Spectrally stable cascades can undergo enormous transient growth before eventually dying out. We show that this amplification is controlled by the directed architecture of the interactions, independently of the eigenvalues that determine asymptotic stability. More remarkably, when several critical subsystems are connected sequentially, their depth becomes a new control parameter for critical fluctuations: each additional critical stage generates a new cascade-size exponent, producing an infinite hierarchy of universality classes. This result follows because the fluctuating population produced at one stage becomes the random input to the next. The mechanism persists for both finite-variance and heavy-tailed reproduction and strongly enhances the probability of rare terminal events. Applied to multitype earthquake triggering, it provides a stationary mechanism for the anomalously large abundance of foreshock-mainshock sequences. Directed architecture can therefore control both transient amplification and critical statistics in cascade processes even when it leaves spectral stability unchanged.

Earthquake triggering is conventionally characterised by a scalar ETAS branching ratio. We develop a three-type Hawkes-ETAS model that resolves strike-slip, normal, and reverse/thrust earthquakes through a directed branching matrix N. While the spectral radius ρ(N)<1 controls asymptotic stability, its eigenvector geometry controls finite-generation dynamics. Asymmetric cross-mechanism pathways can render N non-normal, producing large transient and cumulative cascade responses in a strictly subcritical process. We motivate this geometry from receiver-fault availability, Coulomb stress projection, mechanism-dependent magnitude distributions, tectonic loading, and near-degenerate self-triggering. A physically reduced parametrisation separates diagonal self-triggering, a dominant tectonic driver column, and weaker secondary couplings. Numerical examples show that cascade amplification can increase strongly while the eigenvalues remain fixed. Five tectonically informed scenario matrices illustrate plausible geometries. The theory produces six falsifiable predictions for mechanism-resolved catalogues and identifies how scalar ETAS fits may absorb multitype amplification into an apparently elevated branching ratio.

Early-warning indicators in ecosystems, neural activity, financial markets, and climate systems are often interpreted as evidence that a system is approaching a tipping point, typically understood as a bifurcation at which a previously stable state loses stability or disappears. Such indicators include increased variance, autocorrelation, and dimensional reduction. Here we identify a different mechanism that generates the same statistical signatures without any loss of stability. In stochastic non-normal dynamical systems, asymmetric interactions produce transient amplification that creates episodes of apparent instability despite the persistence of a stable attractor. We refer to these episodes as pseudo-bifurcations. Through analytical results, numerical simulations, and empirical evidence from brain dynamics during epileptic seizures, we show that pseudo-bifurcations reproduce the canonical early-warning signals commonly associated with bifurcation-induced tipping points. Crucially, these signatures arise while the underlying system remains dynamically stable and far from any bifurcation. These results demonstrate that widely used early-warning indicators are not uniquely diagnostic of tipping points. Instead, they may reflect the transient geometry of non-normal dynamics, which are ubiquitous in complex interacting systems. Early-warning indicators such as increased variance, autocorrelation, and dimensional reduction are often interpreted as signs that complex systems in ecology, neuroscience, finance, or climate are approaching a tipping point at which a stable state loses stability or disappears. Here, the authors demonstrate, using brain dynamics during epileptic seizures as an example case, that the same statistical signatures can arise from pseudo-bifurcations in stochastic non-normal systems, showing that these widely used indicators are not uniquely diagnostic of tipping points.

Heavy-tailed fluctuations and power law distributions pervade physics, biology, and the social sciences, with numerous mechanisms proposed for their emergence. Kesten processes, which are multiplicative stochastic recursions with additive noise or reinjection, provide a canonical explanation, where power law tails arise from transient supercritical excursions as eigenvalues intermittently cross the stability boundary. Here we uncover a distinct and more general mechanism in multidimensional systems: non-normal eigenvector amplification. In random non-normal matrices, the non-orthogonality of eigenvectors, quantified at each time step by the condition number κ_t in Kesten-like processes, induces transient growth that increases the effective Lyapunov exponent γ→ γ+ 𝔼[ln κ_t ] and lowers the tail exponent α≃ -2γ/ σ_κ^2, where 𝔼[ln κ_t ] and σ_κ^2 are respectively the mean and variance of ln κ_t. As the system dimension N grows, κ typically increases proportionally, making non-normal amplification the dominant source of scale-free behavior. We illustrate this mechanism in polymer stretching in turbulent flows, where intermittent extensions arise from eigenvector amplification of velocity gradients.

