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Kenyon College

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Research library9linked papers
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Selected work

Representative Papers

Combinatorial Bounds for Codes over Metric Spaces: Ramsey-Sidorenko Thresholds and Subgraph Counts

Jul 29, 2026

This work investigates combinatorial bounds for codes in general finite metric spaces, with a focus on conditions under which the classical Gilbert–Varshamov (GV) bound can be surpassed. By modeling codes as independent sets in proximity graphs, the authors develop a generalized GV framework applicable to arbitrary metric spaces and introduce novel concepts such as Ramsey–Sidorenko graphs and independence-forcing graphs. Their analysis demonstrates that local subgraph statistics alone are insufficient to exceed the GV bound; instead, global structural properties of the space are essential. Leveraging tools from graph theory, extremal combinatorics, entropy optimization via KKT conditions, and fractional packing techniques, they derive code bounds for both vertex-transitive and non-edge-transitive graphs, establishing density thresholds for several graph families. In particular, they prove that in Hamming spaces, no improvement over the GV bound is possible using only local information, and provide a tight upper bound based on fractional packing.

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New Codes from Cyclic and Negacyclic Codes of Even Length over $\mathbb{Z}_4$

Jun 07, 2026

This study addresses the construction of linear codes with improved parameters and high-performance binary quantum codes by systematically investigating cyclic and negacyclic codes over even-length quaternary rings for the first time. Leveraging algebraic coding theory and structural analysis, the authors develop an efficient computer-aided search algorithm that identifies 2,500 new cyclic codes and 730 new negacyclic codes, all of which surpass the best-known codes in terms of parameters. These newly discovered codes further enable the derivation of a collection of binary quantum codes with excellent parameters, significantly expanding the current repertoire of available codes for quantum error correction.

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On the History of the Square and Multiply Algorithm

May 30, 2026

This study investigates the historical origins and formalization of the square-and-multiply algorithm, clarifying its cross-cultural evolution spanning over two millennia. Through rigorous historical documentation, textual analysis, and comparative historiography of mathematics, the paper systematically traces the algorithm’s development from its embryonic binary notions in Pingala’s Sanskrit prosody in ancient India, through refinements by Arabic scholars al-Uqlidisi and al-Biruni, to its first explicit articulation as a general-purpose algorithm by al-Kashi. The research affirms al-Kashi’s originality in formulating the algorithm in its universal form, elucidates the profound mathematical significance underlying Pingala’s early work, and fills a critical gap in scholarly understanding of the origins of this foundational computational method.

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The AI Fiction Paradox

Mar 13, 2026

This study addresses the “AI fiction paradox”—the puzzling inability of current AI systems to generate high-quality fictional narratives despite being trained extensively on modern novels. The work systematically examines the fundamental limitations of Transformer-based models in novel generation through three interrelated dimensions: narrative causality, information re-evaluation, and multi-scale emotional architecture. It introduces, for the first time, the concepts of “narrative causality” and “information re-evaluation,” exposing an inherent conflict between temporal logic in storytelling and the attention mechanism’s static token processing. Furthermore, the paper proposes a multi-scale emotional modeling framework that integrates narrative theory with empirical evidence from seven-year emotional arcs. Beyond explaining why AI struggles to replicate human-authored fiction, the research also issues a critical warning: overcoming these limitations could enable large-scale manipulation of human behavior.

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Recent publications

Latest Papers

Combinatorial Bounds for Codes over Metric Spaces: Ramsey-Sidorenko Thresholds and Subgraph Counts

Jul 29, 2026

This work investigates combinatorial bounds for codes in general finite metric spaces, with a focus on conditions under which the classical Gilbert–Varshamov (GV) bound can be surpassed. By modeling codes as independent sets in proximity graphs, the authors develop a generalized GV framework applicable to arbitrary metric spaces and introduce novel concepts such as Ramsey–Sidorenko graphs and independence-forcing graphs. Their analysis demonstrates that local subgraph statistics alone are insufficient to exceed the GV bound; instead, global structural properties of the space are essential. Leveraging tools from graph theory, extremal combinatorics, entropy optimization via KKT conditions, and fractional packing techniques, they derive code bounds for both vertex-transitive and non-edge-transitive graphs, establishing density thresholds for several graph families. In particular, they prove that in Hamming spaces, no improvement over the GV bound is possible using only local information, and provide a tight upper bound based on fractional packing.

0 citationsRead paper

New Codes from Cyclic and Negacyclic Codes of Even Length over $\mathbb{Z}_4$

Jun 07, 2026

This study addresses the construction of linear codes with improved parameters and high-performance binary quantum codes by systematically investigating cyclic and negacyclic codes over even-length quaternary rings for the first time. Leveraging algebraic coding theory and structural analysis, the authors develop an efficient computer-aided search algorithm that identifies 2,500 new cyclic codes and 730 new negacyclic codes, all of which surpass the best-known codes in terms of parameters. These newly discovered codes further enable the derivation of a collection of binary quantum codes with excellent parameters, significantly expanding the current repertoire of available codes for quantum error correction.

0 citationsRead paper

On the History of the Square and Multiply Algorithm

May 30, 2026

This study investigates the historical origins and formalization of the square-and-multiply algorithm, clarifying its cross-cultural evolution spanning over two millennia. Through rigorous historical documentation, textual analysis, and comparative historiography of mathematics, the paper systematically traces the algorithm’s development from its embryonic binary notions in Pingala’s Sanskrit prosody in ancient India, through refinements by Arabic scholars al-Uqlidisi and al-Biruni, to its first explicit articulation as a general-purpose algorithm by al-Kashi. The research affirms al-Kashi’s originality in formulating the algorithm in its universal form, elucidates the profound mathematical significance underlying Pingala’s early work, and fills a critical gap in scholarly understanding of the origins of this foundational computational method.

0 citationsRead paper

The AI Fiction Paradox

Mar 13, 2026

This study addresses the “AI fiction paradox”—the puzzling inability of current AI systems to generate high-quality fictional narratives despite being trained extensively on modern novels. The work systematically examines the fundamental limitations of Transformer-based models in novel generation through three interrelated dimensions: narrative causality, information re-evaluation, and multi-scale emotional architecture. It introduces, for the first time, the concepts of “narrative causality” and “information re-evaluation,” exposing an inherent conflict between temporal logic in storytelling and the attention mechanism’s static token processing. Furthermore, the paper proposes a multi-scale emotional modeling framework that integrates narrative theory with empirical evidence from seven-year emotional arcs. Beyond explaining why AI struggles to replicate human-authored fiction, the research also issues a critical warning: overcoming these limitations could enable large-scale manipulation of human behavior.

0 citationsRead paper