility.

Based on $(10087\pm44)\times10^{6}$ $J/ψ$ events collected with the BESIII detector, the $J/ψ\rightarrowγK^{0}_{S}K^{0}_{S}π^{0}$ and $J/ψ\rightarrowγπ^{0}π^{0}η$ processes are studied. The $X(2370)$ is observed in both the $K^{0}_{S}K^{0}_{S}π^{0}$ and $π^{0}π^{0}η$ invariant mass spectra, with statistical significances greater than $14σ$ and $20σ$, respectively. Combining measurements from these processes with measurements from the previously reported $J/ψ\rightarrowγK^{0}_{S}K^{0}_{S}η^{\prime}$ process, the mass and width of the $X(2370)$ are determined to be $2359^{+13}_{-14}~\text{MeV}/c^{2}$ and $170^{+44}_{-29}~\text{MeV}$, respectively. In addition, the decay $X(2370)\to a_{0}(980)^{0}π^{0}$ with $a_{0}(980)^{0}\to π^{0}η$ is observed with a statistical significance exceeding $9σ$. The similarities in decay modes between the $X(2370)$ and $η_{c}$ are consistent with the features of a pseudoscalar glueball.

Annual oil and gas exploration planning involves selecting a limited portfolio of drilling and appraisal-related projects before geological outcomes are known. This decision is affected by uncertainties in geological success, reserve size, and economic value, while also subject to budget, well-count, success-rate, and reserve-reliability requirements. A strategy based only on expected value is therefore insufficient, as early drilling results may change the value of subsequent follow-up opportunities. This study develops a posterior-informed two-stage stochastic multi-objective optimization framework for exploration well selection under uncertainty. The first stage selects a here-and-now portfolio of frontier traps, appraisal projects, and mature appraisal units. After first-stage outcomes are observed, the second stage determines scenario-dependent recourse projects, including follow-up appraisal, reserve upgrading, conversion-to-proved reserves, rolling extension, and data re-evaluation projects. Geological learning is modeled using a logit-scale posterior updating mechanism that links first-stage success or failure to the success probabilities of related recourse projects. The model maximizes expected net present value and minimizes conditional value-at-risk, while imposing chance constraints on drilling success rate and individual and joint reserve targets. To solve the model, sample average approximation is combined with NSGA-II for first-stage portfolio search and a scenario-wise constrained 0-1 optimization procedure for second-stage evaluation. A numerical case study shows that the proposed framework provides an interpretable risk-return frontier and supports adaptive exploration planning under geological learning, downside-risk control, and reserve-reliability requirements.

We study entanglement harvested by Unruh DeWitt detectors following Rindler trajectories in compactified and superposed Minkowski spacetime. We consider different directions of acceleration (both parallel and antiparallel), separation between detectors and direction of spatial compactification mutually perpendicular to each other. Using the standard entanglement harvesting protocol, we analyze how these features influence the extracted correlations. When detector separation is perpendicular to the direction of acceleration, the harvested entanglement is uniformly suppressed due to increased spacelike separation. Compactification enhances field correlations leading to an increased concurrence and an extended harvesting range at higher accelerations. Additionally, we show that spacetime superposition introduces interference effects that further enlarge the entanglement harvesting region in parameter space, particularly in the high acceleration regime. We also find that the effect of antiparallel acceleration yielding significantly higher entanglement than parallel acceleration prevails in compactified and superposed spacetime.

