Standard dynamical systems approaches to economic modeling, such as those deriving the Cobb-Douglas and CES production functions from exponential growth trajectories, typically rely on integer-order differential equations. While effective, these models assume that economic output depends solely on the instantaneous state of capital and labor, effectively ignoring the long-term ``memory effects'' inherent in policy, infrastructure, and technological adoption. This paper extends the exponential framework by introducing the Caputo fractional derivative into the underlying dynamical systems governing factor inputs. By replacing standard growth rates with fractional-order counterparts of order $0 < α\le 1$, we model economic trajectories where the rate of change is a non-local function of the system's entire history. We demonstrate that the Mittag-Leffler function emerges as the natural growth solution in this context, providing a nested generalization of the classical exponential model. Using this fractional approach, we derive a new class of time-independent invariants that serve as generalized production functions. We show that as the fractional order approaches unity, these forms converge exactly to the classical Cobb-Douglas function.

We introduce and study the axiom of null player neutrality in the context of cooperative games with transferable utility (TU-games). This axiom weakens the classical coalitional strategic equivalence: rather than requiring that augmenting a game by a null-player game leaves that player's payoff unchanged, it only requires that any change in payoff be independent of the specific augmenting game, provided both the null-player condition and the grand-coalition value are preserved. We show that efficiency, linearity, symmetry, and null player neutrality together characterize the family of all real linear combinations of the Shapley value and the equal division solution, a family that strictly extends the well-known class of $α$-egalitarian Shapley values (convex combinations, $α\in [0,1]$) to arbitrary $α\in \mathbb{R}$. Replacing null player neutrality by its natural analogue for nullifying players uniquely pins down the equal division solution.

In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test statistics based on a deconvolved residual-marked empirical process and establish their asymptotic properties in both ordinary smooth and supersmooth cases, assuming the measurement error distribution is known. The issue of an unknown measurement error distribution is addressed by employing estimators of the measurement error characteristic function based on repeated measurements. Furthermore, depending on whether the measurement error distribution is known or not, to obtain critical values from the case-dependent limiting null distributions, we propose two computationally attractive multiplier bootstrap methods where the "parameter estimation effect" is successfully addressed. Finally, simulation results and empirical studies about corn yields and household budget shares confirm the favorable properties of the proposed tests.

Multimodal density estimation is a fundamental problem in scientific computing. Determining the number of modes in a distribution is a core numerical challenge with applications across ecology, economics, genomics, and astronomy. While the R ecosystem provides mature tools through the multimode package, the Python ecosystem has lacked an equivalent cohesive implementation. We present critband, a Python package for critical bandwidth bimodality detection based on Silverman's kernel density approach. The package implements critical bandwidth search with a robust bracketed mode-count solver and FFT-accelerated KDE, and provides additional features including k-mode detection, component decomposition, bimodality strength quantification, and excess mass estimation. Validation against twelve benchmark cases spanning separation regimes, unequal variances, unequal weights, and small sample sizes shows stable estimates for clearly separated cases and expected instability for boundary cases. Performance benchmarks show critband is typically 3-10 times faster per case than R's modetest() in the tested setup.

We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical. The model captures realistic features observed in many economic observables, which can be explained as market-driven firm entries/exits, worker inflow/outflow, and income growth/loss. This model is not conservative and, despite the asymmetry in the entry and exit rates, we find that the system eventually relaxes to a stationary distribution. Moreover, our analysis reveals three distinct dynamical regimes in the moments of the distribution, arising from the interplay between volatility, drift, entry, and exit rates. We further derive the survival probability and the mean first-passage time associated with the observed variable reaching certain threshold under the competing entry-exit processes. Interestingly, we identify an optimal exit rate that minimizes the mean first-passage time, providing insights into how entry and exit policies can influence the outcome of the system. These results should be useful for understanding the long-run behavior of economic systems in which growth, volatility, entry, and exit jointly shape the evolution of heterogeneous units.

