Interference is a universal consequence of superposition, yet in composite quantum systems it can encode correlations between subsystems. We show that in coupled electron-nuclear dynamics, interference in the nuclear density can arise dynamically even when it is initially absent. Starting from a superposition of orthogonal Born-Oppenheimer electronic states, we demonstrate within the exact factorisation framework that genuine non-adiabatic electron-nuclear correlations induce de-orthogonalisation of the electronic factors, thereby generating interference terms in the nuclear density. Such interference has no counterpart in adiabatic evolution. Unlike conventional nuclear wave-packet interference or interference that merely reflects electronic coherence in a chosen basis, the effect identified here is a manifestation of the compositeness of the full electron-nuclear state. Nuclear density interference thus emerges as a direct dynamical signature of correlated quantum motion in composite systems.

Let $S$ be an Enriques surface. In this paper we study the semistability of the restriction $Ω_{S}|_C$ for a general curve $C \in |H|$, where $H$ is a globally generated and ample line bundle on $S$. We show that $Ω_{S}|_C$ is semistable when $H^2 \ge 6$, or when $H^2 \ge 2$ and $S$ is very general. Moreover, we give explicit constructions of families of smooth irreducible curves that destabilize $Ω_S$.

SQL injection remains a major threat to web applications, as existing defenses often fail against obfuscation and evolving attacks because of neglecting the request-response context. This paper presents a context-enriched SQL injection detection framework, focusing on constructing a high-quality request-response dataset via a multi-agent honeypot system: the Request Generator Agent produces diverse malicious/benign requests, the Database Response Agent mediates interactions to ensure authentic responses while protecting production data, and the Traffic Monitor pairs requests with responses, assigns labels, and cleans data, yielding totally 140,973 labeled pairs with contextual cues absent in payload-only data. Experiments show that models trained on this context dataset outperform payload-only counterparts: CNN and BiLSTM achieve over 40\% accuracy improvement in different tasks, validating that the request-response context enhances the detection of evolving and obfuscated attacks.

An antimagic labelling of a graph $G = (V,E)$ is a bijection from $E$ to $\{1,2, \ldots, |E|\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A graph is said to be antimagic if it has an antimagic labelling. It has been proven that graphs $G$ with $Δ(G) \geq n - 3$ are antimagic, where $Δ(G)$ is the maximum degree of a vertex in $G$ and $n = |V|$. In this article, we extend this result to graphs with $Δ(G) = n - 4$, provided that $|E| \geq 7n$.

This paper introduces `Math Battles with AI', an innovative competitive format designed at ITMO University to redefine the role of generative AI in mathematics education. Moving away from a purely defensive stance, the authors propose an AI agent with intentionally increased hallucination likelihood in specific modes to train verification skills. We describe the three-stage tournament structure and a specialized assessment system that rewards critical verification over blind reliance. Initial results indicate a significant shift in student mindsets, fostering essential skills in digital hygiene and prompt engineering. This work serves as a practical guide for academic institutions aiming to leverage AI for enhancing, rather than undermining, intellectual development.

Accurate time-dependent quantum dynamics of Coulombic systems on grid-based representations remains computationally demanding due to the singularity of the Coulomb potential, which necessitates extremely fine spatial grids to mitigate discretisation errors. We propose two complementary correction schemes that, under identical resource budgets, consistently outperform the uncorrected counterparts. The first scheme modifies the potential operator to incorporate grid-basis structure into its representation, while the second introduces a corrected initial wavefunction inspired by analytical solutions of softened Coulomb potentials. Applied to hydrogenic systems, these corrections deliver improved energy accuracy and time fidelity across long evolutions. Beyond classical simulations, the proposed framework aligns naturally with quantum computing architectures, where the corrected operators and states can be encoded through truncated Walsh and Fourier series expansions. A resource analysis for the representative 2D hydrogen system yields a circuit depth of $1.5\times10^{8}$ gates over 6,000 Trotter steps. This study thus establishes practical strategies toward high-accuracy Coulombic dynamics on both classical and emerging quantum platforms.

We study morphisms between commutative $BV_\infty$ algebras and show that, under suitable additional assumptions, a quasi-isomorphism of commutative $BV_\infty$ algebras induces an identification of $\frac{\infty}{2}$-variations of Hodge structures with polarizations, and consequently of Frobenius manifolds. An explicit example arising from singularity theory is provided to illustrate the result.

