The thermosensitive behavior of microgel particles suspended in solvents, i.e. their temperature-dependent swelling properties, has triggered ongoing interest in industry and academia over the past forty years. The most-studied polymer is poly(N-isopropylacrylamide) - PNIPAM -, where the volume phase transition temperature is well known to depend on the detailed molecular architecture of the monomers. In this article, we focus on publications mostly of the past five years in chemical synthesis, aiming at shifting or controlling the volume phase transition temperature (VPTT) of such polymers by copolymerization of a main monomer - often from the PNIPAM family - with either monomers of different hydrophobicity, or with ones bearing ionizable groups. In some cases, hydrophobicity may be modulated by light as external switching parameter, whereas ionic strength or pH may act on the thermosensitivity of the microgels containing charged groups. Due to either differences in reactivity, or specific synthesis routes, particular microgel morphologies, such as molecular gradient, core-shell, interpenetrated, or patchy (multi-lobular) structures may be generated. They may give rise to spatial modulations of thermosensitivity within particles and are highlighted in this review. Our short overview shows that multiple external control of VPTT and morphology is commonly achieved nowadays.

Let $τ(n)$ denote the classical divisor function. In this paper, we consider the hyperbolic fractional sum of the divisor function defined by $$ T(x) = \sum_{n_1 n_2 \leqslant x} τ\left( \left[ \frac{x}{n_1 n_2} \right] \right) = \sum_{n \leqslant x} τ\left( \left[ \frac{x}{n} \right] \right) τ(n), $$ where $[t]$ denotes the integral part of the real number $t$. By establishing new estimates for a class of three-dimensional exponential sums with constant perturbation, we obtain an improved asymptotic formula for $T(x)$. In particular, we show that for any $\varepsilon > 0$, the error term in the asymptotic expansion of $T(x)$ is bounded by $O(x^{17/30+\varepsilon})$. This result breaks the $4/7$-barrier which corresponds to the application of the classical divisor problem conjecture $1/4+\varepsilon$.

In recent years, WiFi sensing has been recognized as a promising technology to bring respiratory monitoring into everyday homes, thanks to its contactless nature and ubiquitous availability. However, existing WiFi-based respiratory monitoring systems still fall short of deployment-oriented performance: they suffer from restrained hardware scalability, limited accuracy, and are highly sensitive to user location. To overcome these limitations and push WiFi sensing towards clinically meaningful precision, we propose RespirFi, a novel system that robustly delivers high-fidelity respiratory waveforms with WiFi Channel State Information (CSI), thereby enabling accurate estimation of key physiological biomarkers. At the core of RespirFi is a theoretical human reflection model, through which we perform an in-depth characterization of how CSI variations are shaped by both subcarrier frequency and spatial user location. Guided by these insights, we develop a location-robust waveform construction method that adaptively selects high quality subcarriers and aligns their waveform trends, ensuring accurate waveform recovery. Furthermore, we propose a breathing phase identification method that leverages inter-subcarrier CSI differences to reliably distinguish inhalation from exhalation. We implement RespirFi over commodity WiFi devices, and extensive experiments demonstrate that it outperforms state-of-the-art approaches across a wide range of clinically relevant respiratory metrics.

We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/ε)$ space that outputs a split within additive $ε$ error of the optimal split, improving upon the two-pass algorithm of Pham et al. (ISIT 2025). Furthermore, we provide a matching one-pass lower bound showing that $Ω(M^2/ε)$ space is indeed necessary. For classification, we also obtain a one-pass algorithm using $\tilde{O}(1/ε)$ space for approximating the optimal Gini split, improving upon the previous $\tilde{O}(1/ε^2)$-space algorithm. We complement these results with matching space lower bounds: $Ω(1/ε)$ for Gini impurity and $Ω(1/ε)$ for misclassification (which matches the upper bound obtained by sampling). Our algorithms exploit the Lipschitz property of the loss functions and use reservoir sampling along with Count--Min sketches with range queries. Our lower bounds follow from careful reductions from the INDEX problem.

Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of matrices which are obtained by amalgamating the entries of two smaller matrices. In particular, this gives formulae for multivariable Vandermonde determinants as a sum of completely factorising terms, each of which is a Vandermonde determinant in fewer variables. As an application, we deduce an elementary proof of the multiplicativity of the transfinite diameter for products of compact sets.

