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gr-qc2026
Trilinear Kernel Structure and Its Gravitational Realization
Takeshi Fukuyama
We clarify the structural role of trilinear kernels in multidimensional integrable hierarchies and in stationary axisymmetric gravity. The Yu--Toda--Fukuyama (YTF) trilinear equati…
gr-qc2025
Tau--Function Multilinear Hierarchy of the Tomimatsu--Sato Spacetime: A Gravitational Realization of the YTSF Integrable Structure
Takeshi Fukuyama
The Tomimatsu--Sato (TS) family generalizes the Kerr black hole to higher multipole order and has long been regarded as algebraically complicated without any clear integrabilit…