Sky Pelletier Waterpeace

arXiv2026

SoK: Evolution, Security, and Fundamental Properties of Transactional Systems

Transaction processing systems underpin modern commerce, finance, and critical infrastructure, yet their security has never been studied across the full evolutionary arc of these systems. Over five decades, transaction processing has progressed through four distinct generations, from centralized databases, to distributed databases, to blockchain and distributed ledger technologies (DLTs), finally to multi-context systems that span cyber-physical components under real-time constraints. Each generation has introduced new transaction types and new classes of vulnerabilities, yet security research remains fragmented by domain, and the foundational ACID transaction model has not been revisited to reflect the demands of contemporary systems. We classify 163 papers on transaction security by evolutionary generation, security focus, and relevant Common Weakness Enumeration (CWE) entries, and distill a curated set of 41 high-impact or seminal papers spanning all four generations. We make three principal contributions. First, we develop a four-generation evolutionary taxonomy that contextualizes each work within the broader trajectory of transaction processing. Second, we map each paper's security focus to CWE identifiers, providing a systems-oriented vocabulary for analyzing transaction-specific threats across otherwise siloed domains. Third, we demonstrate that the classical ACID properties are insufficient for modern transactional systems and introduce RANCID, extending ACID with Real-timeness (R) and N-many Contexts (N), as a property set for reasoning about the security and correctness of systems that must coordinate across heterogeneous contexts under timing constraints. Our systematization exposes a pronounced bias toward DLT security research at the expense of broader transactional security and identifies concrete open problems for the next generation of transaction processing systems.

cs.CR↗

arXiv2025

A Novel Generalization of the Liouville Function $λ(n)$ and a Convergence Result for the Associated Dirichlet Series

We introduce a novel arithmetic function $w(n)$, a generalization of the Liouville function $λ(n)$, as the coefficients of a Dirichlet series. By spatially encoding information in a natural way about the distribution of prime factors among natural numbers, $w(n)$ allows results to be obtained which rely intrinsically on the distribution of primes without having direct knowledge of that distribution. We prove some properties of the distribution of $w(n)$ and then provide a result on the convergence of its Dirichlet series. A parametrized family of functions $w_m(n)$ is defined of which $w(n)$ is a special case. We show that each function $w_m(n)$ injectively maps $\mathbb{N}$ into a dense subset of the unit circle in $\mathbb{C}$ and that each $F_m(s) = \sum_n \frac{w_m(n)}{n^s}$ converges for all $s$ with $\Re(s)\in\left(\frac{1}{2},1\right)$. Finally, we show that the family of functions $w_m(n)$ converges to $λ(n)$ and that $F_m(s)$ converges uniformly in $m$ to $\sum_n \frac{λ(n)}{n^s}$, implying convergence of that series in the same region and thereby proving an interesting property about a closely related function.

math.NT↗