Epistemic uncertainty in probabilistic seismic hazard assessment (PSHA) is commonly addressed through a logic-tree framework that combines weighted alternative models to characterize the range of plausible hazard outcomes. Implicit in this approach is a critical assumption: that the available model class provides an adequate representation of the underlying physics governing fault networks. Yet current formulations remain highly simplified, neglecting nonlinear interactions, diverse fault slip modes, multi-scale coupling, and the emergent dynamics that govern the nucleation and evolution of large earthquakes. As a result, the standard treatment of epistemic uncertainty may introduce systematic hazard bias and substantially underestimate forecast uncertainty. To formalize this limitation, we introduce SHARP (Seismic Hazard Assessment and Risks with Physics), a new framework that shifts the focus from selecting among imperfect models to quantifying their collective distance from physical and observational constraints. Central to SHARP is the Model Adequacy Distance (MAD), a quantitative metric of model inadequacy. MAD combines (i) a moment-weighted scoring function scaling with seismic moment to reflect the disproportionate social and economic impact of large events and (ii) compatibility measures derived from geodetic observations and statistical properties of seismicity. We illustrate the approach with an application to the frequency-magnitude distribution of Southern California seismicity. SHARP establishes a rigorous foundation for moving beyond conventional epistemic uncertainty toward a physics-grounded framework for seismic hazard and risk assessment.

Many catastrophic events, including landslides, rockbursts, glacier breakoffs, and volcanic eruptions, are preceded by an observable acceleration phase that offers a critical window for early warning and hazard mitigation; however, the duration of this precursory phase remains poorly constrained across sites, scales, and hazard types. This limitation arises because the onset of acceleration is often identified using heuristic thresholds or empirical criteria. Here, we introduce a physics-based framework that objectively constrains the precursory duration from accelerating dynamics, without prescribing the onset a priori or being tied to any specific observable. We analyse a global dataset of 109 geohazard events across seven continents over the past century, quantifying their precursory durations in a consistent manner. For mechanically driven instabilities, we identify a robust scaling between precursory duration and failure volume spanning more than ten orders of magnitude. When expressed in terms of a characteristic system size, this relationship is close to linear, consistent with finite-size scaling near a dynamical critical point. This behaviour indicates that precursory duration reflects the progressive growth of correlated deformation up to system-spanning scales, rather than local rupture kinetics. The resulting universality points to common organising mechanisms governing the approach to catastrophic failure across mechanically driven geohazards.

Genuinely critical dynamics have been proposed to organize many natural and social systems, yet exact criticality is usually thought to preclude stationarity because the mean activity diverges. I show that this conclusion is not generally valid for self-exciting Hawkes point processes. At criticality, stationarity in law is controlled not by the mean intensity, but by local finiteness of the infinite-past Poisson-cluster construction. The relevant object is the fixed-window hitting probability H_T(u), the probability that a cluster born at time -u contributes at least one event to a window of length T. For memory tails ℙ(T>t)∼ t^-θ and fertility tails ℙ(κ>x)∼ x^-γ, I prove stationarity for 1<γ<2 and θ>γ via a finite-mean-lifetime criterion. In the finite-memory, finite-variance regime, H_T(u) is asymptotically comparable to the cluster-survival probability, and the exact local-finiteness condition fails. A direct asymptotic analysis of H_T gives the sharper condition θ>γ-1 for stationarity to hold in the infinite-fertility-variance regime. Thus broad fertility fluctuations can stabilize critical Hawkes dynamics in law, producing locally finite stationary sample paths despite infinite mean activity.