We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many markets, we show that stable matchings exist when choice correspondences satisfy substitutability and a new general acyclicity condition. We provide a constructive proof using a Grow or Discard Algorithm that iteratively expands or eliminates contracts until a strongly maximal individually rational set is reached. We provide an algorithm to obtain stable matchings in which rejected contracts are not permanently discarded, distinguishing our approach significantly from standard DAA-type algorithms. For one-to-one markets, we introduce a replacement-based notion of stability and provide an algorithm that constructs stable matchings when choice correspondences satisfy binary acyclicity, a property weaker than path independence. JEL classification: C62, C78, D01, D47 Keywords: choice correspondences, substitutability, general acyclicity, many-to-many matching, matching with contracts, Grow or Discard algorithm, replacement stability, binary acyclicity.

Many policy counterfactuals depend on how consumers value product attributes such as sugar, sodium, caffeine, alcohol, or emissions. Standard hedonic and differentiated-products models interpret these valuations statically. That interpretation is restrictive when attributes are habit forming: observed prices then reflect both contemporaneous marginal value and the continuation value generated by current consumption. I develop a nonparametric revealed-preference framework for dynamic hedonic valuation, deriving necessary and sufficient conditions for rationalising observed prices and choices. Using household scanner data on cereal purchases, I show that the hedonic representation places real restrictions on prices, while habit formation improves behavioural coherence conditional on that representation. The results provide a diagnostic for when static attribute valuation is justified and when prices reveal more than contemporaneous marginal values.

A central problem in multiagent systems is the fair assignment of objects to agents. In this paper, we initiate the analysis of classic majoritarian social choice functions in assignment. Exploiting the special structure of the assignment domain, we show a number of surprising results with no counterparts in general social choice. In particular, we establish a near one-to-one correspondence between preference profiles and majority graphs. This correspondence implies that key properties of assignments -- such as Pareto-optimality, least unpopularity, and mixed popularity -- can be determined solely by the associated majority graph. We further show that all Pareto-optimal assignments are semi-popular and belong to the top cycle. Elements of the top cycle can thus easily be found via serial dictatorships. Our main result is a complete characterization of the top cycle, which implies the top cycle can only consist of one, two, all but two, all but one, or all assignments. By contrast, we find that the uncovered set contains only very few assignments.

We provide a simple distribution regression estimator for treatment effects in the difference-in-differences (DiD) design. Our procedure is particularly useful when the treatment effect differs across the distribution of the outcome variable. Our proposed estimator easily incorporates covariates and, importantly, can be extended to settings where the treatment potentially affects the joint distribution of multiple outcomes. Our key identifying restriction is that the untreated outcome distribution does not exhibit an interaction effect of group and time. This assumption results in a parallel trend assumption on a transformation of the distribution. We highlight the relationship between our procedure and assumptions with the changes-in-changes approach of Athey and Imbens (2006). We also reexamine the Card and Krueger (1994) study of the impact of minimum wages on employment to illustrate the utility of our approach.

Multiplicative Kantian equilibrium explains cooperative behavior in social dilemmas without abandoning methodological individualism. However, its outcomes depend critically on the parametrization of the strategy space - the property of strategic non-equivalence. We investigate what fraction of the Pareto frontier can be attained by varying the strategy space. We show that the set of achievable Kantian equilibria is the entire Pareto frontier: for any interior Pareto-efficient point there exists a shift of coordinates - imposing lower bounds on actions - that makes it a Multiplicative Kantian equilibrium. The proof is constructive and relies on a intuitive geometric property: moving the origin to a point on the common tangent to players' indifference curves. This result separates the problem of efficiency from the problem of fairness, allowing any normative criterion to be implemented without loss of Pareto optimality.

This study investigates the macroeconomic determinants and dynamic behaviour of personal remittances as a share of Gross Domestic Product (GDP) in Nepal, emphasizing external demand in major destination countries and domestic monetary policy. Using annual data (1993-2024), we construct composite indices via Principal Component Analysis (PCA) for multi-country external demand and a domestic Monetary Conditions Index (MCI). Our small-sample econometric pipeline includes Autoregressive Distributed Lag (ARDL) bounds testing, Engle-Granger cointegration, Dynamic OLS (DOLS), and a two-step Error Correction Model (ECM). We also employ Granger causality tests and multi-model forecasting using machine learning and ECM scenarios. The analysis reveals a strong positive long-run effect of external demand on remittances and a significant negative impact of tighter domestic monetary conditions. The ECM confirms a stable cointegrating relationship, correcting approximately 26% of disequilibria annually. Medium-term projections indicate remittances will remain structurally important, reaching around 28.3% of GDP by 2030 under baseline conditions, while exhibiting high sensitivity to external demand shocks. This study advances the literature by integrating PCA-derived external demand and monetary conditions indices within a unified ARDL-ECM framework for small samples. Focusing on one of the world's most remittance-dependent economies, it offers actionable insights for monetary policy calibration, migration diversification, and the productive utilization of remittance inflows.