Given a digraph $D$, we denote by $\vecα(D)$ the maximum size of an acyclic set of $D$ (i.e. a set of vertices which induces a subdigraph with no directed cycles), and by $\vecχ(D)$ the minimum number of acyclic sets into which $V(D)$ can be partitioned. In this paper, we study $\vecα(D)$ and $\vecχ(D)$ from various perspectives, including restrictions on degrees and cycle lengths. A main result is that, if $D$ is a random $r$-regular digon-free simple digraph of order $n$, then $\vecα(D) = Θ(n \log r /r)$ with high probability. This corresponds to a result of Spencer and Subramanian on the Erdős--Rényi random digraph model. Along the way, we derive some related results and propose some conjectures. An example of this is an analogue of the theorem of Bondy which bounds the chromatic number of a graph by the circumference of any strong orientation.

Self-Admitted Technical Debt (SATD) refers to technical compromises explicitly admitted by developers in natural language artifacts such as code comments, commit messages, and issue trackers. Among its types, Architecture Technical Debt (ATD) is particularly difficult to detect due to its abstract and context-dependent nature. Manual annotation of ATD is costly, time-consuming, and challenging to scale. This study focuses on reducing labeling effort in ATD detection by combining keyword-based filtering with active learning and explainable AI. We refined an existing dataset of 116 ATD-related Jira issues from prior work, producing 57 expert-validated items used to extract representative keywords. These were applied to identify over 103,000 candidate issues across ten open-source projects. To assess the reliability of this keyword-based filtering, we conducted a qualitative evaluation of a statistically representative sample of labeled issues. Building on this filtered dataset, we applied active learning with multiple query strategies to prioritize the most informative samples for annotation. Our results show that the Breaking Ties strategy consistently improves model performance, achieving the highest F1-score of 0.72 while reducing the annotation effort by 49\%. In order to enhance model transparency, we applied SHAP and LIME to explain the outcomes of automated ATD classification. Expert evaluation revealed that both LIME and SHAP provided reasonable explanations, with the usefulness of the explanations often depending on the relevance of the highlighted features. Notably, experts preferred LIME overall for its clarity and ease of use.

The two-dimensional spatial distribution of stellar specific angular momentum (sAM) within galaxies has never been previously analysed. We investigate its morpho-kinematics and its relation to total stellar sAM (jstar) and stellar mass (Mstar) for 30 spiral and irregular galaxies from the GHASP survey. We constructed high-resolution stellar sAM surface density (sAMSD) maps by combining 3.4 micron WISE photometry with Halpha velocity fields and HI rotation curves. Their structure was quantified using non-parametric morphological indicators (concentration, asymmetry, smoothness) plus two additional coefficients measuring similarity to an axisymmetric Freeman disc and the strength of bisymmetric substructures in sAMSD space. Each galaxy was assigned to one of five new morpho-kinematic classes based on its dominant sAMSD feature: jstar-ring, jstar-spiral, jstar-bar, jstar-clump, and jstar-irregular. This defines a classification scheme that combines directly morphology and dynamics. For 14 galaxies, the classical morphological type differs from the sAMSD-based category. As expected, jstar correlates strongly with Mstar. We also find correlations between jstar and star formation rate, and between jstar and total HI mass. The mean jstar and Mstar for the different jstar types occupy distinct regions along the Fall relation, with significant internal scatter. The link between the two-dimensional sAMSD distribution and global jstar, together with the location of each type in the jstar-Mstar plane, suggests a possible morpho-kinematic evolutionary sequence for late-type galaxies. The mechanisms reshaping galaxies in sAMSD space appear to be related to disc stability: in low-mass systems, angular momentum redistribution may arise from feedback, dynamical friction, shocks, and resonances, whereas in massive spirals it is likely driven by quasi-stationary rotating density waves.