We develop a general theory of high-harmonic generation (HHG) in solid-state systems, based on a weak-correlation expansion of photonic and matter degrees of freedom. Unlike standard HHG theories, which treat light-matter dynamics through the Schrodinger equation, our approach employs density-matrix evolution, naturally capturing the mixed-state character of both the field and the matter - a critical aspect for describing complex solid-state band structures. We show explicitly that the properties of the emitted fields are governed by the quantum statistics and quantum geometry of the underlying solid. Taking the Su-Schrieffer-Heeger (SSH) model in a one-sided optical cavity as a paradigmatic example and considering the dual regime, we demonstrate that in the topological phase a system exhibits a stronger HHG response and stronger quantum-light signatures than in the trivial phase. Furthermore, we show that cavity-matter interaction gives rise to squeezed high-harmonic quantum light, whose properties are directly imprinted by the current-current fluctuations in the material system. Crucially, the observed squeezing does not rely on a separate quartic Kerr mechanism. In the mesoscopic regime, the genuine quantum Kerr term is higher order in light-matter coupling strength and negligible, while the relevant non-classical effect is governed by current-current fluctuations encoded in the complex susceptibility of the material. This work establishes a direct link between band topology and photon statistics, opening new avenues for topology-sensitive quantum light generation and photon statistics based spectroscopy of solid-state systems.

We study the $l_p$ Hausdorff distance from convex hull of a compact set $A\subset\mathbb{R}^n$, which is the distance \begin{equation*} d^{(l_p)}(A):=\sup_{x\in conv(A)}\inf_{a\in A}\|x-a\|_p, \end{equation*} where $\|\cdot\|_p$ is the $l_p$-norm on $\mathbb{R}^n$. We prove that when $n=2$ and $1\leq p<\infty$, the function $(d^{(l_p)})^p$ is subadditive with respect to Minkowski summation, up to multiplication by the factor $\max\{1,2^{p-2}\}$, and we observe that this bound is sharp.

In this work, we investigate the projected sensitivity of the Beam-Dump eXperiment at the International Linear Collider (ILC-BDX) to inelastic fermionic dark matter coupled to the Standard Model photon through an off-diagonal magnetic dipole operator. We compute the production rate of dark matter states in the bremsstrahlung like process $e^- N \to e^- N γ^* (\to χ_{1} \barχ_0)$, induced by the scattering of high-energy electrons on target nuclei. The resulting boosted dark matter fluxes are then propagated to the detector, where the signal events arise from scattering off detector electrons. The projected exclusion limits are derived using the expected numbers of electrons on target (this implies a typical rate of $4.0~\times~10^{21}/\mbox{year}$) corresponding to 1 year and 10 years of data taking. To characterize the impact of inelasticity, we consider two benchmark relative mass splittings, $Δ=0.05$ and $Δ=0.001$, motivated by thermal dark matter scenarios. Our results show that ILC-BDX can probe inelastic magnetic-dipole dark matter over a phenomenologically relevant region of parameter space.

Optimizing tensor networks with standard first-order methods often leads to slow convergence and entrapment in local minima. Although second-order optimization offers enhanced robustness, explicitly constructing the full Hessian matrix is computationally prohibitive for large-scale systems. In this work, we bypass this bottleneck by introducing an analytical Hessian-vector product kernel designed for arbitrary compositions of linear maps. This two-pass algorithm leverages recursive tangent-state propagation with a bounded virtual bond dimension to guarantee scalability. We demonstrate the practical utility of this kernel by integrating it into a Riemannian trust-region framework for quantum circuit compression. Evaluated on time-evolution circuits for various spin chains, our second-order approach achieves up to a four-order-of-magnitude improvement in fidelity over naive Trotterization, while delivering significantly smoother, faster convergence than conventional first-order methods such as Riemannian ADAM.

In frequency division duplex massive multiple-input multiple-output systems, downlink channel state information must be fed back within a limited uplink budget. While transform coding with Karhunen-Loeve transform and reverse water-filling is rate-distortion optimal for Gaussian channels, its performance is limited by basis mismatch between the user and base station. We analyze this mismatch and propose a practical architecture separating long-term basis feedback from short-term coefficient quantization. Using a random vector quantization, we derive a closed-form end-to-end mean square error expression. This allows us to characterize the optimal rate split and identify a phase transition threshold for basis updates. Simulations on correlated Gaussian and COST2100 channels demonstrate near-optimal performance, robustness to update overhead, and significant complexity reduction compared to deep-learning-based autoencoders.