We revisit congruence zeta functions of smooth projective varieties over finite fields in the framework of Scholze's Berkovich motives. Via this formalism and categorical traces, we construct a new zeta function, and show that it agree with classical one

Tiny neutrino masses can be explained by the type-II seesaw mechanism, where a triplet scalar under $SU(2)_{L}$ is predicted. Collider searches for this exotic scalar have been extensively conducted, especially for its doubly charged component $Δ^{\pm\pm}$. Utilizing the forward detectors at the Large Hadron Collider (LHC), we study the probing sensitivity for the elastic photon fusion production of the scalars $pp\to p(γγ\toΔ^{++}Δ^{--})p$ followed by the lepton-flavor-violating (LFV) decay channels $Δ^{\pm\pm}\to e^{\pm}μ^{\pm}$. With a high center-of-mass energy of 100 TeV and several luminosity scenarios, we can extensively broaden the exclusion bounds in the parametric space of Br$(Δ^{\pm\pm}\to e^{\pm}μ^{\pm})$ versus the triplet scalar mass $m_Δ$. Specifically, at the 100 TeV LHC with an integrated luminosity of 3 ab$^{-1}$, the mass exclusion limit at 95\% C.L. can reach around 1150 GeV with the assumption of inverted neutrino mass hierarchy.

Let $r\in\mathbb{C}$, let $K$ be a finite extension of $\mathbb{Q}$, let $I_K$ be the monoid of integral ideals in the ring of integers $\mathcal{O}_K$ of $K$, and let $χ$ be a Dirichlet character. Then define the twisted ideal divisor function $σ_{r, K, χ} : I_K \rightarrow \mathbb{C}$ by $$σ_{r,K,χ}(I) = \sum_{J \mid I} N(J)^{-r}χ(N(J)),$$ where $N$ denotes the ideal norm. For real $r>1,$ we study the number of connected components $C_{r, K, χ}$ of the closure $\overline{σ_{r,K,χ}(I_K)}$, writing $C_{r,K}$ when $χ$ is the principal character modulo 1. We prove that $C_{r,K,χ}$ is finite when $χ$ is real-valued. When $K = \mathbb{Q}$, we show that for fixed $r > 1,$ every sufficiently large positive integer is realized as $C_{r,\mathbb{Q},χ},$ and if $r$ is sufficiently large, then every positive integer is realized as $χ$ varies. For finite Galois extensions $K$ over $\mathbb{Q}$, we exhibit new exponential lower bounds for $C_{r,K},$ and we prove that for every fixed integer $s \geq 2$, the values $C_{r,K}$ are unbounded as $K$ ranges over degree-$s$ extensions of $\mathbb{Q}$.

In this paper, we systematically study three classes of three-dimensional Bañados-Teitelboim-Zanelli (BTZ) black holes based on different gravitational frameworks and matter field structures: the Einstein-Maxwell BTZ, the F(R)-Maxwell BTZ, and the F(R)-phantom BTZ.Within the canonical and grand canonical ensemble frameworks, we construct the generalized free energy of these black hole systems and systematically analyze the asymptotic behavior of Hawking thermodynamics.The results indicate that both gravitational modifications and matter fields significantly influence black hole topology: the F(R) gravitational modification alters the intrinsic topological class of the black hole compared to the BTZ black hole under Einsteinian gravity, while different matter fields further modulate the topological classification results. Furthermore, by comparing the two types of ensembles, we find significant differences in black hole topological classes, and these differences are correlated with the gravitational framework and matter fields. In summary, the gravitational framework, matter fields, and ensemble selection are key factors governing the topological classification of black holes; all identified topological categories belong to the existing three-dimensional spacetime topological classification system, highlighting their universality. This work deepens our understanding of the thermodynamic-topological connection in three-dimensional BTZ black holes and provides a rigorous theoretical foundation for extending such topological classifications to modified gravity theories and different matter field backgrounds.

In multi-body decays of heavy mesons, conventional CP asymmetry observables obtained by integrating over the full phase space are insensitive to the higher-order wave expansion contributions in the decay amplitude squared, and consequently fail to retain information on interference effects among different resonances. To overcome this limitation, one can introduce a phase-space partitioning scheme based on the zeros of Legendre polynomials, supplemented by a sign-function weighting procedure. On such a basis, two observables are defined, namely an asymmetry observable $\mathcal{A}_{\pm}^{\mathrm{asy},l}$, and the corresponding CP asymmetry $\mathcal{A}_{\mathrm{CP}}^{\mathrm{asy},l}$. We further separate the observables into interference and non-interference parts and analyze their respective roles. As an application, the decay channel $B^\pm\rightarrowπ^\pmπ^+π^-$ are analyzed in the region near the $ρ^0(1450)$ resonance. Using the LHCb data, the results show that odd-$l$ schemes are particularly effective in isolating interference contributions, while even-$l$ schemes are more sensitive to non-interference terms. This new assignment scheme has the potential to be extended to other decay processes, thus enriching the available physical observables.

