We associate to a decorated liability network a liability sheaf on a directed hypergraph whose hyperedges separate the distribution of payments from the collection of receipts. Clearing configurations are precisely the global sections of this sheaf, and the global-section object is canonically the equalizer of the identity and a clearing operator $Φ=A\circ D$ factored into collective distribution $D$ and aggregation $A$; an institution-edge duality identifies it equivalently with the equalizer of the dual operator $D\circ A$ on the edge side. This identifies liability clearing as a finite-limit construction in the ambient data category. The construction is functorial under change of coefficient category: a Clearing Invariance Theorem shows that a finite-limit-preserving functor compatible with constraint subobjects induces a canonical isomorphism on global-section objects, enabling uniform comparison of clearing problems across categories of payment data. Existence, uniqueness, and iterative computation of clearing sections are organized by the structure carried on payment objects: Tarski's theorem yields existence and a complete-lattice structure under complete-lattice global elements; Scott continuity refines this to convergent Kleene iteration; an acyclic underlying graph admits a unique clearing section in finitely many steps with no order or metric hypothesis; and Banach's theorem on global elements yields uniqueness under metric contraction. The Eisenberg--Noe model and lattice liability networks arise as special cases.

For a phenomenon $\boldsymbol{f}$ that is a function of $n$ factors, defined on a finite abelian group $G$, we derive its population statistics solely from its Fourier transform $\hat{\boldsymbol{f}}$. Our main result is an $m$-Coefficient/Index Annihilation Theorem: the $m$th moment of $\boldsymbol{f}$ becomes a series of terms, each with precisely $m$ Fourier coefficients --- and surprisingly, the coefficient indices in each term sum to zero under group addition. This condition acts like a filter, limiting which terms appear in the Fourier domain, and can reveal deeper relationships between the variables driving $\boldsymbol{f}$. These techniques can also be used as an analytical/design tool, or as a feasibility constraint in search algorithms. For functions defined on $\mathbb{Z}_2^n$, we show how the skew, kurtosis, etc. of a binomial distribution can be derived from the Fourier domain. Several other examples are presented.

In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying fungibility across units of notional. AmPOs replace explicit installment payments and the need for lapsing logic with an implicit payment scheme via the decay of the claimable notional. This amortization ensures all units evolve identically, preserving fungibility. We demonstrate that AmPO valuation can be reduced to an equivalent vanilla perpetual American option on a dividend-paying asset. This enables analytical expressions for the exercise boundaries and risk-neutral valuations for calls and puts. These formulas and relations allow us to derive the Greeks and study comparative statics with respect to the amortization rate. Illustrative numerical case studies demonstrate how the amortization rate shapes option behavior and reveal the resulting tradeoffs in the effective volatility sensitivity.

We study a minimal change to an observation-driven Bayesian Dirichlet ARMA (B--DARMA) for compositional time series: replace the raw additive log-ratio (ALR) residual in the moving-average block with a centered innovation that subtracts the Dirichlet conditional ALR mean, available in closed form via digamma identities. We prove a recursion-level first-order equivalence (in $1/ϕ$) between the centered specification and a digamma-link DARMA at fixed parameters, under explicit interior and lag-stability conditions. The result clarifies why the two specifications should be predictively indistinguishable in the high-precision regime but does not by itself govern the geometry of the Bayesian posteriors that re-estimation produces. On weekly Federal Reserve H.8 bank-asset shares (October~2015 through October~2025, $T=522$ weeks), predictive performance is statistically indistinguishable across $104$ rolling weekly origins on every accuracy metric examined, while Hamiltonian Monte Carlo divergent transitions are approximately an order of magnitude more frequent under the raw specification, driven by isolated rolling fits at which the raw posterior exhibits localized pathologies. A four-reference sensitivity analysis confirms that predictive equivalence is reference-invariant and that the geometric advantage of centering is preserved across references but varies with the prevalence of pathological raw fits, from a substantial reduction at the loans reference to parity at the cash reference. The practical implication is operational rather than predictive: centering avoids the catastrophic raw-MA divergence spikes that occur at isolated rolling origins, which matters for production workflows in which posterior simulation feeds downstream stress tests. The adjustment is analytic and plug-in, and requires only a local change to the MA innovation calculation.

This paper introduces the Generality-Accuracy-Simplicity (GAS) framework to analyze how large language models (LLMs) are reshaping organizations and competitive strategy. We argue that viewing AI as a simple reduction in input costs overlooks two critical dynamics: (a) the inherent trade-offs among generality, accuracy, and simplicity, and (b) the redistribution of complexity across stakeholders. While LLMs appear to defy the traditional trade-off by offering high generality and accuracy through simple interfaces, this user-facing simplicity masks a significant shift of complexity to infrastructure, compliance, and specialized personnel. The GAS trade-off, therefore, does not disappear but is relocated from the user to the organization, creating new managerial challenges, particularly around accuracy in high-stakes applications. We contend that competitive advantage no longer stems from mere AI adoption, but from mastering this redistributed complexity through the design of abstraction layers, workflow alignment, and complementary expertise. This study advances AI strategy by clarifying how scalable cognition relocates complexity and redefines the conditions for technology integration.