Gate-modulated nanopores have emerged as a promising platform for achieving ion selectivity and ionic current rectification (ICR) with the advantage of active field-based control. However, the mechanistic origin of these experimentally reported phenomena, arising from electrostatic coupling between the prescribed radial pore surface potential and the axial transmembrane electric field, remains insufficiently understood. Here, using coupled Poisson--Nernst--Planck and Navier--Stokes simulations supported by asymptotic analysis, we show that a uniform surface potential inherently interacts with the axial driving field to generate a three-dimensional, axially nonuniform electric double layer (EDL). This field-induced EDL heterogeneity effectively mimics a linear axial variation in zeta potential, breaking translational symmetry within an otherwise uniform pore. As a result, the system exhibits coupled electrokinetic responses, including ion selectivity, ionic current rectification, and non-canonical electroosmotic flow, all governed by a single asymmetry parameter $α$ derived from the EDL structure. Critical transitions occur at specific values of $α$; in particular, at $α=0$, the EDL becomes axially antisymmetric, leading to reversal of ion selectivity, significant ICR and the emergence of a peculiar negative electroosmotic flow rectification accompanied by internal vortical structures. These findings establish the electrostatic mechanism for axial symmetry breaking as the underlying principle for transport in voltage-gated nanopores, enabling a unified framework for designing tunable electrokinetic functionalities beyond geometry- and chemistry-based strategies.

Memory analysis is a crucial technique in digital forensics that enables investigators to examine the runtime state of a system through physical memory dumps. While significant advances have been made in memory forensics, the detection and analysis of Thread Local Storage (TLS) callbacks remain challenging due to their dual nature as both legitimate Windows constructs and potential vectors for malware execution. An early version of the TlsCheck plugin received recognition in the Volatility Plugin Contest 2024. In this paper, we present an enhanced version of TlsCheck for Volatility 3, designed to detect and analyze TLS callbacks in process memory. It implements precise detection of TLS callback tables through analysis of PE headers and memory structures, combined with disassembly of identified callback routines. The plugin supports both 32-bit and 64-bit architectures, offering investigators insights into callback locations, assembly behavior, and potential signs of suspicious activity. To enhance detection, we incorporate pattern matching using custom regular expressions and YARA rules, helping analysts identify specific code patterns or suspicious constructs within TLS callbacks. The framework also includes instruction-level analysis to highlight behavior often linked to malware, such as anti-debugging, code injection, and process manipulation. This implementation significantly improves defenders' ability to detect and investigate TLS-based threats during memory forensics, supporting more effective malware analysis and incident response operations.

In this letter, we focus on the application of the off-shell recursion method proposed in \cite{Tao:2025fch} in the Yang-Mills planar loop integrands, which starts with solving the classical equation of motion via the perturbiner method. Following the recursion steps, we point out that the pure gluon sector of the planar loop integrands can be written in matrix formalism. This matrix formalism not only makes the off-shell structure of the Yang-Mills planar integrands clearer, but also has potential use in finding amplitude relations at higher-loop levels. Furthermore, we add the ghost contribution and write down the whole recursion step of the Yang-Mills planar loop integrands with ghost contributions. Finally, we consider the 2-loop planar integrand recursion as a special case and conclude a recursion strategy in this case.

QKD technology is being increasingly adopted inside the network core for protecting information transport against any form of computational attacks. However, the use of QKD for wide-area internetworking is still challenging and costly, due to its strong trust assumptions and the low achievable key rates in long QKD links. This paper presents a standards-driven design and implementation of a unified hybrid key delivery service for a network of isolated QKD domains (subnetworks using QKD as provider technology for secret key generation) connected via classical WAN links. The framework follows a distributed architecture and uses a hybrid approach where keys generated in a domain are securely relayed to other domains with PQC (Kyber), dynamically routed, and managed at the system level. The solution has been implemented in an operational testbed comprising three regional subnetworks. We present the design principles, the deployment, and the experimental performance results for this scalable key delivery service.

In this paper, we show that starting from a geodesic ball $\overline{B_{r_0}}(0)$ in $\mathbb{H}^n$, for $n\geq3$, with prescribed non-decreasing rotationally symmetric mean curvature and the fixed conformal class $[g_{\mathbb{S}^{n-1}}]$ on the boundary, the solution $g(t)$ to the normalized Ricci flow $(1.2)$ which is continuous up to the boundary, exists for all $t>0$ and converges locally uniformly in $B_{r_0}(0)$ to a complete hyperbolic metric as $t\to\infty$(see Theorem 1.2 for details). Moreover, the sectional curvature of $g(t)$ maintains less than $-1$ for $t>0$. For dimension $2$, to achieve such a convergence result, we need the additional assumption that the mean curvature on the boundary increases in a certain speed to infinity as $t\to\infty$.

