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Shunpei Shimizu

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#explainable ai Open access Oct 2026

An infinite family of non-star trees admitting Laplacian peak state transfer

Unrefereed AI-assisted preprint, version 0.2.2, 9 October 2026. No author affiliation is given. For each m >= 1, set q = m^2 + m + 1. Attach q intermediate vertices to a root and q - 1 leaves to each intermediate vertex. This produces infinitely many pairwise nonisomorphic non-star trees of order q^2 + 1, with root Lap...

Shunpei Shimizu · 0 citations
#explainable ai Editorial Open access Oct 2026

A Lean-verified proof of the empty-set-free height-five case of Frankl's conjecture

Unrefereed AI-assisted preprint, version 0.4.1, 9 October 2026. Every finite nonempty union-closed family of distinct nonempty finite sets with inclusion height at most five has an element occurring in strictly more than half its members. Height counts members in a strict inclusion chain. This is the empty-set-free hei...

Shunpei Shimizu · 0 citations

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