Manuscript VII-J-ST@1 · VII-J-ST.tex · section · f1f1d82c

The prescribed transverse event

Prescribed spacetime, support, and the incidence input › The prescribed transverse event · lines 309–333

VII-J-ST@1#eq:family, VII-J-ST@1#eq:slices

Use a cut wedge of angle $3 π /2$ , divided into three right-angle sectors. In each sector let the dimensionless coordinates be $ξ, η \geq 0$ , and put

ρ = ξ + η, h = \frac{2}{3} (ξ + η), k = \frac{3}{5} min {ξ, η}, F_{s} = s + min {2, max {h, s + k}}, - 1 \leq s \leq 1.

The functions agree on identified sector rays. The prescribed product markings are

Σ_{s} : τ = F_{s} (x), z = ℓ ζ,

with no axial dependence in $F_{s}$ . The formula is VII-F's transverse family, explicitly lifted rather than identified with a three-dimensional cell count CheungVIIF.

Displayed formulas in this passage

VII-J-ST@1#eq:family · line 314
$ρ = ξ + η, h = \frac{2}{3} (ξ + η), k = \frac{3}{5} min {ξ, η}, F_{s} = s + min {2, max {h, s + k}}, - 1 \leq s \leq 1.$
VII-J-ST@1#eq:slices · line 324
$Σ_{s} : τ = F_{s} (x), z = ℓ ζ,$

The prescribed transverse event

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