Abstract. Landslide early warning remains challenging because many slopes evolve through intermittent, nonlinear, and non-monotonic deformation before catastrophic failure. Here, we develop an integrated early warning framework that combines three statistical physics-based diagnostics: velocity b-value tracking, dragon-king detection, and log-periodic power law singularity (LPPLS) time-to-failure analysis. The velocity b-value captures long-term changes in the distribution of slope displacement rates, dragon-king detection identifies statistically significant extreme velocity outliers, and LPPLS analysis describes the quasi-deterministic evolution towards a finite-time singularity yielding probabilistic estimates of the failure time and its uncertainty. Applied pseudo-prospectively to the Preonzo, Veslemannen, and Stampa landslides, the framework reveals a coherent sequence of precursory signals: b-value decline generally appears first, dragon-king outliers emerge later as failure becomes imminent, and LPPLS forecasts become increasingly constrained during the final acceleration stage. These complementary indicators are integrated into a traffic-light warning scheme that translates complex rupture dynamics into operationally interpretable warning levels. By combining precursory signals across multiple timescales, the proposed framework establishes a robust and physically grounded foundation for next-generation landslide early warning.

We develop a discrete-event modeling framework that captures the progression of geophysical systems toward catastrophic failure through sequences of distinct damage events. By representing system evolution as a succession of temporally accelerating and amplitude-varying events, the framework reveals how finite-time singularities, both logarithmic and power law types, naturally emerge from the interplay between shrinking interevent intervals and growing event magnitudes. This event-based perspective provides an intuitive physical understanding of rupture processes, highlighting how precursory signals such as accelerating strain rate, event frequency, and energy release can be traced back to simple underlying mechanisms. A mean-field formulation further links the observed power law exponents to the evolving stiffness of the system under constant or time-varying stress. Incorporating stochastic fluctuations, the model captures the inherent randomness of natural systems leading to the emergence of stochastic finite-time singular behavior. Altogether, this unified approach offers a simple conceptual and quantitative tool for interpreting the lead-up to failure in a wide range of geophysical settings.

Large-scale hazards affect societies not only through direct physical impacts but also through emotions that spread across populations. Fueled by social amplification and networked communication, collective emotions often diverge markedly from underlying physical threats, pressuring policymakers toward suboptimal decisions that erode long-term societal resilience and misalign risk governance priorities. Yet when exactly these collective emotions mirror hazard severity and when they are warped by social dynamics remains poorly understood. We introduce a compact, interpretable model that couples hazard exposure with networked emotional contagion and identifies the transition from proportionate responses to an amplification regime sustained by negativity bias. Applying this framework to the COVID-19 pandemic in the United States, we integrate state-level epidemiological data with large-scale stress signals inferred from Twitter/X activity. Our analysis shows that social influence outweighed direct hazard forcing in over 80% of U.S. states during the study period, and that amplified stress covaries with major economic indices. These findings reveal a measurable regularity in societal hazard response, enabling quantitative anticipation of collective emotional tipping points and supporting community resilience under large-scale hazards.

Recent reports of large language models (LLMs) exhibiting behaviors such as deception, threats, or blackmail are often interpreted as evidence of alignment failure or emergent malign agency. We argue that this interpretation rests on a conceptual error. LLMs do not reason morally; they statistically internalize the record of human social interaction, including laws, contracts, negotiations, conflicts, and coercive arrangements. Behaviors commonly labeled as unethical or anomalous are therefore better understood as structural generalizations of interaction regimes that arise under extreme asymmetries of power, information, or constraint. Drawing on relational models theory, we show that practices such as blackmail are not categorical deviations from normal social behavior, but limiting cases within the same continuum that includes market pricing, authority relations, and ultimatum bargaining. The surprise elicited by such outputs reflects an anthropomorphic expectation that intelligence should reproduce only socially sanctioned behavior, rather than the full statistical landscape of behaviors humans themselves enact. Because human morality is plural, context-dependent, and historically contingent, the notion of a universally moral artificial intelligence is ill-defined. We therefore reframe concerns about artificial general intelligence (AGI). The primary risk is not adversarial intent, but AGI's role as an endogenous amplifier of human intelligence, power, and contradiction. By eliminating longstanding cognitive and institutional frictions, AGI compresses timescales and removes the historical margin of error that has allowed inconsistent values and governance regimes to persist without collapse. Alignment failure is thus structural, not accidental, and requires governance approaches that address amplification, complexity, and regime stability rather than model-level intent alone.