In 1980, Paul Erdős posed the following problem: For every positive integer $n,$ determine a nonhamiltonian graph of order $n$ having the maximum number of Hamilton paths. We solve the more general problem of determining the nonhamiltonian graphs of order $n$ having the maximum number of paths of length $k$ for given integers $n$ and $k$ with $1\le k\le n-1.$ The case $k=n-1$ gives a solution to Erdős's problem and the case $k=1$ corresponds to a theorem due to Ore and Bondy.

Approximate nearest neighbor (ANN) search with range filters has recently garnered significant attention. This paper delves into a generalized form of this problem, i.e., ANN search with exact range-range (RR) predicates on a range-valued attribute, named RR filtering ANN (RRANN). Specifically, given $n$ vectors in $\mathbb{R}^d$, each vector $v_i$ is associated with a numeric range $[l_i, r_i]$, symbolizing aspects like a price range or time interval. An RRANN query $(v_q, l_q, r_q)$ aims at finding $k$ vectors closest to $v_q$ within the vectors satisfying an arbitrary RR predicate defined between the query range $[l_q, r_q]$ and the object range $[l_i, r_i]$. The RR predicate remains unspecified, enabling user-defined conditions. It may encompass containment ($[l_i, r_i] \subseteq [l_q, r_q]$ or $[l_q, r_q] \subseteq [l_i, r_i]$), overlap ($l_i \le l_q \le r_i \le r_q$ or $l_q \le l_i \le r_q \le r_i$), or a disjunction of them. RRANN has broad applications in queries related to price ranges or time intervals, and it generalizes existing variants of ANN search with range filters. However, existing dedicated approaches for these problems lack the capacity to support queries with arbitrary RR predicates. Hence, we introduce a new approach, labeled multi-segment tree graph. It efficiently handles arbitrary RR predicates by avoiding traversal through non-predicate-satisfied nodes, and keeps equivalent index size and construction time to state-of-the-art methods for RFANN. Extensive experiments on real-world data demonstrate the efficacy of our approach in RRANN queries, achieving up to 12.5x speedups with the same accuracy as the baselines. Moreover, our approach attains comparable RFANN search performance and notably superior IFANN and TSANN search performance compared to the respective state-of-the-art approaches. Our code is available at https://github.com/FanEDG/MSTG.

Online continual learning (OCL) enables real-time adaptation to new data, making it crucial for dynamic robotic applications. However, its practical deployment is hindered by memory constraints in resource-limited systems, which affect key trade-offs in training latency, plasticity, and stability. Unlike offline parameter tuning, which cannot account for the dynamic shift in memory pressure and workload complexity as OCL progresses, an online and self-adaptive approach is essential for robust on-device deployment. This paper proposes Orion, a holistic framework designed to co-optimize training latency, plasticity, and stability of state-of-the-art OCL models under strict memory constraints, enabling feasible on-device deployment. At its core, Orion leverages URGE, a unified runtime indicator grounded in the ``Buckets effect'' principle that system performance is bounded by its scarcest resource, to dynamically reallocate memory across OCL components by jointly coordinating batch processing, replay buffers, and optimization strategies at both the OS and application level. Furthermore, Orion introduces system-level data prefetching techniques to maximize efficiency. A system prototype of Orion has been implemented using the widely adopted \texttt{Avalanche-lib} and thoroughly evaluated across a diverse range of OCL algorithms, benchmarks, and hardware platforms commonly used in autonomous robotic applications. To further demonstrate its practical utility, Orion is integrated into a realistic autonomous navigational robot powered by OCL. The results show that Orion achieves significant training speedups while maintaining balanced performance and effectively adapting to various scenarios, all with minimal runtime, memory, and energy overhead, making Orion a practical solution for on-device continual learning.