This chapter reviews indirect estimators of intergenerational mobility, focusing on approaches that infer parent-child or other family associations when direct income data are incomplete or unavailable. We synthesize methods based on instrumental variables, imputation using observable characteristics such as education and occupation, surname-based estimators, and multigenerational linkages. To unify these approaches, we introduce a stylized framework in which socioeconomic status is transmitted through multiple pathways with heterogeneous persistence rates. Within this framework, both direct and indirect estimators can be interpreted as weighted averages of these underlying transmission channels. A central insight is that the choice of instrument or imputation strategy determines these weights, leading different methods to capture distinct aspects of the transmission process. We highlight implications for interpretation, showing that indirect estimators need not recover conventional parent-child correlations but can instead provide complementary evidence on long-run persistence and the mechanisms underlying persistent inequalities.

We extend the optimin notion of Ismail (2025) from mixed strategy profiles to correlated distributions. A correlated distribution is evaluated by the worst expected payoff each player can receive when opponents may either obey their private recommendations or make unilateral recommendation-contingent deviations that are strictly profitable under the posterior induced by the distribution. Correlated optimins are Pareto optimal with respect to this vector of guaranteed payoffs. We show that a correlated optimin exists in every finite game. In addition, for every correlated equilibrium, there exists a correlated optimin such that every player's guaranteed payoff is weakly higher than his or her correlated equilibrium payoff. In two-player zero-sum games, correlated optimin coincides with correlated equilibrium and yields the maximin value. Outside zero-sum games, correlated optimin may strictly improve upon all correlated equilibria. We illustrate this with a simple 2x2 game with a unique correlated and coarse correlated equilibrium, in which there exists a correlated optimin that strictly Pareto dominates the equilibrium payoff.

Westudy how a planner can design dynamic interventions to overcome status-quo inertia in living temporal games, where strategic agents control their state (active, sleep, partially dead) on a temporal network. Building on the continuous-time stochastic game framework of our companion paper, we introduce three intervention classes: bounded transfers (price based), structural modifications (edge deletion, addition, or replacement), and information signals. We formalize the notion of inertia depth and prove a threshold theorem: the status quo equilibrium survives all transfer perturbations whose magnitude is below a critical bound that depends on the remaining horizon. A central structural dominance result shows that for any finite transfer budget there exists a family of games where no bounded price intervention can eliminate the inefficient equilibrium, yet a single edge replacement (continuous-flow to discrete-transport) succeeds. We then study private-information subclasses with static types. Using a uniformization reduction, we prove an impossibility result: no direct mechanism can simultaneously satisfy ex post incentive compatibility, ex post budget balance, and history privacy while always implementing an efficient equilibrium. In the same subclass we construct a dynamic pivot mechanism that achieves second-best efficiency with bounded deficit. Finally, we show that replacing continuous-flow edges by discrete-transport edges weakly expands the set of implementable outcomes, highlighting the importance of temporal semantics for mechanism design. Our results extend the static analysis of [5] to continuous time strategic networks and provide a rigorous foundation for subsequent papers on learning and mean-field design.

