Manuscript VII-E@1 · VII-E.tex · section · b713cf3c

Four moving affine faces

One certified four-face slicing exchange › Four moving affine faces · lines 1995–2011

VII-E@1#eq:transverse

The exchange is transverse:

ℓ ˙_{-} (0^{-}) = - \frac{16}{25} < 0, ℓ ˙_{+} (0^{+}) = \frac{16}{39} > 0.

The mixed adjacencies $E N, E S, W N, W S$ persist. In their respective quadrants they satisfy

p ∣ x ∣ - q ∣ y ∣ = δ s .

The only remaining core pairs are $E W$ and $N S$ , already determined. The exchange is forced by this prescribed maximum rule, not by a uniqueness theorem for all slicings of the spacetime.

Displayed formulas in this passage

VII-E@1#eq:transverse · line 1998
$ℓ ˙_{-} (0^{-}) = - \frac{16}{25} < 0, ℓ ˙_{+} (0^{+}) = \frac{16}{39} > 0.$
unlabeled · line 2005
$p ∣ x ∣ - q ∣ y ∣ = δ s .$

Nearby in this section

section: Four moving affine faces
proposition: Proposition: Spacelike ordering and central exchange