We extend our gauge-covariant stochastic neural-field framework by promoting architecture-level parameters to slow stochastic variables evolving in function space. Our effective theory is formulated in terms of classical commuting fields and provides symmetry-constrained diagnostics of marginality and finite-width effects through the maximal Lyapunov exponent, the amplification factor, and dressed spectral kernels. On top of this dynamics, we introduce a Markovian evolutionary scheme compatible with the local $U(1)$ structure of the effective model. By using a minimal implementation, the genotype is reduced to the weight-variance parameter $σ_w^2$, and the fitness functional combines spectral agreement, marginal stability, and a symmetry-constrained critical anchor. Comparing three evolutionary models, we find that only the fully symmetry-constrained Ginibre $U(1)$ version robustly approaches a narrow near-marginal regime and reproduces the predicted low-frequency finite-width spectral behavior. These results support the use of symmetry-guided effective stability diagnostics as practical principles for stochastic architecture search in controlled settings.

A two-qutrit extension of the quantum Rabi model is studied. Despite its increased complexity, the model results to be integrable under specific, physically relevant conditions. This feature allows for the emergence of analytically tractable subdynamics. In this framework, the ground-state phase diagram can be derived, and the analysis reveals critical phenomena linked to both level crossings and quantum phase transitions.

We study the rate-cost tradeoff in rate-limited control of general stochastic control systems, including nonlinear systems, over a finite horizon. At each time step, an encoder observes the state and transmits a description to a controller, which then selects the control action. For an average control-cost threshold $D$, we characterize the minimum achievable communication rate $R_n(D)$ via a nonasymptotic bound: $R_n(D)$ lies within an additive logarithmic gap of the optimal value of a directed-information minimization $F_n(D)$, namely, we show that $F_n(D) \le R_n(D) \le F_n(D)+\log \bigl(F_n(D)+3.4\bigr)+2+\frac{1}{n}$, in bits. This establishes directed information as the operationally relevant quantity governing rate-limited control, thereby broadening its utility beyond its previously established roles in causal source coding and linear quadratic Gaussian (LQG) control to general nonlinear control systems. We prove the upper bound constructively by building an encoding-and-control policy using the strong functional representation lemma at each time step. As special cases of our setting, our framework yields nonasymptotic bounds for sequential (causal) rate-distortion and LQG control.

Through adaptive antenna repositioning, the movable antenna (MA) technology enables on-demand reconfiguration of wireless channels, thereby creating an additional spatial degree of freedom in improving communication performance. This paper investigates a multiuser uplink communication system aided by MAs, where a base station (BS) equipped with multiple MAs serves multiple single-antenna users. Specifically, given that an optimized array geometry cannot guarantee rate fairness, we focus on designing antenna trajectory at the BS to maximize the minimum achievable rate among all users over a finite time period. The resulting optimization problem is fundamentally challenging to solve due to the continuous-time nature. To address it, we first examine an ideal case with infinitely fast MA movement and demonstrate that the relaxed problem can be optimally solved via the Lagrangian dual method. The obtained trajectory solution reveals that the BS should employ a finite set of MA deployment patterns, each allocated an optimal time duration. Building on this, we then study the general case with limited MA movement speed and propose a heuristic trajectory design inspired by the optimal patterns identified in the ideal scenario. Several insights are also gained by examining the simplified special case. Finally, numerical results are provided to validate the effectiveness of the proposed designs compared to competitive benchmarks.

The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an $N$-qubit chain quantum Rabi models.

We derive spectral fluctuation--dissipation--response inequalities for finite-state Markov jump processes. By comparing the causal susceptibility to its passive equilibrium reference, we establish frequency-resolved and frequency-integrated inequalities that bound their mismatch in terms of the steady-state entropy production rate, probe variance, short-time perturbation diffusion, and reversible relaxation timescales. Our bounds exactly recover the standard fluctuation--dissipation theorem at equilibrium and apply directly to measurable causal susceptibilities, providing experimentally testable thermodynamic limits on FDT breakdown in driven steady states.

Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art performance in various imaging applications. However, their stability and convergence within iterative regularization frameworks remain largely unexplored. In this work, we extend the framework of Regularization by Denoising (RED) by introducing a novel denoiser-driven iterative regularization scheme, referred to as \texttt{DDIR}, that incorporates a new regularization functional based on averaged denoisers. The proposed approach employs an adaptive step-size strategy together with an \emph{a posteriori} stopping rule to ensure stability while alleviating oscillatory behavior and semi-convergence effects induced by noise. As our main theoretical contribution, we prove that the resulting reconstruction method constitutes a stable and convergent regularization scheme in the classical sense. To the best of our knowledge, this provides the first rigorous justification of \texttt{DDIR} within the framework of regularization theory. Finally, we demonstrate the performance of the proposed method through numerical experiments on image deblurring and phase retrieval Computed Tomography (CT) using three denoisers, namely median, TNRD, and TV proximal. The results highlight the effectiveness of the method in terms of reconstruction accuracy and computational efficiency.

This paper introduces partial results, in the current situation, of ongoing considerations corresponding to the above title. A construction on exact relativistic quantum field model with the space time dimension $d \in {\mathbb N}$, including the case where $d \geq 4$, is going to be discussed. Firstly, Hermitian scalar quantum fields $<{\cal H}, U, ψ, D>$, within a relaxed framework of the Gårding-Wightman Axioms, is constructed by making use of the stochastic calculus arguments with respect to the {\it{stationary additive random fields }} on ${\mathbb R}^d$, i.e., the {\it{L{é}vy random fields}} on ${\mathbb R}^d$. The first constructed $<{\cal H}, U, ψ, D>$, here, satisfy all the requirements of the the Gårding-Wightman Axioms, except that the field operators $ψ(f)$ with $f \in {\cal S}({\mathbb R}^d \to {\mathbb R})$ are symmetric operators on the physical Hilbert space ${\cal H}$, which situation is denoted here as {\it{a relaxed framework}} of the Gårding-Wightman Axioms. Secondly, by taking the adequate subspaces of ${\cal H}$, non trivial exact Wightman quantum fields, which satisfy all the requirements of the Gårding-Wightman Axioms, are constructed actually. keywords: Axiomatic quantum field theory, Gårding-Wightman axioms, Bochner-Minlos theorem, L{é}vy fields on ${\mathbb R}^d$.

Third-order nonlinear Hall effects (THE) have recently attracted considerable experimental interest as powerful probes for quantum geometric properties in emergent quantum materials, encompassing quadrupole moments of quantum metric and Berry curvature. Here, we report a fundamentally new THE in room-temperature van der Waals ferromagnet Fe3GaTe2 from second-order Berry connection polarizability, which manifests a higher-order characterization of band geometry called symplectic connection. Our observations show that the third-order transverse response in Fe3GaTe2 is odd to magnetization, vanishes above the Curie temperature and remains independent of driving current directions. Scaling law analysis combined with first-principles calculations establishes this response as the symplectic-connection-induced THE. This discovery opens the door to probing high-order quantum geometric properties beyond Berry curvature and quantum metric through nonlinear transport, unveiling the potential of exploring nonlinear Hall phenomena in broad classes of magnets without breaking inversion symmetry. Moreover, the room-temperature manipulation of THE holds promises for device applications based on harnessing the quantum-geometric connection structure.

The exact microscopic origin, symmetry, and thermal melting mechanism of the charge density wave (CDW) phase in TiSe$_{2}$ remain a subject of intense debate, particularly regarding the presence of chiral structural order and a multi-step phase transition. Here, we resolve the finite-temperature structural dynamics of the monolayer TiSe$_{2}$ using large-scale molecular dynamics simulations driven by an accurate, first-principles-trained machine-learning interatomic potential. We demonstrate that the CDW melting deviates from a conventional second-order phase transition, while it undergoes a two-step melting process characterised by an extended fluctuation regime between $T^{\ast}\approx200$ K and $T_{\mathrm{CDW}}\approx250$ K, with proliferation of topological defects and domain walls, and accompanied by a completely overdamped soft optical phonon. Furthermore, we reveal that anisotropic long-wavelength thermal fluctuations spontaneously stabilise an asymmetric $3Q$ chiral CDW order with $C2$ symmetry. These findings provide a unified microscopic framework for understanding complex fluctuation-driven phase transitions in 2D quantum materials, demonstrating that the intricate CDW physics of TiSe$_{2}$ can be largely captured without invoking excitonic correlations.

We show that the construction of the linear interferometer in the Supplemental Material of arXiv:1909.09581 is flawed, leading to a generally suboptimal solution. We then provide the correct derivation of the optimal interferometric configuration that achieves the quantum Fisher information limit for imaging N weak incoherent emitters.