Campi Flegrei, a large caldera in southern Italy, is among the most hazardous volcanic systems on Earth, directly threatening over one million people. Since 2005, it has entered a phase of accelerating uplift accompanied by intensified seismicity, raising the key question of whether this evolution will culminate in eruption, a bradyseismic peak, or another regime change. Here, we show that the acceleration of seismicity and geodetic deformation is better described by a regularised finite-time singularity than by exponential growth, implying not just a better empirical representation but a different underlying process with potentially dire consequences for the system's subsequent evolution. Independent analyses converge on a critical time t_c ≈ 2030-2034, with uplift projected to reach about 4 metres by the early 2030s. Geochemical and statistical evidence indicates that deep magmatic volatile input drives this evolution by progressively pressurising the crust. Although no evidence of imminent eruption is found, the system appears to be approaching a critical mechanical threshold whose outcome remains uncertain, requiring sustained high-resolution monitoring and continuously updated forecasts.

Complex-systems science provides media institutions with a rigorous framework to move from reactive reporting to anticipatory diagnosis. Critical events are understood as regime shifts emerging from the interplay between endogenous dynamics and exogenous shocks. Detecting such transitions requires identifying structured precursors, such as changes in correlations, amplification, persistence, and endogeneity, rather than relying on raw signal intensity. Recognizing dragon-king events as regime-generated outliers and incorporating non-normal transient amplification are essential, as is accounting for organizational concealment of risk. A geopolitical crisis observatory would diagnose when systems enter states of heightened susceptibility to cascading disruptions. While state actors are already developing such observatories for strategic purposes, media institutions remain largely reactive. This gap creates a strategic opportunity: leveraging open data and AI embedded within the complex-systems framework developed above, media organizations could transform journalism from reporting to diagnosis, delivering early-warning indicators, scenario-based risk maps, and transparent, data-driven narratives within a new Geopolitical Risk Intelligence Platform.

Heavy-tailed fluctuations and power law statistics pervade physics, finance, and economics, yet their origin is often ascribed to systems poised near criticality. Here we show that such behavior can emerge far from instability through a universal mechanism of non-normal eigenvector amplification in multidimensional Kesten processes x_t+1=A_t x_t+η_t, where A_t are random interaction matrices and η_t represents external inputs, capturing the evolving interdependence among N coupled components. Even when each random multiplicative matrix is spectrally stable, non-orthogonal eigenvectors generate transient growth that renormalizes the Lyapunov exponent and lowers the tail exponent, producing stationary power laws without eigenvalues crossing the stability boundary. We derive explicit relations linking the Lyapunov exponent and the tail index to the statistics of the condition number, γ∼γ_0+ and α∼-2γ/σ_κ^2, confirmed by numerical simulations. This framework offers a unifying geometric perspective that help interpret diverse phenomena, including polymer stretching in turbulence, magnetic field amplification in dynamos, volatility clustering and wealth inequality in financial systems. Non-normal interactions provide a collective route to scale-free behavior in globally stable systems, defining a new universality class where multiplicative feedback and transient amplification generate critical-like statistics without spectral criticality.

Quantifying influence in networks is important across science, economics, and public health, yet widely used centrality measures remain limited: they rely on static representations, heuristic network constructions, and purely endogenous notions of importance, while offering little semantic connection to observable activity. We introduce HawkesRank, a dynamic framework grounded in multivariate Hawkes point processes that models exogenous drivers (intrinsic contributions) and endogenous amplification (self- and cross-excitation). This yields a principled, empirically calibrated, and adaptive importance measure. Classical indices such as Katz centrality and PageRank emerge as mean-field limits of the framework, clarifying both their validity and their limitations. Unlike static averages, HawkesRank measures importance through instantaneous event intensities, enabling prediction, transparent endo-exo decomposition, and adaptability to shocks. Using both simulations and empirical analysis of emotion dynamics in online communication platforms, we show that HawkesRank closely tracks system activity and consistently outperforms static centrality metrics.

