Manuscript VIII-A@3 · VIII-A-v3.tex · section · 2398a747

Marked sectors and the graph family

The complete fixed-cone construction › Marked sectors and the graph family · lines 1456–1476

VIII-A@3#A:eq:particle

No regular tangent plane at the singular particle is asserted. The worldline intersection is

P_{s} = {(s, 0, 0), (2 s, 0, 0), s \leq 0, s \geq 0.

It moves along the fixed worldline; this does not change the packet.

Take the compact patch $ρ \leq 4$ and the marked collar $7/2 \leq ρ \leq 4$ . The collar and exterior are resting spatially, with equation $T = 2 + s$ . “Prescribed exterior” means this translating resting exterior, not a frozen embedded time slice.

Displayed formulas in this passage

VIII-A@3#A:eq:particle · line 1460
$P_{s} = {(s, 0, 0), (2 s, 0, 0), s \leq 0, s \geq 0.$

Nearby in this section

section: Marked sectors and the graph family
figure: Developed wedge and one seam crossing
lemma: Lemma: Uniform realization bounds