Additively separable hedonic games (ASHGs) are a prominent model of coalition formation where agents' preferences are derived from their individual valuations of peers. While social welfare maximization in ASHGs has traditionally focused mostly on utilitarian welfare, Nash welfare -- a well-established metric in economics which balances fairness with efficiency and offers scale invariance -- has been entirely overlooked. In this paper, we initiate the study of Nash welfare in ASHGs. We point out desirable properties fulfilled by partitions with high Nash welfare. This includes guaranteed contractual Nash stability in symmetric games, even for any approximation of Nash welfare. This is particularly appealing since, as for other welfare notions, Nash welfare turns out to be NP-hard to maximize, even for the ASHG subclass of symmetric aversion to enemies games (AEGs). A main focus of our study is on approximation algorithms for the Nash welfare objective. We present packing-based algorithms with approximation ratios for well-established subclasses of ASHGs: $n-1$ for AEGs and $2n$ for appreciation of friends games. This is complemented by a strict inapproximability result showing it is NP-hard to approximate Nash welfare within a factor of $1.0000759$ in general ASHGs. Further, we investigate the restricted settings with an upper bound on the coalition size or number of coalitions, and draw the boundary between the cases admitting efficient algorithms and those yielding NP-hardness: bounding the allowed size or number of coalitions by $2$ admits polynomial-time solvability, whereas bounds of $3$ or more yield NP-hardness or unbounded inapproximability.

We compare how well agents aggregate information in two repeated social learning environments. In the first setting agents have access to a public data set. In the second they have access to the same data, and also to the past actions of others. Despite the fact that actions contain no additional payoff-relevant information, and despite potential herd behavior, free riding and information overload issues, observing and imitating the actions of others leads agents to take the optimal action more often in the second setting. We also investigate the effect of group size, as well as a setting in which agents observe private data and others' actions.

Treatment effects estimated from a randomized controlled trial are local not only to the study population but also to the time at which the trial was conducted. The literature on generalizing experimental findings to new populations is extensive, yet transporting effects across time has received far less attention, and even defining the target estimand is nonobvious. We formalize the transported average treatment effect under a separable temporal effects assumption, derive two identification strategies: replicated trials and common arm, and develop doubly robust, semiparametrically efficient estimators for each. Applied to a large archive of headline A/B tests, the common arm strategy is substantially more precise but exhibits systematic bias when the temporal factor depends on the gap between intervention and measurement rather than on measurement time alone, while the replicated trials strategy, which allows this dependence, tracks the ground truth more faithfully. Simulation studies investigate when each strategy is reliable and when it silently fails.

We propose a high-dimensional structural vector autoregression framework with a factor structure in the error terms that accommodates a large number of linear inequality restrictions on both impact impulse responses and structural shocks. Our framework extends recent advances in large sign-restricted VARs by allowing narrative restrictions to be imposed directly through constraints on structural shocks via prior distributions, thereby sharpening identification and enhancing the economic interpretability of the structural shocks. To estimate the model, we develop a computationally efficient sampling algorithm that scales well with both model dimension and the number of imposed restrictions, while avoiding the low acceptance-rate problems associated with existing rejection-based approaches. We apply our methodology to a large-scale structural VAR model of the U.S. economy, identifying ten structural shocks and tracing their dynamic effects across thirty-nine macroeconomic and financial variables. The empirical application demonstrates that the incorporation of narrative restrictions improves structural identification in high-dimensional settings by reducing the uncertainty surrounding impulse response functions and facilitating a clearer economic interpretation of the identified structural shocks.

This study introduces a data-driven, machine learning-based method to detect suitable control variables and instruments for assessing the causal effect of a treatment on an outcome in observational data. Our approach tests the joint existence of instruments, which are associated with the treatment but not directly with the outcome (at least conditional on observables), and suitable control variables, conditional on which the treatment is exogenous, and learns the partition of instruments and control variables from the observed data. The detection of sets of instruments and control variables relies on the condition that proper instruments are conditionally independent of the outcome given the treatment and suitable control variables. We establish the consistency of our method for detecting control variables and instruments under certain regularity conditions, investigate the finite sample performance through a simulation study, and provide an empirical application to health data from the Oregon Health Insurance Experiment.

Lotteries are a prevalent form of gambling between a seller and buyers. Designing a lottery requires a model of how buyers make decisions when confronted with uncertain outcomes. Cumulative prospect theory (CPT) is a descriptive model that captures people's propensity to overestimate extreme events and their different attitudes toward gains and losses. In this study, we design a lottery that maximizes the seller's profit when the buyers' decision-making adheres to the CPT framework. The main difficulty is the nonconvexity of the CPT framework, which we overcome by reformulating the problem as a three-level optimization problem and characterizing its optimal solution. Based on the analysis, we propose a linear-time algorithm that computes the optimal lottery. Furthermore, we present an efficient algorithm applicable to a broader setting with a ticket price constraint. This is the first study to employ the CPT framework in designing an optimal lottery with more than two outcomes.

