PICO is an ultra-lightweight substitution–permutation network block cipher designed for resource-constrained devices such as Internet of Things terminals and edge agents. For fixed endpoints, summing the characteristic probabilities over an enumerated finite weight window gives a verifiable lower bound on the differential probability. We use a PICO-specific workflow that combines mixed-integer linear programming bounds on active substitution boxes, exact-weight Boolean satisfiability search, optional Matsui pruning, and fixed-endpoint enumeration. For the selected endpoints, enumeration over W=63,…,76 and W=66,…,79 gives finite-window lower bounds of 2−59.95 and 2−61.95 for 21 and 22 rounds, respectively. We prepend two rounds and append three rounds to the 21-round differential distinguisher. The resulting 26-round analysis is an analytical equivalent-round-key filtering-and-ranking procedure for a 108-bit tuple. The verified 21-round finite-window probability input is a factor of 20.8032≈1.745 larger than the previously reported input, increasing the expected right-tuple support at fixed S under the analytical accounting. For the illustrative choice S=242, the analytical resources are D=262 chosen plaintexts, a normalized substitution-box filtering workload of T=2100.11 equivalent 26-round encryptions, and M=262 stored plaintext–ciphertext records. This setting is not tied to a demonstrated success probability and does not establish an equal-success complexity advantage over prior work.
Accurate station-scale weather forecasts support renewable-energy and transportation operations, yet gridded numerical weather prediction (NWP) is affected by representativeness errors and regional biases when transferred to irregularly distributed stations. We propose TF-STNet, a time–frequency dual-branch spatiotemporal network for NWP-to-station bias correction. A station-centered K-nearest-neighbor (KNN) operator retains multiple local NWP trajectories. The time-domain pathway separately encodes recent observations and future NWP, aligns them over the forecast horizon using gated dilated causal convolutions, and propagates lead-resolved states through a coordinate-conditioned directed station graph. The frequency-domain pathway learns spectral weights and applies separate attention to amplitude and phase across neighboring NWP cells. Prediction-level fusion combines the two station forecasts by variable, station, and lead time. The evaluation uses hourly data for wind speed, pressure, relative humidity, and temperature from 455 stations in Hebei, Shandong, Fujian, and Sichuan. Across five independent runs on 16 region–variable tasks, TF-STNet achieves the lowest mean absolute error (MAE) in 15 tasks and the highest Pearson correlation coefficient (PCC) in 15 tasks; its pressure MAE reduction relative to the strongest learned comparator ranges from 16.2% to 57.4% across the four regions. It has lower MAE than raw NWP in seven of eight high-wind or rapid-change event tests and than simple pressure model-output-statistics corrections in all four regions. The Shandong–temperature task and the Hebei–high-wind case illustrate the limits of the present point-forecast formulation.
Solomonoff induction mixes all computable explanations with description-length weights, but it is incomputable. This theory-and-position paper argues that practical approximation must be category-native: one should first declare the mathematical category in which a computable shadow will live, then use that category’s native comparison functional, complexity code, and inductive object. The proposal is not an omnibus theorem asserting that all categories are equivalent. It is a research architecture that separates comparison, representation, and prediction and makes the information lost by each projection explicit. The metric–measure branch supplies the developed realization. Compression data define an empirical Solomonoff space; Gromov–Wasserstein (GW) distance supplies relational distortion; minimum description length (MDL) controls candidate complexity; and distance-to-kernel embedding produces a positive-semidefinite predictor. For finite or countable coded classes, we prove existence and stability results, a held-out validation oracle inequality, a Kolmogorov–Solomonoff kernel unification, conditional empirical-GW consistency, and a coding-redundancy bound. Stronger learning-oracle statements remain conditional on marked/predictive selection, candidate-family adequacy, and kernel stability. Topological, Banach/Barron, graph, tree, and operator branches are presented as a constructional and testable research programme, with their maturity stated explicitly.