Chaotic trajectories in multi-body dynamical systems play a crucial role in designing low-energy trajectories in astrodynamics. However, predicting these trajectories is inherently difficult, as small errors in initial conditions can grow exponentially, making long-term predictions unreliable. This study introduces a novel methodology using Dynamic Mode Decomposition (DMD) to predict chaotic transitions in the periapsis Poincaré map of the circular restricted three-body problem (CRTBP). Unlike standard DMD approaches that model continuous equations of motion, the proposed method approximates deformations in a low-dimensional Poincaré map, enabling trajectory prediction and revealing transition structures. Two approaches are developed: the Local Deformation Map-based DMD (LDMD) and the Global Deformation Map-based DMD (GDMD). LDMD constructs discrete maps to track local deformations of periapsis sets, while GDMD captures global deformations using widely distributed data. A key advantage of this framework is that it approximates nonlinear chaotic transport using a linear operator, which enables fast prediction of periapsis evolution via matrix powers and direct access to geometric structures. To validate the proposed method, the deformation map is applied to design ballistic transfer trajectories to the Moon using a targeting strategy, demonstrating its practical relevance in astrodynamics. This work highlights the potential of data-driven modeling to bridge chaotic dynamics with systematic trajectory design.

Two-dimensional (2D) superconductors provide a powerful building block for engineering emergent quantum states shaped by reduced dimensionality, enhanced quantum fluctuations, and interfacial symmetry breaking. In van der Waals heterostructures, atomically sharp and lattice-mismatch-free interfaces enable superconductivity to be deliberately coupled with magnetism, spin orbit interaction, and band topology, allowing collective electronic orders to be combined and reconfigured in ways unattainable in bulk materials. This Review summarizes recent advances in vdW heterostructures of 2D superconductors, focusing on superconductor/magnet, superconductor/topological material, and superconductor/superconductor junctions. We discuss the microscopic mechanisms underlying proximity effects and highlight how interfacial exchange fields, spin orbit coupling, and twist-controlled tunneling give rise to unconventional pairing, long-range spin-triplet supercurrents, nonreciprocal Josephson transport, and topological superconductivity potentially hosting Majorana bound states. Beyond their fundamental significance, the ability to controllably generate topological and nonreciprocal superconducting states positions 2D superconductor heterostructures as promising building blocks for emerging quantum technologies, including ultra-sensitive quantum sensing, programmable superconducting logic, and energy-efficient quantum and neuromorphic computing architectures. Looking forward, advances in materials synthesis, interface engineering, and device integration are expected to further expand the scope and functionality of 2D superconductor heterostructures, reinforcing their role as a central platform for exploring and controlling emergent quantum phases.

Constituent quark number scaling of elliptic flow has been proposed as one key observable to identify the phase transition or the absence of the Quark-Gluon Plasma (QGP) in heavy-ion collisions. At the fixed target program at RHIC the STAR collaboration has recently reported that NCQ scaling breaks when decreasing the collision energy from $\sqrt{s_\mathrm{NN}} = 4.5$ to $3.0$ GeV. However, the generation of elliptic flow is dominated by a highly intricate interplay of spectator shadowing, squeeze-out and geometry dependent hadron emission governed by their cross sections. Therefore in this article we will disentangle the shadowing contribution from the harmonic flow signal of the particle emitting source, effectively ``unshadowing'' the source. We introduce Fourier coefficients that quantify the azimuthal absorption rate of hadrons decoupling from the system. We benchmark the derived results using a toy model based on a ballistic Glauber description of the penetrating nuclei and calculate how shadowing qualitatively alters the constituent quark number scaling of the hadron emitting source. The results are thus relevant for interpreting recent STAR measurements as well as the upcoming measurements by CBM at FAIR.

Partial discharge originates from microscopic insulation imperfections in high-voltage apparatus and is widely considered a critical marker of incipient deterioration. Conventional partial discharge detection methods are typically constrained by limited bandwidth and often rely on predefined feature extraction, which impedes reliable recognition of broadband transient signals. In this work, we employ a Rydberg atomic sensor to directly capture time-domain responses of partial discharge emissions and construct distinctive spectral fingerprints for different types. A 1D ResNet deep learning model is then applied to recognize these fingerprints from time-domain signals without manual feature engineering. Under increased source-antenna distances, where spectral features are significantly attenuated, the model attains a recognition accuracy of approximately 94\% across four partial discharge categories, demonstrating robustness to attenuation and noise. We further validate the approach in a simulated early-warning scenario, where partial discharge signals mixed with noise are analyzed and the model successfully generates predictive alarms. These results underscore the potential of integrating Rydberg-based broadband sensing with data-driven analysis for non-invasive, high-sensitivity diagnostics of electrical insulation systems.