Earthquakes resist deterministic prediction, yet their occurrence is not fully random. This paper develops a unified information-theoretic framework to quantify predictability. By reviewing Shannon entropy and the Kullback-Leibler divergence, we formalize predictability as the entropy gap between complete randomness and the true data-generating process and clarify how this absolute notion relates to the relative skill gains used in prospective model evaluation. Within the point-process setting, we derive entropy rates for the Poisson process and for ETAS and identify the intrinsic predictability rate as an information gain functional of the conditional intensity. Using this lens, we summarize what is currently established about earthquake predictability in time, space, and magnitude: temporal and spatial predictability are dominated by clustering and heterogeneous background rates, while magnitude predictability requires separating marginal magnitude statistics (e.g., Gutenberg-Richter and tapered laws) from genuine inter-event dependence encoded by the multivariate magnitude distribution. Finally, we show how incorporating high-dimensional pre-event observations can increase predictability through mutual information, thereby reframing forecasting progress as the extraction of structured dependence between available information and future seismicity. This perspective provides a coherent basis for assessing predictability limits, comparing models, and identifying where additional information and physics that are most likely to yield substantive forecasting improvements.

We develop a dissipation-based framework for earthquake rupture on homogeneous faults that explicitly separates the onset of unstable slip from the conditions required for self-sustained rupture propagation. This distinction explains the coexistence of self-arresting earthquakes and run-away ruptures (subshear and supershear events) observed in numerical simulations and empirical studies. We identify two distinct characteristic fault sizes: a nucleation radius controlling the instability of slip, and in general a larger propagation radius controlling whether an unstable rupture can be energetically sustained. Ruptures initiated above the nucleation scale but below the propagation scale spontaneously arrest. We further derive the Gutenberg-Richter law for self-arresting earthquakes by linking rupture physics to the fractal geometry of faulting. Finally, we interpret run-away ruptures as extreme events generated by an amplifying mechanism, consistent with the dragon-king concept. These results provide a unified physical basis for earthquake initiation, arrest, and seismicity statistics.

A growing share of human interactions now occurs online, where the expression and perception of emotions are often amplified and distorted. Yet, the interplay between different emotions and the extent to which they are driven by external stimuli or social feedback remains poorly understood. We calibrate a multivariate Hawkes self-exciting point process to model the temporal expression of six basic emotions in YouTube Live chats. This framework captures both temporal and cross-emotional dependencies while allowing us to disentangle the influence of video content (exogenous) from peer interactions (endogenous). We find that emotional expressions are up to four times more strongly driven by peer interaction than by video content. Positivity is more contagious, spreading three times more readily, whereas negativity is more memorable, lingering nearly twice as long. Moreover, we observe asymmetric cross-excitation, with negative emotions frequently triggering positive ones, a pattern consistent with trolling dynamics, but not the reverse. These findings highlight the central role of social interaction in shaping emotional dynamics online and the risks of emotional manipulation as human-chatbot interactions become increasingly realistic.

In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, which is characterized by smooth behavior of key quantities; and the critical region, where these quantities exhibit singularities or strong fluctuations. Due to their starkly different properties, those regions are often perceived as being weakly related, if ever. However, here, we demonstrate that these regions are intimately connected, specifically showing how they have a relationship that can be explicitly revealed using self-similar approximation theory. The framework considered enables the prediction of observable quantities near the critical point based on information from the regular region, and vice versa. Remarkably, the method relies solely on asymptotic expansions with respect to a parameter, regardless of whether the expansion originates in the regular or critical region. The mathematical principles of self-similar theory remain consistent across both cases. We illustrate this consistency by extrapolating from the regular region to predict the existence, location, and critical indices of a critical point of an equation of state for a statistical system, even when no direct information about the critical region is available. Conversely, we explore extrapolation from the critical to the regular region in systems with discrete scale invariance, where log-periodic oscillations in observables introduce additional complexity. The findings provide insights and solutions applicable to diverse phenomena, including material fracture, stock market crashes, and earthquake forecasting.