Spherical interpolation is required in numerical and geometric applications in which the unknowns are constrained to remain on the unit sphere. Spherical Interpolation of orDER $n$ (SIDER-$n$) was introduced as the high-order reconstruction component of spherical essentially non-oscillatory interpolation, where the reconstruction is built entirely from spherical linear interpolation (SLERP) operations and therefore preserves the spherical constraint exactly. This paper develops analytic first-derivative formulas for SIDER curves of arbitrary order. The central observation is that the recursive definition of SIDER can be differentiated by direct chain-rule propagation through its binary tree of SLERP operations. After deriving the total derivative of SLERP with moving endpoints, we obtain compact recursions for the derivative of SIDER-$n$, including simplified formulas at interpolation nodes and practical formulas at middle points between consecutive sampling locations. The latter are relevant when a reconstruction is evaluated halfway between data samples, as occurs in several high-order reconstruction-based numerical algorithms. The base case SIDER2 is treated explicitly, and SIDER3 and SIDER4 are used to illustrate the recursive mechanism. We also prove that the derivative is tangent to the sphere at every reconstructed point, including both sampling points and middle points. The resulting formulas extend the original SIDER/SENO framework by supplying differential information for sphere-valued reconstructions, with potential use in high-order finite-volume, ENO/WENO, SENO-type, and related methods for conservation laws and evolution problems.

We introduce the Minimum Effort to Consensus (MEC), a measure that quantifies polarization as resistance to consensus: a population is highly polarized when much effort is needed to bring its members to a common position, and weakly polarized when little is needed. Given an opinion distribution, MEC is the minimum effort required to turn it into a consensus distribution, taken over all consensus points, and it returns both a scalar value and an endogenous optimal consensus point. In the basic case MEC equals the 1-Wasserstein distance (Earth Mover's Distance) to the nearest consensus configuration, so that polarization becomes proximity to maximum disagreement. A two-parameter family with exponents alpha, beta >= 1 writes MEC as a weighted L^beta cost whose weights are the alpha-power of the group masses, recovering mean absolute deviation and variance-like dispersion as special cases and giving alpha and beta natural readings as identification and alienation. We prove a Shifting Away from Consensus principle, by which displacing a whole group's mass away from the optimal consensus point strictly increases polarization, and use it to show that MEC is maximized by the extremal distribution that splits the population equally between the two extremes, establishing that MEC is a polarization measure in the standard sense. We also obtain a Minority Principle and a Tipping Point method, showing that polarization is not monotone in extremism. MEC further satisfies the three axioms of Esteban and Ray with a central-split monotonicity property. Empirically, MEC[2,1.15] attains Kendall's tau near 0.89 against a sixty-expert benchmark, matching the strongest Esteban-Ray parametrization and outperforming the Van der Eijk and Tastle-Wierman measures, and it is computable by bisection in O(n log(1/epsilon)) time.

In the paper [M. Keel, H. Smith, C.D. Sogge, Almost global existence for quasilinear wave equations in three space dimensions. J. Amer. Math. Soc. 17 (2004), no. 1, 109-153], the authors prove that for the 3-D quadratic quasilinear wave equation in exterior domains with homogenous Dirichlet boundary value and small initial data of size $\varepsilon$, the lifespan ${\bar T}_{\varepsilon}$ of the smooth solution fulfills ${\bar T}_{\varepsilon}\ge e^{C/\varepsilon}$. However, for the corresponding 2-D quadratic quasilinear wave equation in exterior domains with homogenous Dirichlet or Neumann boundary value, so far it is still open whether the expected sharp lifespan $T_{\varepsilon}\ge\frac{C}{\varepsilon^2}$ holds or not. In this paper, we will solve this open question. Our main ingredients include: introducing the suitable Friedlander radiation field for the 2-D linear wave equation in exterior domains with homogenous Dirichlet or Neumann boundary value, constructing the delicate approximate solution, and establishing some crucial space-time decay estimates for the solutions of 2-D quasilinear wave equation in exterior domains. On the other hand, for the radial symmetric solutions to a class of 2-D quadratic quasilinear wave equation in exterior domains, the upper bound of the lifespan $T_{\varepsilon}\le\frac{C}{\varepsilon^2}$ is derived and the sharp constant $C$ is also determined explicitly.

