arXiv subjects

Didier Sornette

Publications and source records attributed to Didier Sornette.

At least 19 recordsLinked to original sources

arXiv2026

Axial Seamount Eruption Forecasting Experiment

We introduce the Axial Seamount Eruption Forecasting Experiment (EFE), a real-time initiative designed to test the predictability of volcanic eruptions through a transparent, physics-based framework. The experiment is inspired by the Financial Bubble Experiment, adapting its principles of digital authentication, timestamped archiving, and delayed disclosure to the field of volcanology. The EFE implements a reproducible protocol in which each forecast is securely timestamped and cryptographically hashed (SHA-256) before being made public. The corresponding forecast documents, containing detailed diagnostics and probabilistic analyses, will be released after the next eruption or, if the forecasts are proven incorrect, at a later date. This procedure ensures full transparency while preventing premature interpretation or controversy surrounding public predictions. Forecasts will be issued monthly, or more frequently if required, using real-time monitoring data from the Ocean Observatories Initiative's Regional Cabled Array at Axial Seamount. By committing to publish all forecasts, successful or not, the EFE establishes a scientifically rigorous, falsifiable protocol to evaluate the limits of eruption forecasting. The ultimate goal is to transform eruption prediction into a cumulative and testable science founded on open verification, reproducibility, and physical understanding.

physics.geo-ph↗

arXiv2026

Directed Cascades Generate New Critical Universality Classes

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.

physics.gen-ph↗

arXiv2026

How to quantify earthquake predictability? Advances in earthquake forecasting and predictability limits

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.

physics.geo-ph↗

arXiv2026

Non-normal amplification in multitype Hawkes-ETAS models of earthquake triggering

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.

physics.geo-ph↗

arXiv2026

Haicheng and Tangshan Earthquakes as potential Dragon-Kings

The dragon-king earthquake hypothesis proposes that some very large to great earthquakes are not merely the extreme end of the frequency-magnitude Gutenberg-Richter distribution (FMD), but are generated by distinct physical mechanisms, making them statistical outliers. We develop a data-driven framework to systematically test the dragon-king earthquake hypothesis. Our method combines objective spatial clustering, based on data-adaptive kernel density estimation (KDE), with a high-power sequential outlier detection technique. For each identified cluster, we exam sine the tail of the FMD to identify anomalous events. Candidate dragon-kings are evaluated via robust statistical tests, primarily the max-robust-sum (MRS) test with inward sequential testing. For each observed statistic of the MRS test, we calculate its p-value defined as the probability that this statistic could be generated by the null distribution. We apply this framework to seismicity surrounding the 1975 Haicheng mL 7.4 and 1976 Tangshan mL 7.9 earthquakes. For Haicheng, the mainshock shows a strong dragon-king signature in its pre-mainshock sequence, with p-values between 0.03 and 0.07 across a stable range of KDE density thresholds used to define natural seismicity clusters. Post-mainshock and combined sequences yield slightly higher p-values (up to 0.09). In contrast, the Tangshan mainshock exhibits a weaker outlier signal before the event (p-values in the range 0.05-0.15) but a stronger dragon-king signature afterward, with p-values from 0.015 to 0.05. The evidence that the Haicheng and Tangshan mainshocks exhibit dragon-king characteristics supports the idea that some large and great earthquakes arise from a maturation process that may enhance predictability. Haicheng provides a clear case study, while retrospective analyses suggest that Tangshan might also have been forecasted under more systematic procedures.

physics.geo-ph↗

arXiv2026

Toward a Geopolitical Crisis Observatory: Diagnosing Systemic Risk in News Flows Using Complex Systems Science

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.

physics.soc-ph↗

arXiv2026

Critical Hawkes Processes with Random Fertilities: Stationarity in Law Beyond Infinite Mean Activity

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 $\mathbb{P}(T>t)\sim t^{-θ}$ and fertility tails $\mathbb{P}(κ>x)\sim x^{-γ}$, 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.

physics.gen-ph↗

arXiv2026

Accelerating unrest at Campi Flegrei signals a critical transition within the next decade

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 $t_c \approx 2030-2034$, 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.

physics.geo-ph↗

arXiv2026

Social Amplification Dominates Collective Hazard Response

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.