In this article we model chaotic dynamics in financial markets by treating the market price, and market makers' inventory, as anharmonic oscillators with a nonlinear coupling. The market makers' risk appetite being the key parameter that determines the degree of chaos in the system. The article demonstrates that whilst external shocks and random noise are important in the treatment of financial time-series, they are not necessary in order to generate unpredictable price changes.

Many tractable TANK models treat redistribution as a contemporaneous wedge. I show that this view is incomplete once wage contracts are type-specific. In a tractable Two-Agent New Keynesian model, each household type adjusts its nominal wage relative to its own previous wage. This own-lag contract makes the cross-type wage gap a payoff-relevant distributional state variable. The wage gap follows a second-order expectational law of motion and feeds back into aggregate demand through consumption dispersion. Inflation stabilization or contemporaneous profit-wedge neutralization therefore generally fails to restore the corresponding representative-agent allocation. Under the maintained commitment benchmark, RANK-equivalent stabilization from period $t=1$ onward requires history-dependent transfers that respond to inherited wage dispersion, not only current profits. In the benchmark calibration, wage rigidity raises the peak output response to a transfer shock by a factor of 3.27, from $2.49\times 10^{-4}$ to $8.14\times 10^{-4}$.

We develop a model of choice over social norms that allows for complementarities along two dimensions: \textit{technological}, analogous to complementarities between consumption goods, and social, capturing returns from conformity. Together, these determine whether two norms are complements, substitutes, or independent, as defined by how the equilibrium prevalence of one norm responds to a marginal shift in the utility of another. We estimate the model using repeated cross-sections from Sierra Leone and Nigeria, focusing on female genital cutting, polygyny, and child marriage. Social returns are significant across all specifications. For female genital cutting and child marriage, we find evidence of complementarities, especially strong in Sierra Leone. For polygyny and child marriage, we find evidence of social substitutability, particularly in Nigeria. We interpret these differences using insights from anthropology. Finally, we iterate the model forward to study policy counterfactuals, assessing the potential effects of legal reforms and social interventions.

Instruction-tuned language models exhibit behavioural fairness in high-stakes decisions while retaining biased associations in their internal representations. However, whether these suppressed representations can affect model outputs - and whether such causal potency is symmetric across demographic groups - remains unknown. We investigate the use of open-weight models for mortgage underwriting using matched applications that differ only in racially-associated names and reveal a critical disconnect: models show no output-level bias, yet retain and amplify demographic representations across model layers. Through activation steering and novel cross-layer interventions, we demonstrate that this suppressed information is decision-relevant: when reinjected at critical layers, it produces near-complete decision reversals. Critically, this latent bias is asymmetric - steering interventions affect decisions in one demographic direction, while producing minimal effects in reverse - and susceptible to adversarial prompt engineering and parameter-efficient fine-tuning. These findings demonstrate that behavioural audits focused on outputs are insufficient: fair outputs can mask exploitable internal biases. They also motivate dual-layer testing frameworks combining output evaluation with representational analysis for AI governance in high-stakes decisions.

Financial markets such as bond, derivatives, and repo markets form networks of interdependent obligations. Existing multilateral netting methods typically trade off the extent of netting against preservation of counterparty exposure: central clearing reallocates exposure to a central counterparty, while trade compression may alter bilateral counterparty relationships. TradeMech is a mechanism for markets in which one or two homogeneous fungible objects are traded. The mechanism transforms a network of initial bilateral contracts into chains and cycles, nets the designated object multilaterally on those chains and cycles, and replaces initial contracts with multiparty contracts whose assigned trades remain fractions of the original bilateral trades. The construction achieves maximal multilateral netting of the designated object while preserving each agent's contractual profit and preserving the location of counterparty risk. When a party fails to pre-commit a required object, the affected assigned trade is recovered as a bilateral contract between the same original counterparties and the remaining assigned trades are re-netted on residual chains, so no new counterparty exposure is created.

In educational settings, AI can be used as a learning aid, but can also be used to avoid schoolwork, thereby passing classes while learning little. Many existing studies on the impact of AI on education focus on AI use in controlled settings or with specialized tools. In this paper, the dropoff in ChatGPT activity during non-school summer months in 2023 and 2024 is used to identify areas with heavy educational AI use and thus estimate the educational impact of AI as it is actually used. I find no meaningful impact of AI usage on high school test score averages in either direction. These results imply that, to the extent that high school students use AI to avoid learning, it either does not matter much for their test performance or is cancelled out by positive uses of AI in the aggregate.