Most quantum communication networks around the world are used for a single task: quantum key distribution. In order to initiate the transition to multi-purpose quantum communication networks, we demonstrate the implementation of two different tasks on the same quantum key distribution hardware. Specifically, we focus on quantum oblivious transfer and quantum tokens. Our main contribution is to establish a methodology that greatly simplifies the expertise required to achieve the deployment, assess its performance, and evaluate its feasibility at a large scale. The implementation that we present is full-stack. It is based on a development framework that allows running user-defined applications both with simulated or real quantum communication backend. The hardware used for the implementation is VeriQloud's Qline. The simulation backend reproduces exactly the inputs and outputs of the real hardware, but also its losses and errors. It can therefore be used to validate the implementation before running it on the real hardware. The sources of the software that we use are fully open, making our research reproducible. The security of the implementations on real hardware are discussed with respect to security bounds previously known in the literature. We also discuss the engineering choices that we made in order to make the implementations feasible. By establishing a methodology to evaluate the performance and security of quantum communication protocols, we take a significant step towards industrializing and deploying large-scale, multi-purpose quantum communication networks.

This paper studies a one-dimensional Mean-Field Planning (MFP) system with a non-local, rank-based coupling. Using a potential formulation, we rewrite the system as an associated scalar partial differential equation. We prove an equivalence between classical solutions to the ranking MFP system with positive density and classical solutions to the associated potential problem, and we derive explicit reconstruction formulas. We then identify a monotonicity structure in the associated operator, which, under strict convexity assumptions, yields uniqueness of classical solutions to the associated problem and, hence, uniqueness of the ranking MFP system up to an additive constant in the value function. Finally, under superlinear growth assumptions, we exploit monotonicity to address existence in a low-regularity setting. By formulating a variational inequality for a q-Laplacian regularized operator, we apply Minty's method to establish the existence of weak solutions in the space of functions of bounded variation for a relaxed potential formulation.

We prove a parabolic analogue of Wolff's inequality adapted to the intrinsic scaling $δ_c(x,t)=(cx,c^2t)$ and formulated in terms of time-backward parabolic dyadic rectangles. As a consequence, we obtain equivalent characterizations of parabolic $(α,q)$-thinness in this geometric setting and establish the associated Kellogg and Choquet properties. We further use the notion of $(α,2)$-thinness defined in terms of fractional heat balls and prove that the sets of irregular boundary points $z_0\in\partialΩ$ for the heat operator $\partial_t-Δ$ and for the degenerate operator $\mathscr{L}a=\partial_t(|y|^a\cdot)-\operatorname{div}(|y|^a\nabla\cdot)$ in $Ω\subset\mathbb{R}^{d+1}$ are negligible with respect to the thermal capacity $\mathrm{cap}^{\mathcal T}$ and the parabolic Bessel capacity $C_{α,2}$, respectively.

Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a single delay time in the coupling term, for which exact anticipation can arise as a solution. Here we extend this framework to configurations with distributed delay times. Our main result is that, for a given delay distribution, approximate anticipated synchronisation can emerge over a range of coupling strengths. We analyse this phenomenon analytically for systems of linear oscillators, where we identify simple cases exhibiting exact synchronisation--up to a constant amplitude factor. Numerical simulations of nonlinear chaotic systems reveal stable forms of approximate anticipated synchronisation.

We present first results for triply polarized $WWW$ events at the LHC. The calculation is performed at leading order for fully leptonic decays using the Standard Model. Employing an inclusive kinematic cut setup, we found that the triply-transverse polarization fraction is about $51\%$, while the triply-longitudinal (LLL) fraction is smallest with $1.4\%$ for the $W^-W^+W^+$ process. The interference between different polarization amplitudes amounts to $+1.8\%$. Results for the $W^+W^-W^-$ case are similar. Based on known higher-order results for the diboson processes, radiative corrections are not expected to increase the LLL fraction to the level of tens of percent. This means that measuring the LLL cross section at the LHC will be very challenging. A new on-shell mapping for triboson processes, being a crucial element of polarized cross-section calculation, is also presented.

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply one-point-quadrature to the terms in the discrete equations. The resulting system coincides with the commonly used meshfree discretization using a regular lattice, including the possibility of using partial area algorithms to improve the numerical behavior. We again prove convergence, this time for fixed choices of a weighting function commonly used in literature and stronger assumptions on the input data. We note however, that these assumptions are not significantly restrictive for practical purposes. In particular, they still allow discontinuities in the material parameters and external body forces.