Advanced seismic hazard assessment frameworks rely on stochastic models which include aftershock production in the form of branching or self-exciting point processes. Such empirical constructs are based on debated statistical laws observed across catalogs of natural seismicity, which lack a derivation from first principles. Here, we derive the statistics of aftershock production in a generalized mean-field model of avalanche dynamics with static random thresholds and bimodal relaxation. The number of direct aftershocks is statistically characterized as a renewal counting process accounting for Borel-distributed refractory intervals. At the large-number limit, the expected number of aftershocks is proportional to the size of the parent event with a characteristic scale linearly depending only on the branching parameter governing refractory intervals, whereas the variance follows a distinct parabolic dependence with the same parameter. This model provides a rationale for the overdispersion in aftershock production observed in field data with respect to the Poissonian offspring numbers of standard Hawkes models, but it cannot explain the ubiquity of self-similar aftershock production found in catalogs and lab experiments.
Identifying the small group of customers who hold a given policy in severely imbalanced tabular data is a recurring screening problem in insurance analytics. This study considers binary caravan-insurance policy-ownership classification on the COIL 2000 benchmark, where the positive-class prevalence is below 6%. The benchmark is a single cross-section, so the label describes current ownership rather than a future purchase event. We propose an Attention-based Symmetric AutoEncoder (ASAE) that combines an auxiliary symmetric reconstruction branch, a channel attention gate, and a marginal log-variance regularizer on a 32-dimensional latent representation. The regularizer operates on individual latent variances and is treated as a heuristic rather than as an estimator of joint differential entropy. Under a common tuning and evaluation protocol on a stratified partition, the ASAE is compared with five conventional machine learning methods and seven neural models. Across five paired runs, it achieves an F1-score of 0.6008 ± 0.0115 and an area under the receiver operating characteristic curve (AUC) of 0.8584 ± 0.0034. Relative to TabNet, the strongest baseline considered, the mean differences are 0.064 in F1-score (95% confidence interval 0.043–0.085) and 0.032 in AUC (95% confidence interval 0.017–0.048). The ordering is preserved across five stratified re-splits, four imbalance-handling configurations, and a complete type-consistent preprocessing rerun in which nominal attributes are one-hot encoded, oversampled with SMOTENC, and reconstructed with categorical cross-entropy losses (F1-score 0.6241 ± 0.0074, AUC 0.8702 ± 0.0050). All reported results use stratified random partitions of COIL 2000. Because 27% of the records share an identical predictor vector with another record, the official challenge separation and two grouped partitions are also defined, so that exact-duplicate and sociodemographic overlap can be isolated from the primary split. The training code, split indices, and per-run predictions used for the reported tables are publicly available.
Commodity futures markets exhibit pronounced non-stationarity, nonlinearity, and multifractal characteristics that challenge traditional linear models. We employ a multiscale framework integrating four methodologies—MF-DCCA, PG irreversibility index, MSWPE, and JS-divergence segmentation—to analyze these features using daily closing prices for WTI crude oil, agricultural commodities (US soybeans, meal, oil, and wheat), the US dollar index, and Chinese No. 2 soybeans, spanning from 2 January 2018 to 1 October 2025, sourced from Investing.com and Matteo Iacoviello’s GPR database. The analysis yields three key results. First, scale dependence varies across commodities and is shaped by supply adjustment elasticity: energy markets show scale-dependent amplification and directional sign reversals, while agricultural markets maintain near-monofractal structures. Second, multiple methods converge on a characteristic time scale of approximately 20 days, linking physical logistics rhythms with financial pricing. Third, the persistence of structural reconstruction after shocks depends on systemic penetration depth, with exogenous macroeconomic uncertainty exerting stronger and more lasting effects than market-internal events. Together, supply elasticity, physical logistics rhythms, and systemic penetration depth constitute the three fundamental determinants of nonlinear commodity futures dynamics, with implications for cross-commodity allocation, multi-horizon risk management, and geopolitical scenario analysis.
Temporal interaction streams are often distributed across data owners, while downstream labels and communication budgets remain limited. Existing temporal graph prompts typically adapt at a centralized trainer, whereas federated graph methods commonly exchange larger trainable states. This paper presents FedTIP, a prompt-level federated method for client-local few-shot adaptation of temporal interaction graphs. A centralized historical stage constructs a temporal knowledge bank whose encoder is frozen during downstream federation. Clients optimize interaction-conditioned prompts on local supervised events and transmit a compact prompt-side message. Prototype anchoring and a reliability rule based on support coverage and update magnitude combine heterogeneous client updates, while prompt-side proximal regularization and stage-scoped negative sampling preserve the temporal protocol. Experiments on Wikipedia, Reddit, and MOOC cover temporal node classification and transductive and inductive link prediction. FedTIP records the highest mean AUC-ROC in the nine reported task–dataset cells, with gains of 1.83–14.69 points over the strongest federated baseline in each cell. Its measured cumulative float32 uplink is 0.40 MiB per downstream task, 64.6–99.6% below the evaluated baselines.