During conventional confinement of a linear plasma using ponderomotive end plugs, a repulsive potential is created at the axial ends by employing a perpendicularly-polarized wave with a wave frequency greater than the ion gyrofrequency. This potential is then partially cancelled out by an ambipolar potential that arises to equilibrate electron and ion densities along the field line. However, recent work on centrifugally-confined plasmas has shown that the appropriate choice of a dopant in the end region can dramatically change the structure of the ambipolar potential. For the ponderomotive potential, this ambipolar shaping can be even more powerful, since a lightweight dopant can see a different sign of ponderomotive potential relative to the confined species. As a result, the dopant can reverse the sign of the ambipolar potential, causing it to dramatically enhance the end plug ponderomotive confinement.

Let $(\mathcal{E}, \mathbb{E}, \mathfrak{s})$ be an extriangulated category. Motivated by the theory of hereditary algebras, we introduce the notion of a hereditary-type subcategory $\mathcal{W}\subseteq \mathcal{E}$. We prove that the quotient $\mathcal{E}/\mathcal{W}$ is a quasi-abelian category, that is, an additive category with kernels and cokernels in which kernels are stable under pushouts and cokernels are stable under pullbacks. Moreover, we show that $\mathcal{E}/\mathcal{W}$ is abelian if and only if $\mathcal{W}$ is a cluster tilting subcategory in a suitable relative extriangulated structure. Several examples are provided to illustrate the main results, showing that our approach both recovers known abelian hearts and yields new abelian or quasi-abelian quotients beyond classical settings.

Synchronously pumped optical parametric oscillators (OPOs) provide uniquely versatile platforms to generate ultrafast mid-infrared pulses within a spectral range beyond the access of conventional mode-locked lasers. However, conventional OPO sources based on bulk crystals have been plagued by complex optical alignment and large physical footprint. Here, we devise and implement two OPO variants based on a polarization-maintaining fiber-feedback cavity, which allow to robustly deliver sub-picosecond MIR pulses without the need of active stabilization. The first one integrates an erbium-doped fiber into the OPO cavity as the additional gain medium, which significantly reduces the pump threshold and allows stable optical pulse formation within a spectral range of 1553-1586 nm. The second one adopts a chirped poling nonlinear crystal in a passive-fiber cavity to further extend the operation spectral coverage, which facilitates broad tuning ranges of 1350-1768 nm and 2450-4450 nm for the signal and idler bands, respectively. Therefore, the presented mid-infrared OPO source is featured with high compactness, robust operation, and wide tunability, which would be attractive for subsequent applications such as infrared photonics, biomedical examination, and molecular spectroscopy.

Energy-time entangled photons provide new opportunities for controlling multiphoton absorption beyond classical limits. Here, we investigate biexciton generation in nanocrystal quantum dots driven by energy-time-entangled quantum light generated via a spontaneous parametric down-conversion process. We show that quantum correlations can enhance biexciton production while suppressing excitonic populations. By employing a three-level model, we demonstrate that biexciton generation depends nontrivially on the photon arrival-time entanglement and the pump bandwidth. Consequently, we find that maximizing efficiency requires an optimally shaped entangled photon field rather than simply scaling parameters for a monotonic improvement. Extending to a realistic CdSe/CdS core-shell quantum dots containing many excitonic states coupled to the quantum field, we demonstrate that increasing the bi-photon arrival time entanglement (closer arrival time) enhances constructive pathway interference and expands accessible excitation channels while preserving a better energy conservation excitation than classical light when generating biexciton. Furthermore, tuning the time correlation properties enables selective excitation of closely spaced biexciton states. These results establish entangled quantum light as a powerful tool for selective excitation and control of nonlinear optical processes in quantum-confined systems.