We perform numerical simulations to investigate high-power wind accretion in massive binary systems undergoing enhanced mass-loss episodes. The primary star is taken in the mass range $M_{1} = 60$--$90\,\mathrm{M_{\odot}}$, while the companion is a $30\,\mathrm{M_{\odot}}$ hot star. We model binary orbits with eccentricities of $e = 0$--$0.6$ and orbital periods of $P=455$--$1155$ days. We initiate strong eruptive events for the primary with mass-loss rates of $\dot{M}_{\rm w} = 10^{-2}$ -- $10^{-1}\,\rm{M_{\odot}~{yr}^{-1}}$, lasting for $1.5$ years. A fraction of the ejected wind material is accreted by the companion, with the accretion efficiency determined by the orbital separation, eccentricity, and stellar mass ratio. We analyze the resulting accretion rates and provide an analytical relation describing their dependence on the stellar mass ratio, mass-loss rate, and orbital parameters. We find that although the accretion modifies the stellar parameters of the secondary, the companion remains in thermal equilibrium and does not undergo significant radial expansion. We further include wind mass loss from the companion during wind accretion and find a substantial reduction in accretion efficiency compared to no wind scenario. For longer orbital periods, the models yield negative accretion rates, implying that any captured material is expelled or prevented from settling onto the accretor. These results provide new insight into the role of eccentric orbits and extreme mass-loss events in shaping the mass-transfer processes in massive binaries.

Building speech deepfake detection models that are generalizable to unseen attacks remains a challenging problem. Although the field has shifted toward a pre-training and fine-tuning paradigm using speech foundation models, most approaches rely solely on supervised fine-tuning (SFT). Inspired by the field of large language models, wherein reinforcement learning (RL) is used for model fine-tuning, we investigate the impact of RL, specifically Group Relative Policy Optimization (GRPO). The results from experiments using multiple detectors and test sets indicate that pure GRPO-based fine-tuning improves performance on out-of-domain test sets while maintaining performance on target-domain test data. This approach outperforms both SFT-only and hybrid setups. Our ablation studies further suggest that the negative reward in GRPO may be a key factor in this improvement.

Proof Theory and Type Theory are two branches of mathematical logic and theoretical computer science that explore the structure of mathematical proofs and the foundations of computation. Both are crucial for understanding formal systems, programming languages, and constructive mathematics. Stefano Berardi is an influential researcher in these fields, particularly known for his work on constructive logic, dependent types, and more recently, cyclic proofs. These proceedings intend to collect papers by researchers who are active in the field and often have been coauthors of Stefano, aimed to illustrate the achievements and the perspectives of this research area.

Previously, a novel type of rubrene microcrystals was reported, forming two distinct sectors -- diamond- and triangular-shaped -- that exhibit pronounced contrasts in photoluminescence (PL) spectra and exciton dynamics. In the present work, their internal electronic structure is investigated using time-of-flight photoemission electron spectroscopy (TOF-PES), revealing that the two sector's different charging characteristics arising from anisotropic conductivities. Upon photoemission via a one-photon photoemission (1PPE) process excited by 6.2 eV (200 nm) photons, the diamond-shaped sectors accumulate significant charge, whereas the triangular sectors remain essentially uncharged. The charge accumulation in the diamond sectors can be neutralized by additional sub-threshold illumination, which generates charge carriers through internal photoeffect. The dynamics and energetics of the observed band shifting is described quantitatively by a model combining surface capacitance and drift-diffusion. These crystalline systems enable the creation of built-in charge landscapes that can be manipulated both spatially and temporally.

We develop the direct scattering theory for the KdV equation with step-like finite-gap backgrounds under perturbations. More precisely, we consider initial data that asymptotically approach two distinct one-gap periodic travelling wave solutions as \(x \to \pm \infty\). Under suitable assumptions on the perturbation, we formulate the direct scattering problem and establish the analytic structure of the associated scattering data. In particular, we reformulate the problem in terms of a vector Riemann--Hilbert problem, which provides a foundation for the study of long-time asymptotics of perturbed finite-gap potentials. This formulation highlights the connection between step-like finite-gap scattering theory and the Riemann--Hilbert framework arising in soliton-gas type settings.