Automatic modulation classification (AMC) suffers from performance degradation under low signal-to-noise ratio (SNR) conditions, where modulation characteristics are affected by noise and signals belonging to the same modulation family exhibit similar feature representations. To address these challenges, this paper proposes a Transformer-based spatiotemporal fusion network that jointly exploits local spatial waveform characteristics and temporal dependency information while leveraging the global context modeling capability of the Transformer to integrate complementary multi-dimensional features. The proposed architecture improves feature representation capability under different SNR conditions. Experimental results demonstrate that the proposed method achieves improved classification performance compared with comparative approaches under different SNR conditions. In particular, it achieves an overall classification accuracy of 82.45% over the SNR range from −10 to 18 dB, and an average accuracy of 95.55% at SNRs of 2 dB and above, showing improved classification performance in the low-to-medium SNR transition region.
The transformation of a diffuse molecular cloud into a star necessarily increases the entropy of the universe, chiefly through the radiation emitted as gravitational binding energy is released. We present a compact, fully closed-form thermodynamic model of this process: the Sackur–Tetrode equation gives the entropy of the initial cloud and, generously, of the stellar material itself, while the released gravitational potential energy is converted into a radiation-entropy term Srad=ΔEpot/(2Teff), the factor of one-half following from the virial theorem for a self-gravitating star in hydrostatic equilibrium. For a solar-type star we obtain ΔS≃1.9×1037JK−1, consistent with independent literature estimates of stellar and interstellar entropy. Extending the calculation across the main sequence (O through M) gives ΔS∝M0.71, rising from 1.2×1037JK−1 for a 0.3M⊙ M dwarf to 2.0×1038JK−1 for a 20M⊙ O star. We then map the full (M,R,Teff) parameter space to locate the locus of ΔS=0—the formal boundary of thermodynamic feasibility for a single monolithic collapse—and show that every real main-sequence star lies deep in the entropy-producing region, with the boundary itself displaced to radii and masses far outside the stellar regime. Applying the same closed-form model to representative red giants, supergiants, white dwarfs and neutron stars (not as a model of their true formation, but as a diagnostic of how compactness controls radiative entropy production) shows that ΔS is set primarily by the compactness GM2/(RTeff) of the final configuration, so that degenerate remnants—if they were assembled by a single collapse from a diffuse cloud—would be substantially larger entropy sources than main-sequence stars, while extended giants are comparatively modest ones. The same closed-form machinery gives direct access to a full thermodynamic feasibility map, something that would otherwise require a large grid of numerical simulations to reconstruct, and we compare our results throughout with the current literature on stellar and cosmic entropy rather than with ad hoc benchmarks.
High-dimensional gene expression datasets in chemometric and biomedical research present significant challenges for machine learning because the number of genes greatly exceeds the number of available samples, increasing the risk of overfitting and reducing classification reliability. Existing gene selection methods are often sensitive to noise and outliers, leading to unstable feature subsets and degraded classification performance. To address these limitations, this study proposes a Robust Masked Painter (RMP) framework that integrates robust measures of location and dispersion, namely the Median and the Rousseeuw & Croux statistic (Qn), for reliable gene selection. The proposed framework operates in two stages. First, we identify informative genes using a round-robin strategy with a greedy search algorithm and robust core intervals to reduce the influence of noise and outliers. Second, Dominant Class (DC) analysis and Overlapping Scores (OS) further refine the selected gene subset by minimizing class overlap. We evaluate the proposed method on four publicly available gene expression datasets and compare it with several established feature selection methods using Random Forest, K-Nearest Neighbors, and Support Vector Machine classifiers. We assess classification performance using the Classification Error Rate. Experimental results and simulation studies demonstrate that the proposed RMP framework consistently outperforms competing methods by selecting highly informative genes that improve classification accuracy, robustness, and generalization.
