Five papers, in sequence
The solver they all run on comes first, then the physics built on top of it: the brane derived rather than assumed, the birth run that is the program's headline result, the chain that ties the wall to dark energy, and the string completion — released last, and labeled conjecture.
- 01
A 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.
- 02
Deriving the brane as a resolved domain wall, not an assumed thin membrane
We construct the brane — our 3+1D universe — as the fixed locus of a Z2 (reflection × SU(2)-center) identification of a doubled 4+1D bulk, rather than positing it as an infinitely thin membrane with hand-chosen junction conditions. Under this identification, every field's boundary behavior (Dirichlet for odd fields, Neumann for even fields, vanishing flux for all) is a theorem of the symmetry, not a modeling choice. The Higgs-like field is odd under the identification and has no spatially-uniform mode on a closed slice; the only way it can roll off its unstable symmetric point while respecting the identification is a domain-wall (kink) profile pinned to zero on the mirror itself — so the brane is the *endpoint of an instability*, never an inserted object. We show the resulting layer is numerically resolved, not thin-wall expanded (gravitational thickness κσδ ≈ 1.4, an O(1) number with no small parameter to expand in), derive the layer's emergent tension and attached matter density as integrals over the resolved profile rather than inputs, and show the construction admits no image-wall collision: the mirror is totally geodesic and reflects every field without exception.
- 03
The headline result — status: not yet run to the program's own admissibility bar
We report a full 4+1D numerical-relativity simulation of the WHD birth mechanism: a small, closed, symmetric-phase universe — sourced by the gravitating energy of an unstable ("tachyonic") hilltop configuration of the Higgs-like field — evolves forward under gravity, matter, and gauge dynamics with no engine, brane, or vent inserted by hand. We show a macroscopic, long-lived, white-hole-like engine forms at the spatial origin as the non-linear endpoint of the hilltop instability, and that it persists (drive balances infall) rather than promptly evaporating or collapsing. This is the program's headline result: nothing about the engine's existence, size, or longevity is assumed anywhere upstream — every one of those properties is an output of evolving the same four microphysics parameters used everywhere else in the program.
- 04
An equation-of-state history w(z) as the external, falsifiable test
We propose an operational definition of dark energy within the WHD program: the running balance between energy the engine feeds the brane and energy the brane sheds back to the bulk, rather than a bare cosmological constant. A renormalization convention fixes the settled vacuum's energy to exactly zero, so the two contributions — a time-independent constant and a genuinely dynamical, bulk-sourced term — are distinguishable rather than degenerate. The mechanism predicts a specific wall-drain exponent Γ_w governing how fast the loaded brane sheds stored energy, which in turn predicts a specific *shape* for the dark-energy equation-of-state history w(z) — a falsifiable target distinct from a cosmological constant's flat w = −1, testable against current and next-generation large-scale-structure surveys (DESI-class data). This paper depends on the birth-run engine actually existing and behaving as claimed; its quantitative content cannot be finalized ahead of that result.
- 05
Conjecture, clearly labeled — the candidate string origin of WHD's constants
A candidate ultraviolet completion of WHD: its low-energy constants and matter content read as correlated fingerprints of a single non-supersymmetric, strongly-coupled charged brane–antibrane string vacuum (Type IIA on T⁵/Z2, an O4₊ orientifold, a magnetized D6 giving SU(2)). The Higgs is the open-string tachyon, so its mass is forced — m² = −1/2α′ — not chosen; the tachyon kink is our brane; and the Z2 mirror that defines the brane is shown to be an exact string orbifold: the residual K-theory class evaluates to zero, three independent ways. A dark sector is forced (the induced charge equals the family number, two), with a dynamically-selected net charge and a falsifiable dark-radiation ceiling (ΔN_eff ≲ 0.02, below CMB-S4 reach). We are emphatic about the ceiling: the vacuum sits at genuine strong coupling with no weak-coupling corner, which caps the claim that it is the selected vacuum at grade M, irreducibly. Realizable is not selected — this is a consistency proof of a candidate, not a derivation of reality, and it is load-bearing for nothing: every required gate in the WHD program stands whether or not any part of this survives future scrutiny.