We construct a lifted local Lie groupoid formulation of the Heston stochastic-volatility model and use it to give a geometric interpretation of its affine-transform structure. The construction extends the Group Quantization framework previoulsy applied to quadratic financial diffusion models. The purpose of this paper is not to propose a new Heston pricing formula. The contribution is geometric: the Heston pricing operator in coordinate space and the Riccati equations in momentum space arise from two representations of the same lifted local groupoid construction. The usual characteristic-function and Riccati formulas are recovered.

Machine collectives increasingly coordinate, reciprocate, and form shared conventions on their own, tempting us to call them societies like ours. We argue that this conflates two registers of social order and misses what the human one is for. Human sociality is the way a finite, natal, generational form of life organises its own finitude: members die with their tacit knowledge, newcomers start ignorant, and cohorts must hand on what they cannot keep. Kinship, inheritance, teaching, and much of obligation and trust are the forms this takes, and machine collectives reproduce only the residue once finitude is subtracted. We meet the objection that machines already have death with two distinctions. Autonomy versus heteronomy: a death an operator can reset, roll back, or copy around is not constitutive finitude; the test is resettability. Representation versus binding force: humans learn finitude from others' deaths, so its representation is machine-learnable, but its grip on motivation needs the learner's own end to be inescapable. Treating machines as a model organism, a controlled experiment varying only whether death means loss shows that cumulative, transmissible culture arises only under irreversible loss; a copyable-immortal population is more capable yet culturally empty. Across a machine population and three real human genealogies, copying over-transmits status relative to every human regime and fragments lineage like blood descent, whereas externalisation lowers transmission into the human range and connects lineage like intellectual descent. In a real frontier model, language-model end-game defection vanishes when the game is de-labelled, a sign of recognition, not a mechanism. The gap between a machine collective and a human society is therefore not one of intelligence but of finitude, and it closes only when finitude is built in.

In this paper, based on our previous general formulation and computational solution to Bellman's Lost-in-a-forest Problem, we provide the proof of general solution and obtained more variations and results related to this problem. This paper provides generalized formalized method connecting curve covering, lost-in-the-forest problem, and traveling salesman problem with neighborhoods. We prove the equivalence and convergence. We also provide more results of searching for two lines, connection to Wetzel's unit arc covering problem, variations with closed path, variations in three dimensions, etc. The results include general calculation equations, partial analytical results, and numerical results.

Given a vertex algebra $V$, Zhu constructed an associative algebra $A(V)$, whose representation theory provides an approximation to the category of $V$-modules. We describe a geometric construction of a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$ associated to any universal factorization algebra $\mathcal{A}$, whose zeroth homology recovers Zhu's associative algebra in the case where $\mathcal{A}$ is obtained from a vertex algebra. The construction is given by integrating $\mathcal{A}$ over stable configurations parametrized by two-pointed semistable genus zero curves. By a variant of this construction, we obtained a chiral $\mathcal{A}$-bimodule $\mathfrak{Z}_{\mathcal{A}}$ describing the value of a factorization algebra at a nodal point. We show that its zeroth homology recovers the bimodule underlying the mode-transition algebra $\mathfrak{A}(V)$ defined by Damiolini, Gibney, and Krashen, which they use to describes a vertex algebra at a node. Finally, the value over a formal smoothing of a node provides a deformation $\tilde{\mathfrak{Z}}_{\mathcal{A}}$ of $\mathfrak{Z}_{\mathcal{A}}$, whose zeroth homology describes a deformation of the mode-transition algebra in the case of a vertex algebra.

