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arXiv:2410.09574hep-th

Amplituhedra and origami, I: tree level

Pavel Galashin

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Abstract

We establish a precise correspondence between points of the $m=4$ tree momentum amplituhedron and origami crease patterns. As an application, we prove that the BCFW (Britto-Cachazo-Feng-Witten) cells triangulate the $m=4$ tree amplituhedron both in momentum space and in momentum-twistor space. As another application, we show that every nondegenerate weighted planar bipartite graph $Γ$ admits a t-embedding, i.e., an embedding of the planar dual of $Γ$ such that the sum of angles of white (equivalently, black) faces around each vertex is equal to $π$.

arXiv comments
79 pages, 16 figures. First paper in the series (see arXiv:2606.03439 for part 2). v2: Major revision. Added a proof of the BCFW tiling conjecture in momentum-twistor space via T-duality and a new proof of the origami-amplituhedron correspondence using double-dimer model identities. Full changelog at the end of the introduction. v3: Minor updates
Journal reference
DOI
Subjects
hep-thHigh Energy Physics, Theory math-phMathematical Physics math.AGAlgebraic Geometry math.COCombinatorics

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Linked by 1 identifiable commenter in 2 comments across 2 threads, from Oct 2025 to Jul 2026. Found in 1 HN submission from Oct 2025 to Oct 2025. Open submission discussions.

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Discussed in comments2 threads

  1. Make an Origami Circuit Board 1 comment

    • "Amplituhedra and origami" (2025) https://arxiv.org/abs/2410.09574 ... "Origami Patterns Solve a Major Physics Riddle" (2025) https://news.ycombinator.com/item?id=45492704 : > In a proof posted in October 2024 (opens a new tab), he showed that patterns that arise in origami can…

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  2. [dead] 1 comment

    • From https://news.ycombinator.com/item?id=45241431 : > "Perihelion precession of planetary orbits solved from quantum field theory" (2025) https://arxiv.org/abs/2506.14447 : >> We derive the perihelion precession of planetary orbits using quantum field theory extending the…

      westurnerView on HNParent context

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