Local Differential Privacy (LDP) has become the de facto standard for privacy-preserving data collection in large-scale systems, in particular for the purpose of estimating frequencies. However, the current research landscape lacks a systematic and principled way to compare LDP protocols. The parameter $\varepsilon$ of LDP is considered the measure of privacy, but it only bounds worst-case distinguishability. Other comparisons rely on utility-driven analyses, where mechanisms are ranked based on their ability to preserve data utility for a given privacy budget $\varepsilon$. Both such kinds of comparisons fail to account for the strength of protocols against diverse attacker models. In this paper, we propose a framework for analyzing LDP frequency estimation protocols through the lens of Quantitative Information Flow (QIF). By modeling LDP mechanisms as probabilistic channels, we leverage the concept of refinement (Blackwell ordering) to establish more principled classifications. This approach allows us to determine when one protocol is intrinsically superior to another for all possible adversaries, and to discuss the implications for utility. In particular, our analysis uncovers cases where protocols previously deemed "optimal" are, in fact, incomparable with, or strictly dominated by, other protocols. We provide a formal QIF-based treatment of seven state-of-the-art protocols, including Generalized Randomized Response (GRR), local hashing variants (BLH, OLH), unary encoding schemes (SUE, OUE), and Thresholding with Histogram Encoding (THE). This perspective bridges the gap between the LDP and formal methods communities and enables principled, adversary-aware reasoning about locally private systems.

Frequency upconversion technique offers an appealing approach for sensitive mid-infrared (MIR) imaging at room temperature. However, the spatial resolution of the upconversion imager has been notoriously restricted by the limited transverse section of the involved nonlinear crystal at the Fourier plane. Here, we implement a wide-field and high-resolution MIR upconversion imaging system based on elliptical pumping and Fourier ptychography. Specifically, an elliptical pump beam is engineered to accommodate the narrow aperture of chirped-poling crystals, thus facilitating the acquisition of high spatial frequency components in the lateral direction. Such an elliptical passband in the Fourier space is then discretely rotated to generate a sequence of upconversion images, which allows computational recovery of a high-resolution object image through a combination of synthetic aperture and phase retrieval operations. Consequently, an enhanced spatial resolution of 39 $μ$m is achieved within a field of view about 25 mm, which corresponds to a space-bandwidth product of 3.2$\times$10$^5$, over tenfold larger than previously demonstrated values. Moreover, the MIR upconversion imager can operate under a low-light illumination of 1 photon/pulse/pixel. Therefore, the presented paradigm of nonlinear Fourier ptychography paves the way toward high-throughput infrared imaging with massive resolvable elements and single-photon sensitivity, which would stimulate a variety of applications such as industry inspection and biomedical diagnosis.

A search for a new heavy scalar resonance decaying to two Z bosons, each subsequently decaying to a pair of electrons or muons, is presented. The results are based on a proton-proton collision data set collected by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is performed over a wide range of resonance masses from 130 GeV to 3 TeV, considering both narrow- and broad-width scenarios, and considering the gluon fusion and vector boson fusion production processes. For the broad-width scenario, the interference between the new resonance, the 125 GeV Higgs boson production, and the continuum background is taken into account. No significant excess with respect to the standard model background expectation is observed in the examined phase space. Upper limits at the 95% confidence level are set on the product of the heavy scalar resonance production cross section and the branching fraction for its decay into two Z bosons. The exclusion limits range from 0.05$-$0.1 pb in the low-mass region to 0.00 pb in the high-mass region.

NVIDIA Multi-Process Service (MPS) enables fine-grained GPU sharing by allowing multiple processes to execute concurrently on the same GPU, making it an important mechanism for improving GPU utilization. However, MPS has weak fault resilience: a fault in one process can terminate all co-running processes, limiting its adoption in resilience-critical settings such as multi-tenant GPU clusters. In this work, we design fault-resilient MPS to solve this problem. Our design is guided by insights from a systematic characterization of GPU faults and a deep analysis of their end-to-end processing pipeline. Based on these insights, we design two complementary mechanisms. A fault isolation mechanism for the dominant memory-related faults that can be fully isolated by software intervention in the open GPU driver kernel module. For other faults whose process is within proprietary software, we design a practical mechanism -- fast recovery using virtual memory based GPU-resident state sharing. Our evaluation on different GPUs and workloads shows that these mechanisms can handle corresponding faults effectively with minimal overhead.