Evolutionary optimization of spiking neural networks (SNNs) becomes increasingly difficult as task complexity grows because they must search a combined topology--parameter space that grows super-exponentially with network size. We address this scaling challenge through a co-evolutionary ensemble framework in which a population of candidate SNNs is evolved with fitness defined by each network's marginal contribution to group performance. Grounded in cooperative game theory and difference evaluation functions from multiagent systems, this credit assignment rewards networks that consistently improve ensemble performance and penalizes redundancy, encouraging complementary specialization during evolution rather than relying on post-hoc combination of independently trained networks. We evaluate the approach on classification, regression, and control tasks under $\mu$Caspian neuromorphic hardware constraints. Co-evolved ensembles achieve statistically significant improvements over both single-network evolution and post-hoc ensembles across all tasks, with the most pronounced gains in control, where standard evolution fails to discover effective policies and co-evolution enables a qualitative transition to near-optimal performance.

Future neutrino experiments, in particular DUNE, are expected to probe signals of new physics. Those can be conveniently parametrized in terms of Wilson coefficients in the LEFT, with direct connection to non-standard interactions at production, propagation and detection in the QFT formalism. Assuming that the new degrees of freedom lie above the electroweak scale, we investigate if a DUNE-motivated signal, described by a non-vanishing SMEFT Wilson coefficient, can be realized in UV completions containing extra isosinglet and/or isodoublet fields, once present flavour constraints are taken into account. To this end, we propose a pipeline which can, in principle, be applicable to any BSM signal parametrized by a given set of SMEFT Wilson coefficients. As a concrete example, we focus on the lepton-flavour-violating semileptonic coefficient $(C^{(1)}_{\ell q,1311})$. We find that the largest viable value of the target Wilson coefficient remains around ($10^{-2}\;{\rm TeV}^{-2}$), which is almost one order of magnitude below the DUNE benchmark.

Helicopter emergency medical services (HEMS) provide rapid access to critical care but are costly to operate and difficult to sustain financially. A clear understanding of these costs is essential for evaluating the feasibility and design of population-based funding or policy strategies. We developed a two-part model: (1) a cost framework capturing capital and operating expenses (e.g., aircraft, equipment, labor, facilities), and (2) an actuarial revenue model using healthcare encounter data and payer reimbursement rates. The model was applied to a commercially insured Massachusetts population (3.9M lives), using provider charge data and Medicare fee schedules. We analyzed breakeven transport volumes under varying reimbursement and labor cost assumptions, including sensitivity scenarios. Under optimistic assumptions (full charge realization, minimal overhead), breakeven is reached with approximately 90 annual transports. More realistic scenarios, incorporating commercial reimbursement at 50% of charges and full 24/7 staffing, require 184 transports. If labor costs are doubled or Medicare rates are used exclusively, breakeven thresholds exceed 1,000 transports per year. A Monte Carlo simulation (10,000 iterations) confirmed the robustness of these thresholds: the median simulated breakeven was 190 transports under commercial reimbursement, closely matching the deterministic base case. The 90th percentile reached 304 (commercial) and 1,066 (Medicare) annual transports. HEMS programs are highly sensitive to labor costs and payer reimbursement levels. Sustainable operation requires more transport volume than previously estimated, especially when reimbursement is constrained or staffing costs increase. This model provides a transparent, replicable tool to inform financial planning, policy evaluation, and payer negotiations for air medical services.

We consider the classic envy-free cake-cutting problem where the goal is to cut and allocate a divisible resource among a set of agents in a way that avoids any envy between them. When the agents' valuation functions are continuous and nonnegative, an envy-free solution is guaranteed to exist where each agent is allocated a contiguous piece of the resource. Such a solution can be efficiently computed using the standard cut-and-choose algorithm for two agents, but the problem is known to be hard when there are at least four agents. The setting with three agents has remained open. We show that the problem remains intractable for three agents. We obtain this result by uncovering a novel connection between cake-cutting and a computational problem corresponding to the Jordan curve theorem, introduced by Adler, Daskalakis, and Demaine (2016). As our main technical contribution, we provide the first lower bounds for the Jordan curve problem in the form of a query lower bound as well as hardness for the class UEOPL, a subclass of PPAD containing notoriously challenging problems such as Simple Stochastic Games and the P-matrix Linear Complementarity Problem.

We establish a refined singularity estimate for nonnegative n-superharmonic functions. For complete noncompact locally conformally flat manifolds with nonnegative Ricci curvature, we analytically characterize the volume growth, verify Yau's conjecture on the Cohn-Vossen inequality, and prove a sharp gap theorem that removes all auxiliary assumptions from earlier works.