While continuous-time Hamiltonian dynamics are naturally energy preserving with a symplectic flow, their discrete-time counterparts enhance either geometric or energy preservation properties, but rarely both within a unified framework. It is the object of this paper to more deeply investigate this question. In both linear and nonlinear settings, necessary and sufficient conditions characterizing discrete Hamiltonian dynamics that are conservative and symplectic are derived. The relationship with exact sampled models of continuous-time Hamiltonian dynamics are investigated, showing that such models, that preserve both energy and symplectic structures, do not generally fit into the proposed canonical form. Generalized Hamiltonian structures are, thus, introduced. On these bases, Hamiltonian integrators that preserve both the energy and the symplectic structure up to a prescribed order in the sampling period, are constructed. Some simulations on nonlinear test cases illustrate the theoretical findings.
Earthquakes exhibit well-documented statistical regularities at the catalogue level, such as the Gutenberg–Richter magnitude–frequency relation and the Omori–Utsu aftershock decay, often interpreted as signatures of seismicity as a driven, dissipative system far from thermodynamic equilibrium. However, whether comparable signatures, such as scale invariance and anomalous diffusion, can be detected directly within individual ground motion recordings remains an open question. This work investigates whether acceleration, velocity, and displacement signals recorded during the 2009 Mw 6.1 L’Aquila earthquake display statistical properties consistent with non-equilibrium complex systems, and whether different seismic phases carry distinct, reproducible statistical signatures. P- and S-wave onset times are estimated using AR-AIC, with adaptive search windows centred on theoretical arrivals from the CRUST1.0 velocity model. Coda onset is determined using three complementary criteria combined into a median ensemble, enabling the segmentation of each recording into up to five temporal windows. Displacement moment scaling is analysed for each window and signal type, within the framework of strong anomalous diffusion, yielding the scaling exponents ζ(q). Robustness is systematically assessed against the choice of coda onset method, the empirical thresholds defining coda onset and end, the sub-interval of τ used in the moment scaling fit, and the filter band applied to the ground motion signals. Evidence for anomalous diffusion is nuanced: both its sign and magnitude depend on the seismic phase, with only a subset of configurations remaining stable across all segmentation schemes tested. These results indicate that anomalous scaling signatures, when present, are not universal, and that systematic robustness analyses are essential to distinguish genuine physical effects from segmentation artefacts.
This paper develops asymptotic theory for kernel estimation of density-weighted conditional functionals and regression derivatives when responses are missing at random (MAR) and the observations form a strictly stationary ergodic process. Sequential MAR and positivity identify the complete-data conditional target through an inverse-probability-weighted pseudo-response, while the fully observed covariate density and its derivatives are estimated without unnecessary response weighting. A martingale-predictable decomposition yields uniform almost-sure rates, pointwise Gaussian limits, variance expansions, studentization, and AMISE results under explicit projective/maximal, conditional-moment, conditional-density, and variance-stabilization conditions. These quantitative assumptions are additional to stationarity and ergodicity: the results are not asserted for arbitrary stationary ergodic sequences. Exact-quotient and multi-index identities transfer the primitive-estimator theory to regression derivatives, and feasible propensity estimation contributes an explicit additional remainder. Monte Carlo experiments show that stronger dependence, weak response probabilities, higher derivative order, propensity misspecification, and smoothing bias can materially degrade finite-sample performance; undersmoothing improves centring but need not eliminate coverage distortion at moderate sample sizes.
Mode veering is a modal-interaction phenomenon found in vibration systems. For inertially coupled structures, the combined influence of coupling delay, nonlinear restoring force, and stochastic coupling perturbation remain insufficiently understood. This work analyzes an inertially coupled two-coordinate prototype in which a discrete delay, a delayed cubic stiffness, and positive multiplicative stochastic modulation all enter through the same relative-coordinate coupling channel. We formulate the delayed linear spectrum through a quasi-polynomial characteristic equation. We also characterize the veering by the two positive-frequency characteristic-root branches descending from the mechanical modes. Coupling delay shifts the veering center, alters the minimum frequency gap, and moves the tracked rightmost roots toward the stability boundary. An analytical imaginary-axis-crossing criterion is derived to determine the delay-induced stability boundary of the deterministic linearized system, and the resulting boundary is independently validated by direct multi-start characteristic-root searches and Chebyshev-collocation approximation of the DDE generator. A fixed-reference modal-coordinate representation identifies the off-diagonal modal terms associated with branch exchange while retaining the full delayed characteristic equation. A first-harmonic treatment of the delayed cubic term can yield an amplitude-dependent nonlinear veering backbone. For the stochastic problem, frozen lognormal coupling samples and a time-dependent Ornstein–Uhlenbeck-driven multiplier are constructed from the same unit-mean positive lognormal marginal law. The former is used to quantify realization-wise spectral broadening, whereas the latter retains temporal correlation and is used to evaluate finite-time branch residence and pathwise delayed-work statistics. The pathwise energy balance reveals that the delayed relative-coordinate work rate is sign-indefinite. This provides a common energy-transfer mechanism through which delay, nonlinearity, and stochastic modulation reshape mode veering in the inertially coupled system.
