Manuscript VIII-B@3 · VIII-B-v3.tex · section · 3aa6baa1

Cone, graph, and vertices

Reference specialization at mu0=pi/2 › Cone, graph, and vertices · lines 2536–2578

VIII-B@3#eq:reference-coefficients, VIII-B@3#eq:reference-family

At $μ = μ_{0}$ ,

α = \frac{π}{2}, z_{α} = 0, S_{α} = 1, a = \frac{2}{3}, b = \frac{3}{5}, c = \frac{11}{30}, r = 3, β = \frac{3}{2}, χ = \frac{15}{11} .

Write $d_{i} = e_{i} (μ_{0})$ . The graph is

F_{s}^{(0)} = s + min {2, max {\frac{2}{3} (ξ + ζ), s + \frac{3}{5} min {ξ, ζ}}} .

The rays are successive right-angle boundary rays of three sectors; $d_{3}$ is the developed upper seam copy.

The vertices and times become

A_{i} = 3 d_{i}, D_{i} = 4 d_{i}, B_{i} = \frac{3}{2} s d_{i}, C_{i} = \frac{15}{11} s (d_{i} + d_{i + 1}),

T (A_{i}) = T (D_{i}) = 2 + s, T (B_{i}) = 2 s, T (C_{i}) = \frac{31}{11} s .

The particle time remains $s$ for $s \leq 0$ and $2 s$ for $s \geq 0$ . The resting collar is $7/2 \leq ρ \leq 4$ .

With $A = id$ , the packet is

(p, π /2, W_{0}, t, id, J_{0}), J_{0} = J (π /2) .

The timelike $t$ is not the spatial ray $d_{0}$ .

Displayed formulas in this passage

VIII-B@3#eq:reference-coefficients · line 2539
$α = \frac{π}{2}, z_{α} = 0, S_{α} = 1, a = \frac{2}{3}, b = \frac{3}{5}, c = \frac{11}{30}, r = 3, β = \frac{3}{2}, χ = \frac{15}{11} .$
VIII-B@3#eq:reference-family · line 2548
$F_{s}^{(0)} = s + min {2, max {\frac{2}{3} (ξ + ζ), s + \frac{3}{5} min {ξ, ζ}}} .$
unlabeled · line 2559
$A_{i} = 3 d_{i}, D_{i} = 4 d_{i}, B_{i} = \frac{3}{2} s d_{i}, C_{i} = \frac{15}{11} s (d_{i} + d_{i + 1}),$
unlabeled · line 2564
$T (A_{i}) = T (D_{i}) = 2 + s, T (B_{i}) = 2 s, T (C_{i}) = \frac{31}{11} s .$
unlabeled · line 2573
$(p, π /2, W_{0}, t, id, J_{0}), J_{0} = J (π /2) .$