physics.soc-ph↗

arXiv2026

Primary creep encodes time to failure across laboratory and natural systems

Geomaterials often exhibit progressive creep characterized by an initial decelerating phase, frequently followed by an extended period of approximately constant deformation rate, and ultimately an accelerating regime leading to catastrophic failure. Despite extensive research, the timing of rupture and its relationship to the different creep phases, particularly in natural systems, remain poorly constrained. Here, we compile creep data from laboratory experiments on rocks, composites, papers, and glasses, together with observations from field systems including landslides, rockfalls, and glaciers. We find that the duration of the early-stage creep, marked by the transition to the minimum (or quasi-stationary) deformation rate, correlates nearly linearly with the time to rupture over five orders of magnitude. This unified scaling highlights that the early-time dynamics reflect the full evolution toward failure, providing a simple and robust framework for forecasting rupture across laboratory and natural systems.

physics.geo-ph↗

arXiv2026

HawkesRank: Event-Driven Centrality for Real-Time Importance Ranking

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.

cs.SI↗

arXiv2026

Universal scaling between precursory duration and event size across mechanically driven geohazards

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 analyze 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 behavior 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 organizing mechanisms governing the approach to catastrophic failure across mechanically driven geohazards.

physics.geo-ph↗

arXiv2026

Physics-Based Seismic Hazard and Risk Assessment: A New Paradigm for Earthquake Forecasting

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.

physics.geo-ph↗

arXiv2026

Design and Implementation of a 25-Year Pseudo-Prospective Earthquake Forecasting Experiment in China (AoyuX)

Forecast models in statistical seismology are commonly evaluated with log-likelihood scores of the full distribution P(n) of earthquake numbers, yet heavy tails and out-of-range observations can bias model ranking. We develop a tail-aware evaluation framework that estimates cell-wise P(n) using adaptive Gaussian kernel density estimation and tests three strategies for handling out-of-range counts. Using the AoyuX platform, we perform a ~25-year month-by-month pseudo-prospective forecast experiment in the China Seismic Experimental Site (CSES), comparing Epidemic-Type Aftershock Sequence (ETAS) model with a homogeneous background (ETASμ) to a spatially heterogeneous variant (ETASμ(x,y)) across six spatial resolutions and five magnitude thresholds. Empirical probability density functions (PDFs) of counts per cell are well described by power laws with exponents a = 1.40 +- 0.21 across all settings. Using previous theoretical results, this provides a robust estimate of the productivity exponent, α = 0.57 +- 0.08 using a b-value equal to 0.8, providing a valuable quantification of this key parameter in aftershock modeling. Model ranking is sensitive to how the tail of the full distribution P(n) of earthquake counts is treated: power law extrapolation is both theoretically justified and empirically the most robust. Cumulative information gain (CIG) shows that ETASμ(x,y) outperforms ETASμ in data-rich configurations, whereas in data-poor settings stochastic fluctuations dominate. A coefficient-of-variation analysis of per-window log-likelihood differences distinguishes genuine upward trends in CIG from noise-dominated fluctuations. By aligning a fat-tail-aware scoring methodology with an open testing platform, our work advances fair and statistically grounded assessment of earthquake forecasting models for the CSES and beyond.

physics.geo-ph↗

arXiv2026

Eigenvector Geometry as a New Route to Criticality in Random Multiplicative Systems

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 $γ\to γ+ \mathbb{E}\left[\ln κ_t \right]$ and lowers the tail exponent $α\simeq -2γ/ σ_κ^2$, where $\mathbb{E}\left[\ln κ_t \right]$ 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.

nlin.CD↗

arXiv2026

Self-Arresting and Runaway Earthquakes:Nucleation, Propagation, Gutenberg-Richter law and Dragon-King Events

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.

physics.geo-ph↗

arXiv2026

Why AI Alignment Failure Is Structural: Learned Human Interaction Structures and AGI as an Endogenous Evolutionary Shock

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.

cs.AI↗

arXiv2026

Pregnancy as a dynamical paradox: robustness, control and birth onset

The timing of human labor is among the most critical determinants of neonatal survival, yet the mechanisms that govern the transition from uterine quiescence to coordinated contractions remain elusive. Here we present a dynamical-systems framework that models the pregnant uterus as a spatially extended network of electrically excitable cells regulated by sparse adaptive feedback mimicking hormonal and mechanical influences. This approach reveals how stability during gestation and sensitivity near parturition can be simultaneously maintained through the interplay of control, network structure, and noise. Our analysis shows that spontaneous contractions such as Braxton-Hicks and Alvarez waves are not epiphenomena, but functional components that reduce control effort and preserve responsiveness. Moreover, we identify preterm labor as a boundary-crossing phenomenon arising when control fails to correctly interpret early-warning signals. These results establish a unifying mechanistic theory for labor onset, yield testable predictions, and suggest new therapeutic strategies to mitigate preterm birth risk.

physics.bio-ph↗