Manuscript En03-A@1 · En03-A.tex · proposition · 5398614e

Proposition: Outgoing edge

External conical geometry and certified local moves › Four affine faces · lines 1566–1584 · proof included or linked

En03-A@1#prop:R3, En03-A@1#eq:outgoing-edge, En03-A@1#eq:outgoinglength

For $s > 0$ , $N, S$ share exactly

y = 0, ∣ x ∣ \leq \frac{Δ s}{p}, T = b s .

Its endpoints are $N S E, N S W$ , and its length is

ℓ_{+} (s) = \frac{2Δ}{p} s = \frac{16}{39} s .

Proof. Equality gives $y = 0$ ; dominance requires $p ∣ x ∣ \leq Δ s$ . The displacement is purely spatial.

Displayed formulas in this passage

En03-A@1#eq:outgoing-edge · line 1569
$y = 0, ∣ x ∣ \leq \frac{Δ s}{p}, T = b s .$
En03-A@1#eq:outgoinglength · line 1575
$ℓ_{+} (s) = \frac{2Δ}{p} s = \frac{16}{39} s .$