Our universe as the
skin of a larger space.
A 4+1D numerical-relativity program. It treats our 3+1D universe as the boundary — the brane — of a bulk spacetime with one extra spatial dimension, sourced by a long-lived, white-hole-like engine whose radiation, filtered through that boundary, builds the matter, the vents, and the dark-sector physics we see from the inside.
Five papers
The solver, the derived brane, the birth run, the dark-energy chain, and the string completion.
PicturesThe theory, drawn
From the bulk and its brane through the birth to the vents — every figure marked measured or conceptual.
BibliographyWhat it answers to
The work WHD builds on and the results it has to survive — supports, threats, and context.
NarrativeIn plain language
Short essays that carry the picture one image at a time, before the equations.
Lead paper
The 4+1D Discontinuous Galerkin Engine
DraftingA spectral numerical-relativity solver for a five-dimensional bulk
We present a discontinuous Galerkin (DG) spectral-element solver for generalized-harmonic numerical relativity in 4+1 spacetime dimensions, targeting a hypercubed-sphere domain (eight cubed-sphere wedges per radial shell) with Legendre–Gauss–Lobatto collocation, upwind penalty fluxes at inter-element faces, fourth-order Adams–Bashforth time integration, and a Hesthaven–Warburton modal exponential filter for high-mode control. The vacuum and generalized-harmonic (GH) pipeline is validated end-to-end on a single GPU (sm_120 Blackwell tested), with bit-equality enforced between CPU and GPU kernel evaluations to a per-kernel tolerance of 1e-13 and an end-to-end pipeline tolerance of 1e-12. No finite-difference stencils are used anywhere in the solver; all spatial derivatives are spectral. This paper documents the solver's architecture and its validation methodology — it makes no claim about the physics content (matter sector, brane, or birth mechanism) evolved on top of it; those are the subject of the four papers that follow.
Read the paper →