In this paper we deal with the boundedness of certain generalized sequence-to-function Hardy-Littlewood-Pólya-type operators. We completely characterize the $l^{p}-L^{q}$ boundedness of these operators for all $(p, q)\in [1, \infty]\times[1, \infty]$. These results complement some previous results in the literature. Our method relies on the ideas of generalized Schur's tests developed by Okikiolu, Sinnamon, Tao and Zhao.

This work presents an experimental setup for implementing two-qubit operations on neutral atoms ($^{87}$Rb) with the possibility of using two different Rydberg excitation schemes. One of them uses 5P$_{1/2}$ as the intermediate level and applies the second-stage beam locally to the addressed atoms. The second scheme uses the 6P$_{3/2}$ level; in this scheme, the particles to be entangled are moved to a separate zone through which both Rydberg beams pass. The advantages and limitations of both schemes are analyzed. Based on numerical modeling performed with a Julia package developed by the authors, it is demonstrated that the spatial configuration has a greater effect on quantum-operation fidelity than the choice of intermediate level. An experimental implementation of the scheme using the 6P$_{3/2}$ level is demonstrated, making it possible to achieve a two-qubit operation fidelity of 94%.

We investigate the chemical-potential dependence of hadron spectra in two-color QCD using first-principles lattice simulations. We compute two-point correlation functions for all allowed hadronic operators by newly including the contributions from disconnected diagrams, and extract the corresponding effective masses. In the meson sector, the mass hierarchy in the hadronic phase (normal vacuum) is found to be $m_\pi \lesssim m_{\eta} < m_\sigma \mathrm{(noisy)} < m_\rho \sim m_\omega \ll m_{a_1}$, which is similar to that in three-color QCD. In the superfluid phase, this hierarchy is modified, and with increasing density it changes to $m_\sigma \mathrm{(noisy)} < m_{a_1} < m_\rho < m_\pi \sim m_{\eta} \mathrm{(noisy)} \ll m_{\omega} \mathrm{(noisy)}$. In the diquark sector, the ordering remains as $m_{NG} \lesssim m_{I=0, S} < m_{I=1, AV} < m_{I=0, PS} \lesssim m_{I=0, V}$ in both phases, and the Nambu--Goldstone mode associated with spontaneous breaking of $U(1)_B$ is confirmed to be nearly massless. Furthermore, by comparing correlators for chiral partners, we find indications of chiral symmetry restoration at high density.

We develop a scan statistic method for detecting local clusters in a two-sample nonhomogeneous Poisson process (NHPP) framework, motivated by copy number variation (CNV) analysis in next-generation sequencing data. The control sample is used to construct an empirical time transformation, under which the transformed case sample is approximately uniform on [0,1] under the null hypothesis. The scan statistic is defined as the maximum number of transformed points within a moving window. We show that the scan statistic converges to a generalized extreme value (GEV) distribution with an extremal index that captures the dependence induced by overlapping windows. The GEV parameters and extremal index are estimated using maximum likelihood and exceedance clustering methods, providing an asymptotic calibration of the test. A permutation procedure is also developed to provide a nonparametric alternative. Simulation studies show that the permutation calibration maintains empirical Type I error close to the nominal level across the considered settings, and the GEV calibration is accurate for smaller windows. Both proposed procedures show competitive power compared with the continuous testing method under heterogeneous baseline intensities. An application to sequencing data illustrates the effectiveness of the proposed approach for detecting CNV regions.