The identification of influential nodes in directed networks is fundamental to diffusion analysis, network robustness assessment, and information recommendation. Owing to the asymmetry introduced by directed edges, conventional centrality methods often struggle to jointly characterize the local spreading range, higher-order diffusion potential, and structural bridging roles. To address this issue, this paper proposes KSGR for influential node identification in directed networks. Under the convention that a node can influence its in-neighbors, KSGR integrates the reverse local reachability, reverse diffusion efficiency, hierarchical asymmetry, directed reverse k-shell, reverse structural gravity, bridging capability, and structural diversity enhancement. A lightweight network-profiling mechanism based on the network size, reciprocity, LWCC ratio, and SCC ratio is further used to select structural enhancement branches for different network profiles. Experiments on six real-world directed networks compare KSGR with PageRank, LeaderRank, ClusterRank, In-degree, Adjacency Entropy, BII, and NEM. Under the adopted reverse-edge propagation convention and SI settings, KSGR achieves the highest average normalized spreading AUC and final infection scale in the Top-10 seed experiments among the selected methods. Supplementary Top-5 and Top-20 experiments further indicate that the ranking can be applied to different seed-set sizes. Kendall correlation analysis shows that KSGR produces rankings distinct from traditional centrality and random-walk-based methods. LWCC node-removal experiments provide evidence that highly ranked KSGR nodes influence the weakly connected backbone of the tested networks. Parameter sensitivity and threshold robustness analyses demonstrate that KSGR maintains stable spreading performance under different enhancement settings and moderate perturbations of adaptive branch-selection thresholds.
Traditional coupling coordination degree (CCD) evaluation methods fail to simultaneously ensure the accuracy and reliability of evaluation results. To overcome this limitation, a novel evaluation method that integrates the logical multiplication of connection numbers with stochastic simulations (ECCD-LMS) is developed to assess the CCD of regional water resources, social economy, and ecological environment (WSE) composite systems. The method adopts three-element connection numbers to quantify the comprehensive evaluation level of each system. Overall partial connection numbers and triangular fuzzy numbers then define dynamic value intervals for the connection number components, and the Monte Carlo method is integrated to simulate stochastic variation in each component. The simulated values are substituted into the logical multiplication of connection numbers to generate evaluation results that include both mean CCD estimates and 95% uncertainty intervals. The empirical application of ECCD-LMS in China’s Jing River Basin indicated that the coupling coordination level of the regional WSE composite system exhibited an overall increasing tendency with fluctuations from 2012 to 2023. These fluctuations were closely associated with variations in the comprehensive evaluation level of the water resources system. Spatially, the disparities in evaluation grades among subregions gradually narrowed during the study period. Compared with traditional CCD evaluation methods, ECCD-LMS effectively corrects systematic overestimation while maintaining objectivity and produces more dispersed CCD estimates that reflect differences among evaluation samples with greater clarity. Furthermore, by outputting mean CCD estimates and 95% uncertainty intervals, ECCD-LMS outperforms traditional methods that only provide static point estimates. It thus enables robust and credible evaluation of the coupling coordination level of WSE composite systems under multiple sources of uncertainty, suggesting potential applicability across diverse regional contexts.
