Jonathan Washburn

most citedCoherent Comparison as Information Cost: A Cost-First Ledger Framework for Discrete Dynamics

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math.CO2026

From one generator to loop order on the three-cube

Jonathan Washburn, Milan Zlatanović

We study the monoid $W$ of based closed walks on the $1$ -skeleton of the three-dimensional cube $Q_{3}$ . The fundamental group of this graph is the free group $F_{5}$ . We prov…

math.CO2026

The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs

Sebastian Pardo-Guerra, Anil Thapa, Jonathan Washburn

Let $G$ be a finite connected simple graph with a chosen orientation of its edges. For the edge potential $ψ (t) = cosh t - 1,$ we minimize $\sum_{e \in E^{\to}} ψ (z_{e})$ over each affine c…

math.CO2026

Matching Rules as Cocycle Conditions: Discrete Potentials on Penrose and Canonical Projection Tilings

Sebastian Pardo-Guerra, Jonathan Washburn, Elshad Allahyarov

Aperiodic tilings support two classically studied but hitherto separately presented structures: matching rules, which enforce global order via local constraints, and height functio…