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for and a suspected instrument. Under a causal structure commonly found in empirical applications, the testable conditional independence of the suspected instrument and the outcome given the treatment and the covariates has two implications. First, the instrument is valid, i.e. it does not directly affect the outcome (other than through the treatment) and is unconfounded conditional on the covariates. Second, the treatment is unconfounded conditional on the covariates such that the treatment effect is identified. We suggest tests of this conditional independence based on machine learning methods that account for covariates in a data-driven way and investigate their asymptotic behavior and finite sample performance in a simulation study. We also apply our testing approach to evaluating the impact of fertility on female labor supply when using the sibling sex ratio of the first two children as supposed instrument, which by and large points to a violation of our testable implication for the moderate set of socio-economic covariates considered.

Microsimulation models used by ministries of finance and central banks rely on parametric processes for lifetime earnings that capture only first and second moments of the conditional distribution and miss long-range nonlinear structure. We propose SAGA, a decoder-only transformer for irregular tabular panel sequences, paired with a split conformal calibration wrapper that delivers individual-level prediction intervals with finite-sample marginal coverage guarantees. Trained on the longitudinal Swedish LISA register over 1990 to 2022, comprising 2,143,817 individuals and 61,284,903 person-years, the model forecasts annual labor earnings at horizons of one to thirty years and aggregates them by Monte Carlo into present-discounted lifetime earnings distributions. Against the canonical Guvenen, Karahan, Ozkan, and Song parametric process and tabular and recurrent baselines, SAGA reduces continuous ranked probability score by 31.9 percent at the ten-year horizon and mean absolute error by 37.7 percent at the twenty-year horizon. Conformal intervals achieve nominal coverage to within 0.4 percentage points marginally and within 2.4 percentage points on the worst-case demographic subgroup. The reconstructed lifetime earnings Gini coefficient is 0.327 against the partially observed truth of 0.341 and the GKOS estimate of 0.378. Model weights, calibration tables, and a synthetic equivalent dataset are released for replication outside the protected SCB MONA environment.

This article develops the concept of the agentic economy and diagnoses its measurable preconditions: a transition in which economic action is increasingly distributed among humans, AI agents, industrial robots, executable protocols, compute infrastructures, and energy systems. The paper argues that classical categories such as labour, capital, firm, market, productivity, and trust remain necessary but incomplete when technologies prepare decisions, coordinate workflows, support tasks, verify transactions, and reshape responsibility. Methodologically, the study uses a conceptual-empirical quantitative diagnostic design rather than a causal econometric model. It relies on public institutional data on AI investment, AI adoption, robot installations and operational stock, data-centre electricity demand, and labour-market reallocation. The reported values are transformed through transparent indicators such as relative growth, CAGR, growth multipliers, stock-flow ratios, concentration ratios, and HHI. The results show that AI adoption is accelerating, AI investment signals broad capital allocation, industrial robots represent persistent cyber-physical action capacity, compute expansion increases data-centre electricity pressure, and labour projections are more consistent with task reallocation than labour disappearance. The article contributes an action-capacity framework linking model/software-agent capacity, robotic capacity, compute-energy coupling, protocolisation, auditable trust, and human sovereignty. It concludes that the agentic economy is not yet a completed global order, but its transition pressure is measurable enough to require a distinct economic vocabulary, reproducible diagnostics, and future sector-level measurement.

Decision-makers often deploy the best-performing treatment from a randomized experiment, creating a winner's curse: selection favors treatments whose observed outcomes are high partly because of statistical noise, so the naïve estimate of the winner is upward biased. We distinguish two forms of winner's curse, bias relative to the true best treatment (global) and bias relative to the selected treatment's true mean (selective), and link them to regret from deploying a suboptimal treatment. This framework defines seven decision-relevant evaluation targets: mean bias, mean squared error, and confidence interval coverage for the global and selective winner's curse, and mean regret. We then show that methods that perform well on one target can perform poorly on others, so corrections should be matched to the manager's objective. Across simulations with varying effect sizes, multiple-arm settings, and data calibrated to an online A/B testing platform, no method dominates uniformly: the plug-in estimator performs best when treatment differences are large, cross-fitting performs best when treatments are similar, and resampling methods often achieve low mean squared error for moderate differences. We also introduce an adaptive empirical likelihood procedure that delivers asymptotically valid confidence intervals across settings without the tuning sensitivity of resampling-based methods.