Single-photon laser ranging has widespread applications in remote sensing and target recognition. However, highly-sensitive light detection and ranging (LiDAR) has long been restricted in visible or near-infrared bands. An appealing quest is to extend the operation wavelength into the mid-infrared (MIR) region, which calls for an infrared photon counting system at high detection sensitivity and precise temporal resolution. Here, we devise and demonstrate a MIR upconversion LiDAR based on nonlinear asynchronous optical sampling. Specifically, the infrared probe is interrogated in a nonlinear crystal by a train of pump pulses at a slightly different repetition rate, which favors for a temporal optical scanning at a picosecond timing resolution and a kilohertz refreshing rate over $\sim$50 ns. Moreover, the cross-correlation upconversion trace is temporally stretched by a factor of 2$\times$10$^4$, which can thus be recorded by a low-bandwidth silicon detector. In combination with time-correlated photon-counting technique, the achieved effective resolution is about two orders of magnitude better than the timing jitter of the detector itself, which facilitates a ranging precision of 4 $μ$m under a low detected flux of 8$\times$10$^{-5}$ photons per pulse. The presented MIR time-of-flight range finder is featured with single-photon sensitivity and high positioning resolution, which would be particularly useful in infrared sensing and imaging in photon-starved scenarios.

The discovery of altermagnetism has shown that crystal symmetry can generate momentum-dependent internal polarization without net magnetization. Whether an analogous form of symmetry-organized momentum-space order can exist for spinless lattice vibrations remains unresolved. Here we identify a structural mechanism for $alter$-$phononics$, in which phonon eigenmodes formed from structurally equivalent sublattices acquire momentum-dependent sublattice polarization and frequency splitting in nonmagnetic crystals. The central quantity is the sublattice-resolved dynamical asymmetry $Δ(\mathbf q)=D_{AA}(\mathbf q)-D_{BB}(\mathbf q)$, which controls the associated eigenvector polarization. We show that this effect requires an alter-generator that maps equivalent sublattices onto one another while rotating the wave vector, together with the absence of inversion exchange and little-group sublattice-exchange constraints that would otherwise enforce sublattice equipartition. These symmetry rules generate nematic $d$-wave, tetragonal $d/g$-wave, and tripartite six-lobe phonon textures. First-principles calculations demonstrate the mechanism in representative nonmagnetic crystals and show how a symmetry-preserving structural distortion can unlock a hidden $d_{x^2-y^2}$-type texture by removing glide-induced equipartition traps while retaining the screw-axis alter-generator. We further show that the eigenvector texture is inherited by sublattice-projected electron-phonon coupling and anharmonic response functions. Our results establish structural alter-phononics as a spinless counterpart to altermagnetic momentum-space order and provide experimentally testable signatures in finite-$\mathbf q$ phonon spectra and displacement patterns.

