Abstract The double-cone geometry is a saddle of the gravitational path integral. which explains the chaotic statistics of the spectrum of black hole microstates. This geometry is the usual AdS-Schwarzschild black hole. but with a periodic identification of the time coordinate; the resulting singularity at the black hole horizon is regulated by making the geometry slightly complex. https://macorners.shop/product-category/engravable-bead-name-cuff-bracelet-with-birthstone-gift-box/