Conventional statistical process monitoring approaches primarily focus on changes in location, dispersion, or distributional characteristics. However, process deterioration may also emerge through variations in uncertainty and information structure. Motivated by this limitation, this study proposes an Entropy–EWMA monitoring framework for progressively Type-II censored lifetime data. Developed under the Exponentiated Weibull distribution, the framework incorporates a censoring-adjusted entropy estimator into an adaptive EWMA structure to account for information loss and monitor changes in process uncertainty. The statistical performance of the proposed approach is evaluated through Monte Carlo simulations under different entropy degradation levels, censoring structures, observed sample sizes, and auxiliary shift-estimation smoothing parameter values. Control limits are calibrated to achieve an in-control Average Run Length close to the nominal target of ARL0=370. The results show satisfactory in-control performance and substantially decreasing out-of-control Average Run Length as entropy degradation increases. Comparative simulations further demonstrate shorter run lengths for the Entropy–EWMA scheme under moderate and severe entropy degradation relative to the Classical EWMA. The practical applicability of the method is illustrated using Wind Turbine SCADA data under Uniform and Late Progressive Type-II censoring schemes. Neither method produces false alarms during the in-control phase, while both detect changes during the out-of-control phase. The Classical EWMA provides earlier and more persistent signals associated with location changes, whereas the Entropy–EWMA responds to changes in process uncertainty. These findings demonstrate that the two approaches capture different aspects of process behavior and can be interpreted as complementary monitoring tools.
Rumor events on social media generate opposing camps whose interaction structure is not captured by spreading models or content detectors. This study describes the camp and bridging structure of three rumor events on Sina Weibo, selected from confirmed cases published by the platform’s rumor-refutation channel. Each event is represented as a multilayer interaction network built from repost, comment, and mention relations. Camps are detected by modularity-based community assignment, and overlap is measured through a fractional membership distribution over communities. Three information-theoretic quantities characterize the structure. In the three events, membership entropy separates committed users from bridging users. Structure-to-stance mutual information measures the alignment between interaction communities and text stance. Cross-layer mutual information measures the consistency of camps across interaction types. A co-opetition matrix of mean edge sentiment describes cooperation within camps and competition between camps and identifies alliance structure. In the three events, membership entropy is bimodal, structure-to-stance mutual information is positive and above a permutation null, and the co-opetition matrix has positive diagonal entries. The three events show three distinct temporal patterns, namely a persistent standoff, a hardening toward a single camp after an official correction, and a reversal with an alliance between two camps. The patterns are recovered under a look-ahead-free temporal scheme. In the three events, bridging users hold higher betweenness centrality than non-bridging users. The results describe cross-camp bridging structure in three rumor cascades and connect the structure to a co-opetition reading of camp relations.
Modern out-of-order processors depend critically on TAGE family branch predictors, which often struggle with context-fragile branches whose outcomes are highly sensitive to slight perturbations in the most recent global history. Existing predictors are confined to single-path factual reasoning and lack any mechanism to explicitly probe the local stability of a prediction. We formalise this limitation from an information entropy perspective: a context-fragile branch corresponds to a high conditional entropy region in the joint space of recent history bits and branch outcomes, where a single bit flip in the youngest history can shift the posterior branch probability across the decision boundary. To address this, we propose Mirror-TAGE, a lightweight microarchitectural framework that integrates counterfactual stability modeling with replay-guided selective overrides. Building on a TAGE-SC-L baseline following Seznec, Mirror-TAGE injects controlled bit-level perturbations into the youngest global history bits to construct two mirrored views, screened by an entropy-based reliability filter. We define a local prediction entropy, derive an information-theoretic characterisation of override correctness via DRT-filtered agreement, and decompose uncertainty into aleatoric and epistemic components. Under a paired causally consistent learning framework on synthetic workloads isolating the context-fragile regime, Mirror-TAGE achieves a 0.82 pp gain (66% override correctness, 7.5% overhead). Of successful overrides, 78% occur at entropy > 0.85 bits, consistent with the entropy-guided criterion, though partly driven by the entry gate design. Six SPEC CPU 2017 traces confirm no accuracy degradation, with gains of up to 0.38 pp. These results support entropy-guided counterfactual stability modelling as a promising branch prediction paradigm.
Most multimodal transit studies use pairwise or multilayer graphs that discard route membership. We construct route-preserving bus–metro hypergraphs for 45 Chinese cities. A route-support rule makes node viability depend on the fraction of incident routes that remain viable. Transfer-first attack is the most damaging static strategy in 33 cities. PPCR is associated with greater connectivity retention under random disruption (r=0.807), but with deeper route-support pruning under targeted triggering. Connectivity retention, route-support outcomes, and recovery are only moderately aligned (mean |ρ|=0.52). Three principal components are needed to explain 90% of their variance. Multimodal resilience, therefore, cannot be summarized by one ranking. The hypergraph preserves route-dependent failure as a native model property.