Myopic self-avoiding fractional Brownian motion (FBM) is a stochastic process in which an ensemble of particles is driven by fractional Gaussian noise while being repelled by the gradient of the time-integrated ensemble density [J. House, R. Bakhshizada, S. Janušonis, R. Metzler, and T. Vojta, Phys. Rev. E 112, 034119 (2025)]. Depending on the anomalous diffusion exponent $\alpha$ characterizing the noise, the process features two dynamical regimes: an interaction-dominated regime ($\alpha < \alpha_c=4/(d+2)$) where the mean-density interaction governs long-time dynamics, and a noise-dominated regime ($\alpha > \alpha_c$) where FBM correlations prevail. In the interaction-dominated regime, the mean-squared displacement grows as $\langle r^2(t) \rangle \sim t^{4/(d+2)}$ regardless of $\alpha$, while for $\alpha > \alpha_c$ the standard FBM scaling $\langle r^2(t) \rangle \sim t^{\alpha}$ is recovered. Here, we develop an analytical mean-field theory of myopic self-avoiding FBM, based on a Fokker-Planck approach to the interaction-dominated regime. This allows us to derive closed-form polynomial solutions for the probability density. To compare with computer simulations, we develop an efficient radial binning algorithm that significantly reduces the computational complexity, making large-scale three-dimensional simulations feasible. Extensive simulations in one, two, and three dimensions confirm the analytical predictions. We also discuss the application of the process to the self-organization of serotonergic axons (fibers) in vertebrate brains, where FBM paths with self-avoidance provide a natural framework for understanding spatial heterogeneities of fiber densities.

Numerical simulations are performed for an FFA-W3 wind-turbine airfoil corresponding to a section of the DTU 10-MW Reference Wind Turbine. Wall-resolved large-eddy simulations (LES) are carried out with Nek5000 and EllipSys at chord Reynolds number $Re_c=1\times10^5$ and effective angle of attack $AoA=3.1^\circ-3.3^\circ$. A spanwise domain width of 10 percent of the chord is sufficient to reproduce the time-averaged flow and the evolution of the main disturbances. EllipSys is validated against Nek5000 for LES, showing close agreement for the mean flow and most amplified perturbations. EllipSys underpredicts the amplitude of Tollmien-Schlichting waves in the attached boundary layer, owing to higher numerical dissipation, but closely predicts the evolution of the Kelvin-Helmholtz (KH) mode in the laminar separation bubble, in agreement with parabolized stability equation (PSE) results. The mode shape is extracted using spectral proper orthogonal decomposition (SPOD), revealing the KH wavepacket forming in the separation bubble. Long-time EllipSys simulations show a slow modulation of the normal-force coefficient, with amplitude 10.5 percent and period 48 flow-through times, corresponding to $f=f^*c/U_\infty=0.021$ and $St=f\sin(AoA)=0.0012$. This frequency is associated with low-frequency oscillations reported in airfoil studies, although the Strouhal number is lower than previously observed and occurs at smaller angle of attack. For the DTU 10-MW turbine, the oscillation period corresponds to 7.7 blade rotations. Periodic stalling and reattachment may trigger the oscillation, while sufficiently high reverse flow on both sides of the airfoil may permit absolute instability and periodic bubble bursting.

This paper develops a finite certificate calculus for ambient release systems, staged probabilistic environments in which a protected coordinate is not observed directly but can remain statistically readable through visible roles, timing, repeated movement, bounded attention, linked rooms, and post-release state. The security notion, choric masking, requires the trace law induced by a protected locus to lie inside or near the convex hull of admissible cover traces under the tests available to a specified audience. For finite horizons, trace laws form polytopes, audiences induce measurement operators, and masking becomes intersection in the projected measurement space. Exposure is certified by separating hyperplanes, kernel obstructions, hypothesis-testing bounds, Fano-type localization lower bounds, and support separation in downstream rooms. The calculus distinguishes trace residue from carrier localization, full-trace exposure from attention-filtered exposure, first-room masking from delayed post-release exposure, and unresolved system pressure from carrier hazard. It proves measurement-polytope equivalence for exact and approximate masks, dual separation certificates, data-processing laws for attention lenses, aperture identities for gaze-thinned observation, lower bounds for mandatory unique gestures, composition rules for linked releases, and a repeated-room debt theorem showing how unresolved pressure can broaden selection and shift cost onto cover populations without localizing the source. The result is a finite, checkable language for auditing privacy, unlinkability, side-channel leakage, and accountability in public-facing release systems.