ω Centauri, the remnant nucleus of an accreted dwarf galaxy, is a unique laboratory for studying complex stellar populations. The recently discovered Fimbulthul stream provides a fossil record of its ongoing tidal dissolution. In this work, we investigate the spatial distributions of metal-rich and metal-poor populations within ω Centauri and its stream to constrain the cluster's formation history. Using synthetic photometry from Gaia DR3 XP spectra, we classify stars via a Support Vector Classifier (SVC). The spatial distributions are then compared to a scaling N-body simulation performed with the PeTar code. Our analysis reveals no significant radial gradient in population ratios within the cluster, though the metal-rich stars may be slightly more extended. The population ratio in the tidal stream is consistent with that of the present-day cluster, albeit with large uncertainties. Our simulation indicates that any initial radial gradient must have been shallow, with a maximum fraction difference less than 0.15. Both observational and dynamical results suggest that the metal-rich population is not formed centrally concentrated. By combining our results and existing literature, we propose a new formation scenario for ω Centauri.

Superposition of orthogonal Hermite Gaussian (HG) modes in orthogonal linear polarization states is one of the techniques used for the experimental realization of lower order optical vector beams and vector vortex lattices. To date, it has been widely believed that the vector nature arising from this technique originates from the spatial intensity distribution of the superposed HG modes. Here, we report that the vector characteristics observed during the characterization of vector modes generated via HG mode superposition arise from the azimuthally inhomogeneous intensity distribution and the polarization-dependent Pancharatnam Berry (PB) phase. Our analytical calculations confirm that the vector nature is not inherently present in the superposition state; rather, it becomes observable due to polarization-based optical elements used in the characterization process. This insight provides a fundamental clarification of the physical origin of the experimentally observed vector nature in HG-mode superposition.

This project successfully developed, evaluated and integrated a Voice User Interface (VUI) into a web application that we are developing for immersive molecular graphics. Said app provides augmented and virtual reality (AR and VR) environments where users manipulate molecules with their hands, but this means the hands can't be used to control the app through a regular mouse- and keyboard-based GUI. The speech-based VUI system developed here alleviates this problem, making it easy to control the app via natural spoken (or typed) commands. To achieve this VUI we evaluated two distinct Automated Speech Recognition (ASR) systems: Chrome's native Speech API and OpenAI's Whisper v3. While Whisper offered broader browser compatibility, its tendency to "hallucinate" with specialized scientific jargon proved very problematic. Consequently, we selected Chrome's ASR for its stability, speed, and reliability. For translating transcribed speech into software commands, we tested two Large Language Model (LLM)-driven approaches: either generating executable code, or calling predefined functions. The function call method, powered by OpenAI's GPT-4o-mini, was ultimately adopted due to its superior safety, efficiency, and reliability over the more complex and error-prone code-generation approach. The resulting VUI is then based on an integration of Chrome's ASR with our LLM-based function-calling module, enabling users to command the application using natural language as shown in a video linked inside this report. We provide links to live examples demonstrating all the intermediate components, and details on how we crafted the LLM's prompt in order to teach it the function calls as well as ways to clean up the transcribed speech and to explain itself while generating function calls. For best demonstration of the final system, we provide a video example.

We reformulate the problem of finding conformal immersions of closed Riemannian surfaces in the language of the $h$-principle and we prove that the inclusion from the space of smooth conformal immersions to the space of immersions induces a bijection on the sets of path connected components.

Range-based volatility estimators are widely used in financial econometrics to quantify risk and market stress, yet their application to local commodity markets remains limited. This paper shows how open-high--low-close (OHLC) volatility estimators can be adapted to monitor localized market distress across diverse development contexts, including conflict-affected settings, climate-exposed regions, remote and thinly traded markets, and import- and logistics-constrained urban hubs. Using monthly food price data from the World Bank's Real-Time Prices dataset, several volatility measures -- including the Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang estimators -- are constructed and evaluated against independently documented disruption timelines. Across settings, elevated volatility aligns with episodes linked to insecurity and market fragmentation, extreme weather and disaster shocks, policy and fuel-cost adjustments, and global supply-chain and trade disruptions. Volatility also detects stress that standard momentum indicators such as the relative strength index (RSI) can miss, including symmetric or rapidly reversing shocks in which offsetting supply and demand disturbances dampen net directional price movements while amplifying intra-period dispersion. Overall, OHLC-based volatility indicators provide a robust and interpretable signal of market disruptions and complement price-level monitoring for applications spanning financial risk, humanitarian early warning, and trade.