This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

This paper traces the historical development of the square-and-multiply algorithm, arguing that while its conceptual foundation dates back to ancient Indian prosody, its formal articulation as a gener…

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

The paper introduces COVCAL, a risk-controlled method that precisely determines when a partial formalization signal from an autoformalizer can be trusted to certify the correctness of natural-language…

The paper improves Banaszczyk's inequality, providing a significantly better tail estimate for the discrete Gaussian measure on a lattice, which has applications in analyzing dual attacks against the…

This book provides a compact, derivation-oriented mathematical primer that connects major families of generative AI models, showing their underlying structural relationships.

The paper introduces AutoformBot, a multi-agent system that successfully autoformalizes a large corpus of open-access graduate-level mathematics textbooks into a verified library in Lean 4, demonstrat…

This paper settles the complexity of three sketching problems in graphs and distributions.

The paper introduces a computational framework using Hodge zero-modes to track the geometry of topological features in parameter-dependent data, providing metrics like curvature and holonomy to quanti…

The paper introduces COMPOSE, a dual-graph framework that generates plausible future mathematical theorems by simultaneously conditioning a language model on both the scientific citation context and t…

This paper analyzes the computational complexity of evaluating recurrent functions, showing that the complexity depends heavily on how the input offsets are encoded and the structure of the recurrence…

The paper introduces FormInv, a measurement protocol that reveals significant semantic inconsistencies in existing mathematical reasoning benchmarks, showing that standard accuracy metrics fail to cap…

This paper develops and analyzes various ensemble models, culminating in an XGBoost-based system, to reliably detect UAV intrusions using XAI and advanced statistical methods to pinpoint the root caus…

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

This paper develops a parameterized algorithm for the NP-complete Tree Containment problem, showing it can be solved efficiently based on a structural parameter called scanwidth.

This study investigated the stability and prompt-responsiveness of AI tools in classifying the cognitive demand of math tasks, finding that few-shot prompting was a more reliable performance booster t…

This paper provides the first unconditional proof for Weber's Conjecture for the case $k ext{ up to } 12$, which is crucial for lattice-based cryptography.

The paper provides the first machine-checked universal proof, using ring theory, that value-independence implies identical marginal distributions for arithmetic masking, thereby extending the verifica…

This paper improves the theoretical bounds for estimating discrete probability distributions using the $\ell_\infty$ norm, resolving several open questions in the field.

The paper introduces PostRI, a novel method that allows for computing a Randomization Interval (RI) for differentially private median queries after the median has already been estimated, significantly…