Physics
Initial data for a time machine from dust: an explicit composite construction with a certified ordinary-density scaling regime
An explicit composite initial-data construction: vacuum pp-wave core, umbilical slice, dust envelope, and a verified hand-off to Ori outer layers. The full-layer retune makes both gates positive, with an ordinary-density regime at depth that is a certified scaling extrapolation.
Jonathan Schemoul
This paper constructs explicit initial data for an asymptotically flat time machine in the Ori program: a vacuum pp-wave core with boost-identified z-circles, an umbilical slice with pure-trace extrinsic curvature, a dust envelope, and a verified hand-off to Ori outer layers.
The final construction includes a full-layer retune. A one-knob delay of the stage-one K-relaxation onset removes the collar marginality. At a = 0.02 both constraint gates are positive over the full envelope layer r > w, including the innermost collar: exact interval jets give a subluminal-dust margin of at least 4.55 times 10 to the minus six at one millimetre, a dense exact-jet scan is positive everywhere, and the boundary torus is the exact vacuum continuation. On the gatefast interior band the sampled margins are +0.763129 for the Hamiltonian gate and +0.728189 for the subluminal-dust gate, and the 21/21 plus or minus 30 percent robustness checks still pass. The hand-off to Ori Layer 2 is re-verified.
The dust density scales as k0 squared, but at fixed rho0 and dimensionless z-period the total mass scales only as k0. The canonical corner is not ordinary matter; the ordinary-density regime is reached at the deep rung k0 about 2.2 times 10 to the minus twelve, at 778 kilograms per cubic metre. That regime is a certified scaling extrapolation, not a directly gate-verified point of the canonical family. The scaling group is confirmed to 10 to the minus eight.
Key results
- Full-layer collar retune: both gates positive on r > w at a = 0.02, with exact-jet margins.
- Gatefast interior band: H1 at least 0.7468 and WEC margin at least 0.2736, certified.
- Hand-off to Ori Layer 2 verified; 21/21 robustness passes.
- Mass law: density proportional to k0 squared, total mass proportional to k0 at fixed rho0 and z-period.
- Ordinary density only at the deep-rung scaling regime, which is an extrapolation of the certified scaling law.
Status and limits
This is a 15-page content-complete draft. The certified continuum cell bound, the composite-background elliptic constant, analytic band bounds, the full open-band O(a) uniformity conjecture and late-time evolution remain open. It has not been submitted or peer reviewed.