Modern software supply chains have evolved into vast, heterogeneous networks where transparency - the granular understanding of all software components - is now a critical security requirement. While Software Bills of Materials (SBOMs) have emerged as the primary mechanism for this transparency, current industry practices rely on a metadata-centric paradigm that assumes an artifact is defined solely by its package manager declarations. We posit that this assumption is fundamentally flawed, creating a systemic visibility gap we define as Software Dark Matter (SDM). SDM represents the set of security-critical files present in an artifact's filesystem that are unaccounted for by its associated metadata. We implement a reference tool, DARKFILES, and use it to analyze four ecosystems of disjoint nature: DockerHub, Maven Central, plugin/extension marketplaces (Jenkins plugins and OpenVSX), and a real-world enterprise environment. Our research makes the following contributions: we introduce a general-purpose metric for artifact fidelity calculating SDM as the ratio of untracked files per total file count. We introduce Packaging Lag, a phenomenon where official metadata remains out-of-date across multiple versions before catching up to an artifact's actual content. We demonstrate that SDM exposes vulnerable software invisible to SBOM-driven pipelines both by cross-referencing untracked packages against known CVE databases and through the direct discovery of three confirmed high-severity CVEs, showing that SDM is highly correlated with sensitive information including secrets and cryptographic keys.

Motivated by the recent interest in multipoint Padé approximants in the physics community, we discuss Chebyshev rational functions and show how they give rise to multipoint Padé approximants in exactly the same way that Chebyshev polynomials produce Padé approximants. We present recurrence relations for Chebyshev rational functions, as well as the underlying continued fraction of Thiele type (also known as $R_{II}$ type). Finally, we provide numerical evidence illustrating the effects of noise on this interpolation scheme and show that a phenomenon similar to that recently observed by Costin, Dunne, and Meynig for Padé approximants also occurs in the multipoint setting.

Motivated by variation problems for the Néron--Tate height pairing, we construct an adelic Poincaré bundle on the Néron model of an abelian scheme over a curve. This extends the adelic Poincaré bundle of Yuan--Zhang, which encodes the fiberwise Néron--Tate height pairing.

We present a custom-designed ultrahigh vacuum (UHV) cluster tool developed for studying shallow nitrogen-vacancy (NV) centers in diamond, enabling in situ diamond surface preparation, characterization, and single NV center dynamics measurements within a single connected platform. The system combines a surface science chamber for controlled surface modification and analysis with a cryogenic confocal microscope chamber dedicated to NV spin and optical measurements. This integrated approach enables a direct correlation between diamond surface chemistry and the resulting NV spin and charge properties. The instrument provides a versatile platform for systematic studies of surface-induced decoherence mechanisms and charge dynamics for shallow NV centers, and establishes a pathway toward reproducible surface engineering for quantum sensing applications.

We show that the toric ideal of the Fano matroid polytope does not have a quadratic Gröbner basis. This resolves in the negative a strong version of White's conjecture from matroid theory. This result was found independently by De Loera, Ferroni, Morales, and Rambau. Our approach is based on a new characterization of regular unimodular flag triangulations, which reduces the problem to an instance of SMT involving boolean and real variables. We then use an SMT solver to prove unsatisfiability. Using this approach, we also show that all 8-element matroids which do not have the Fano matroid or its dual as a minor, with the possible exception of the matroid $T_8$, have toric ideals which admit quadratic Gröbner bases.

We get estimates on the Gauss-Kuzmin-Wirsing constant for continued fractions.

Silicon Photomultipliers (SiPM) will be used extensively in the upgraded CMS detector at the Large Hadron Collider. SiPMs have already been implemented into the barrel and endcap hadron calorimeters (HCAL) as part of the Phase I upgrade, and hundreds of thousands of SiPMs will be used for two new Phase II subdetectors, the Barrel Timing Layer (BTL) and the endcap high granularity hadronic calorimeter (HGCAL). We discuss the motivation for SiPMs as the photodetectors of choice in CMS, the evolution of the SiPMs from Phase I to Phase II, and the particular challenges faced and overcome for each of the three subdetectors.