The rapid diffusion of agentic AI has created a new coverage problem for commercial insurance: some AI-mediated losses are now affirmatively insured, some create silent-AI exposure under legacy cyber, technology errors-and-omissions (E&O), directors-and-officers (D&O), employment practices liability (EPLI), crime, and media policies, and others are being actively excluded. This paper maps that emerging boundary by coding 55 AI threat classes against 26 insurance products, endorsements, and exclusion regimes using public carrier materials and OWASP/MITRE threat catalogs. We identify a four-tier insurability frontier: affirmatively insured perils, silent-AI exposures, actively excluded perils, and perils outside conventional private insurance structures. Our coding measures publicly claimed positioning rather than executed contract wording; the headline statistics describe what carriers publicly state about coverage, not what would be paid in any specific claim. Three patterns emerge. First, affirmative AI coverage is beginning to differentiate by primary risk emphasis: public materials often position Munich Re around model performance and drift, Armilla and parts of the Lloyd's market around hallucination and broader AI liability, Tokio Marine Kiln and CFC around IP and technology E&O concerns, Apollo ibott around emerging autonomous system liability, and Coalition around deepfake and AI-enabled cyber response. Second, legacy lines retain silent-AI exposure where AI is an instrumentality rather than the legal cause of loss. Third, foundation model concentration is the clearest genuinely novel insurability frontier because upstream model failure can correlate losses across many cedents at once; the relevant market design question is which insurability constraint each candidate structure relaxes, not merely which systemic risk template exists.

This article develops an intergenerational mean-field-type game (MFTG) to model Mali's and neighbouring countries multi-actor conflict ecosystem, which includes formal state forces, traditional hunters, nonstate militias, jihadists, criminal networks, civil societies, and international proxies. Each decision-maker (agent, a group of agents or representative agent) is defined by a type, state, information structure, and action, with payoffs dependent not only on individual decisions but also on the evolving distribution of all agents' profiles. The model reveals that cycles of violence can persist across multiple generations due to the embedded presence of retaliatory types such as revenger child-soldiers whose trauma-conditioned best-responses favor conflict, and whose behavior reinforces intergenerational transmission of violence. The model also captures the strategic exploitation of institutional fragility by war entrepreneurs who profit from sustained instability through arms sales, militia contracting, and unregistered market mediation. These actors inject minimal resources to trigger profitable escalations, turning latent tensions into self-reinforcing violence economies. We show that in the absence of structural counterincentives, peaceful strategies are non-absorbing, and violence remains dynamically rewarding for war entrepreneurs. However, by embedding incentive-compatible, information-adaptive transfers directly into instantaneous payoffs, rewarding verifiable peacebuilding and penalizing aggression, it is possible to shift the mean-field-type equilibrium distribution intergenerationally toward more peaceful types and drive systemic de-escalation. We also discuss about the funding and the real implementation of such mechanisms in the field.

Scientific inference is often undermined by the vast but rarely explored "multiverse" of defensible modelling choices, which can generate results as variable as the phenomena under study. We introduce RobustiPy, an open-source Python library that systematizes multiverse analysis and model-uncertainty quantification at scale. RobustiPy unifies bootstrap-based inference, combinatorial specification search, model selection and averaging, joint-inference routines, and explainable AI methods within a modular, reproducible framework. Beyond exhaustive specification curves, it supports rigorous out-of-sample validation and quantifies the marginal contribution of each covariate. We demonstrate its utility across five simulation designs and ten empirical case studies spanning economics, sociology, psychology, and medicine, including a re-analysis of widely cited findings with documented discrepancies. Benchmarking on ~672 million simulated regressions shows that RobustiPy delivers state-of-the-art computational efficiency while expanding transparency in empirical research. By standardizing and accelerating robustness analysis, RobustiPy transforms how researchers interrogate sensitivity across the analytical multiverse, offering a practical foundation for more reproducible and interpretable computational science.