Spin-up of a mass gaining component in a binary system is considered taking into account the mass loss from the system during the mass transfer between components in the Hertzsprung gap. The angular momentum that the accreting component gains during mass transfer depends on the increase in the mass of the component at this stage. The increase in the mass was considered over a broad range, from 5% to 100%. The case is considered when, after mass transfer, the mass of the accreting component has a value of 16 M_solar, typical for early Be stars. The transfer of angular momentum within the accreting component occurs due to meridional circulation and shear turbulence. If the accreted mass accounts for more than 30%, the accretor obtains a rotation typical of early Be-stars. This conclusion does not depend on: a) the rotation of the accreting component before mass transfer, b) the amount of angular momentum coming from the boundary layer located between the star and the accretion disk, c) a possible decrease in the angular velocity of the disk below the Keplerian value, d) the efficiency of turbulence in the interior of the accretor.

We implement an algorithm for solving the minimum weight perfect matching problem. Our code significantly outperforms the current state-of-the-art Blossom V algorithm on those families of instances where Blossom V takes superlinear time. In practice, our implementation shows almost-linear runtime on every family of instances on which we have tested it. Our algorithm relies on solving the maximum-cardinality unweighted matching problems during its primal phase. Following the state-of-the-art cherry blossom algorithm, we use cherry trees instead of traditional alternating trees and cherry blossoms instead of traditional blossoms. We shrink cherry blossoms rather than traditional blossoms into supernodes. This strategy allows us to deal with much shallower supernodes.

This article introduces the HYMN (HYbrid Multi-technology Navigation) dataset: a multi-system, and time synchronized dataset for localization research based on opportunistic signals collected in an indoor-outdoor scenario. HYMN comprises measurement data collected in an industrial hall setting for five different positioning systems including Ultra-Wideband (UWB), Bluetooth Low Energy (BLE), WiFi, 5G, and Global Navigation Satellite System (GNSS). Unlike existing datasets that focus on single technologies or purely indoor/outdoor scenarios, HYMN combines five positioning technologies with explicit coverage of indoor-outdoor transitions, enabling multi-sensor fusion research for seamless localization. Each instance of data is identified through a unique measurement id and it represents time-stamped observations relevant for each system respectively along with the ground truth information. HYMN is designed to support a wide range of localization tasks including multi-sensor fingerprinting, cross-technology fusion, and seamless indoor-outdoor positioning. The synchronized measurements from GNSS and other terrestrial systems enable researchers to investigate how heterogeneous signals complement each other to overcome individual technology limitations such as GNSS degradation in covered areas or terrestrial system variability in dynamic environments.

X-ray flashes (XRFs) are a type of gamma-ray bursts (GRBs) with prompt emission predominantly below 30 keV poorly detected by previous missions. The advent of the SVOM mission, with its wide-field instrument ECLAIRs, provides a new way to detect soft X-ray transients such as XRFs. We present photometric and spectroscopic observations of XRF 241001A detected by SVOM, a soft, sub-luminous, and low-energetic burst located in a poorly populated region of the Amati relation. We investigate the origin of its faint, soft high-energy emission to assess its connection to the long GRB population. We analyze the SVOM/ECLAIRs prompt emission and model its afterglow emission from X-ray to-radio. We present JWST/NIRSpec and SVOM/VT observations of the associated supernova (SN 2024aiiq), which we model with an Arnett radioactive decay component and compare its properties with previously detected GRB/SNe. XRF 241001A is located at z = 0.573 and has a prompt emission dominated by photons below 20 keV with a duration of T90 = 3.14 seconds. Its spectrum can be modeled by non-thermal or thermal models, all pointing towards a low Epeak < 10 keV and Eiso ~ 8x10^49 erg. The X-ray-to-radio afterglow modeling favors an origin from a relativistic jet viewed on-axis. In the optical, XRF 241001A exhibits an early blue emission, similar to that detected in some fast X-ray transients and inconsistent with synchrotron emission. The JWST/NIRSpec observations firmly established its collapsar origin by revealing a SN Type Ic with broad lines, comparable to SN 1998bw and SN 2025kg-like events. XRF 241001A is a soft, low-luminosity collapsar event produced by a weak relativistic jet observed on-axis, supporting the view that part of the XRF population forms the low-energy tail of the long GRB population. It demonstrates the potential of SVOM/ECLAIRs to probe the soft regime of the high-energy transient population.