4 papers
Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs
Alan Sorani, Ashvni Narayanan, Michael Shalyt +8
As AI's mathematical capabilities rapidly improve, meaningful benchmarks are shifting from university-level problems and math olympiads to research-level mathematics. The Ramanujan…
Patterned Numbers: A Novel Number Classification with Structural and Quantum Algebraic Perspectives
John TM Campbell
We introduce \emph{patterned numbers}, a digit--divisor-based classification of integers motivated by recreational mathematics. A number is defined to be patterned if at least one…
Optimization of Bottlenecks in Quantum Graphs Guided by Fiedler Vector-Based Spectral Derivatives
John TM Campbell, John Dooley
This paper discusses the relationships between the Fiedler vector, the Cheeger constant, and threshold behaviors in networks of quantum resource nodes represented as Quantum Direct…
Testing Link Fidelity in a Quantum Network using Operational Form of Trace Distance with Error Bounds
John T. M. Campbell, Nicola Marchetti, John Dooley +1
Quantum state comparison, utilizing metrics like fidelity and trace distance, underpins the assessment of quantum networks within quantum information theory. While recent research…