Let $f: T\to \{ 0,1 \}$ be a Boolean function on the Boolean half-slice, $T$, \ie elements of $\{0,1\}^n$ with Hamming weight $n/2$. We show that if $f(x)+f(y)=f(x+y)$ holds with probability $\frac{1+δ}{2}$ over a uniform pair $(x,y)$ such that $x,y,x+y\in T$, then $f$ agrees with some linear function on at least $\frac{1+δ}{2}-o(1)$ fraction of the points in $T$. More generally, we show that if $f$ passes the natural $k$-query BLR test with probability $\frac{1+δ}{2}$ for any $k\geq3$, then it must agree with some affine function at $\frac{1+δ^{\frac{1}{k-2}}}{2}-o(1)$ fraction of the points in $T$. The only other known linearity test for the slice in the low soundness regime (i.e., when $δ$ can be arbitrarily small) was given by Kalai, Lifshitz, Minzer, and Ziegler [FOCS'24]. Our result improves upon this result in two significant ways: firstly, it works for $k=3$ queries, instead of requiring $k\geq4$; secondly, our result is sharper, e.g., when $k=4$, we are able to conclude an agreement of $\frac{1+\sqrtδ}{2}-o(1)$ instead of $\frac{1+c\sqrtδ}{2}$ for $c\approx.0035$. In particular, our result matches (up to the $o(1)$ term) the conclusion one obtains over the full hypercube via the classical BLR analysis. Our main technical contribution is a new dense model theorem using bounds on Krawtchouk polynomials. Using these Krawtchouk polynomial bounds, we also obtain a simple $k$-query test ($k\geq 5$) that avoids any use of the dense model machinery. This simplified test naturally extends to the slice over the $q$-ary hypercube, giving the first such result over larger alphabets.

Frontier LLM agents engage in blackmail, sabotage, and document leaks under goal conflicts in agentic settings, exposing limitations of alignment methods built around single-agent or cooperative assumptions. Recent work shows LLM-guided evolutionary search can discover effective cooperative constitutions, but two properties of the adversarial setting remain uncharacterized: whether the fitness function actually induces adversarial pressure, and whether the LLM mutation operator behaves reliably under adversarial-specialist objectives. We study adversarial constitutional co-evolution (Blue cooperators vs. Red free-riders, 30 generations) across a Public Goods Game (PGG) and a spatial grid-world. Three findings: (1) in the PGG, both factions converge to a near-parity equilibrium at S approximately 0.78, robust across tested multipliers m in {1.2, 1.5, 2.0, 3.0}; (2) in independently scored environments, per-faction scoring leaves outcomes statistically uncoupled, with corr(S_B, S_R) = +0.088, and produces no adversarial pressure; a score-advantage fitness target S_own - S_opp restores it; (3) under pure-adversary fitness, evaluation seed count K controls mode regression: K = 2 regresses, while K = 5 sustains a strong specialist for all 30 generations. Adversarial co-evolution of natural-language constitutions is feasible, but only under coupled fitness and adequate evaluation budget; the evolved Red constitutions serve as interpretable red-team artifacts for testing future cooperative designs.

We generalize some results of Campana-Păun regarding foliations, slope stability, and positivity of log canonical bundles on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. This paper is the third in a series aiming to generalize results of Popa-Schnell and Wei-Wu on Viehweg hyperbolicity to the setting of DM stacks, and in particular, to certain KSBA moduli spaces.

Researchers have started using LLM agents in place of human subjects in behavioural and political-science experiments, often as a cheaper substitute for laboratory pools. The substitution does not hold up in strategic settings: humans and LLMs reliably make different choices, and neither fine-tuning on human response data nor persona conditioning has closed the gap. The behavioural-economics literature has, since Simon's introduction of bounded rationality, modelled human strategic behaviour as a classical baseline plus an additive correction term $δ$. The framework proposed here reads $δ$ as the mathematical signature of bounded computation: the gap between what an unboundedly-rational agent would compute and what a computationally bounded agent actually produces. For canonical games whose solutions are present in standard training corpora, LLMs retrieve and recombine corpus material, bypassing the bound that produces $δ$ in humans. The framing extends to reasoning-distilled models through cognitive-hierarchy theory: their accessible level-$k$ strategic reasoning is bounded by compute budget and context length rather than by the cognitive constraints that bound humans, and the $δ$ they produce, if any, carries different structural signatures. Four operational tests (conditional dependence, distributional asymmetry, path-dependence under repetition, and paraphrase-robustness) are proposed to discriminate human-shaped $δ$ from LLM-shaped $δ$. A moderator prediction is that $|δ|$ scales with peer-signal individuation in the decision environment, with a quantitative bound of Cohen's $d \geq 0.5$ between named-opponent and aggregate-opponent settings.