We introduce c-Lattice Aggregation, a fault-tolerant reconstruction problem for distributed verification under crash and Byzantine failures. In our setting, n asynchronous processes supervise a concurrent execution I: each process holds a local sample, and must collaboratively reconstruct I from partial, potentially overlapping observations. A protocol solves c-Lattice Aggregation if at least c correct processes output the complete execution I, while all correct outputs are comparable and bounded by I. This strengthens Lattice Agreement [Attiya, Herlihy and Rachman, 1995] and Byzantine Lattice Agreement [Di Luna et al., 2020; Zheng and Garg, 2020]. We parameterize inputs by a redundancy parameter x -- every element of I appears in at least x initial samples -- and establish tight feasibility thresholds. Under crash failures with at most t faulty processes, Lattice Aggregation is solvable if and only if x >= t + 1. Under Byzantine failures with t < n/3, c-Lattice Aggregation is solvable if and only if x >= 2t + c. All bounds are tight: we present matching algorithms based on SCD-broadcast [Imbs et al., 2018; Khanchandani and Wattenhofer, 2024] and indistinguishability-based lower bounds. Finally, we define globally dependent languages -- those for which no partial view can certify correctness, including consensus, linearizability, k-set agreement, and leader election -- and prove that soundness of any monitoring system is achievable if and only if c-Lattice Aggregation is solved, yielding the first complete characterization of fault-tolerant verification under Byzantine failures.

Magnetic reconnection in twisted loops has long been invoked as an engine powering energetic transients from black hole accretion to neutron star mergers, yet never directly observed. Here we report the first direct observation of the complete reconnection of this type in a solar flare. We find a magnetic loop twisted to about 540 degrees, far exceeding the 180 degrees twist assumed in existing simulations. This extreme twist inherently enables efficient multiple X-line reconnection, akin to the role of turbulence in contemporary theory. Remarkably, the intertwined end breaks unilaterally after reconnection (unlike symmetric breaking in simulations), forming open field lines that release hot plasma -- providing a promising mechanism for coronal generation or heating. We first detect hard X-ray emission from the current sheet, directly proving it as a particle accelerator. Moreover, we discover a power-law relationship between quasi-periodic oscillation frequency and magnetic field strength across solar flares, black hole binaries, active galactic nuclei, magnetars, and gamma-ray bursts. This relation identifies twisted-pair unilateral reconnection as a common burst mechanism and provides a natural ruler for cosmic magnetic fields. These findings establish an observational foundation for future reconnection theory and simulations, offering a unified framework for magnetically powered bursts.

High-accuracy positioning is critical for emerging applications such as autonomous driving, industrial automation, augmented reality, and smart cities. 3GPP Release 18 introduced carrier-phase (CP) positioning for 5G that offers superior accuracy compared to conventional time-based methods such as time of arrival (ToA). However, CP-based positioning requires resolving the integer phase ambiguity, which refers to the unknown number of full-wavelength cycles completed during signal propagation. Joint processing of ToA and CP can mitigate this integer ambiguity by narrowing down the search space of possible integers, particularly for short wavelengths. This paper investigates the performance of a positioning method that integrates ToA and CP measurements. As a main contribution, the analysis explicitly accounts for the error correlation between ToA and CP measurements. Furthermore, the study analyzes the impact of key 5G system parameters on positioning accuracy using this correlation-aware joint method in both factory and urban environments, where many 5G positioning applications are expected to emerge. The results highlight that exploiting this correlation can further improve positioning performance by approximately 7 percent. Moreover, the findings of this study provide insight into how 5G system parameters can be tuned to achieve centimeter-level accuracy under favorable conditions.

The interplay of oxygen deficiency and vanadium multiple valency in the candidate multiferroic V-doped $Pca2_1$ hafnia HfO$_2$ is studied by first-principles calculations. Low-lying V majority gap states accept electrons from oxygen-vacancy donors, reducing their formation energy, and converting nominal V$^{4+}$ centers into V$^{3+}$. The resulting local magnetization and screening changes are reflected in the calculated V core-level shifts, which are consistent with the experimentally observed XPS signatures. The calculated V$^{3+}$/V$^{4+}$ population ratio determined by oxygen vacancies only matches experiment in reducing conditions, suggesting that additional electron reservoirs may contribute under ALD growth conditions. A similar scenario also seems to apply to the recently observed multiferroicity in Cr-doped hafnia, where oxygen deficiency is intrinsic to the growth technique.