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…

This paper establishes an exact mathematical correspondence between training and inference in deep learning and the solution of Hamilton-Jacobi partial differential equations, unifying multiple theore…

This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.

The paper provides a constructive, intuitionistically valid proof of Rice's Theorem and the Halting Problem undecidability by reducing the problem to the undecidability of Hilbert's Tenth Problem (MRD…

The paper introduces Iteris, an agentic research system, demonstrating its capability to generate numerical evidence, constructions, and proof drafts for open problems in computational mathematics, re…

This paper characterizes the graph structure, including cycle and path lengths, of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, demonstrating strong regularities desp…

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…

The paper uses majorization theory to analyze lattice reduction, showing that local swaps smooth the Gram-Schmidt profile and deriving variational and telescoping identities for the worst-case profile…

The paper presents a novel and significantly faster algorithm for computing the second discrete homology group of a graph by identifying five basic quotient shapes of the 3-cube.

The paper proposes a novel method to identify parsimonious explicit piece-wise polynomial relationships, demonstrating its effectiveness in modeling the inverse kinematics of industrial manipulator ro…

This paper determines that verifying global parameter identifiability for linear ODE models is an NP-hard problem, establishing a computational complexity boundary for the field.

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

The paper provides a unified algebraic framework to determine the formal language expressivity of recurrent neural language models, resolving conflicts in existing literature by linking expressivity 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 validates a specialized mathematical metric (the Burau-Lyapunov exponent) designed for detecting privilege escalation in cloud IAM graphs by applying it to an unrelated physical system: sola…

The paper investigates which quantum encodings can be applied directly to classical data point clouds while preserving the topological invariants necessary for topological data analysis (TDA).

The paper introduces a mathematical and cryptographic framework for exactly recovering a single, noisy, high-dimensional discrete path from aggregated and incomplete observable data.

Ramos and White's theorem on multiplicity stability of rational homology for configuration spaces of certain graphs is extended and computed for various families of graphs using computer algebra.

The paper provides the first machine-checked, tridirectional correctness proof of the OpenZeppelin reentrancy-guard pattern against complex, production-deployed Solidity smart contract source.