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

Proposition: Transversality and isolation

External conical geometry and certified local moves › Four affine faces · lines 1607–1627 · proof included or linked

En03-A@1#prop:R5, En03-A@1#eq:transversality

The central one-sided derivatives are

ℓ ˙_{-} (0^{-}) = - 2Δ/ q < 0, ℓ ˙_{+} (0^{+}) = 2Δ/ p > 0.

Mixed adjacencies $E N, E S, W N, W S$ persist. No other core pair exchanges a positive-length edge near the event.

Proof. Differentiate the central laws. In each quadrant a mixed adjacency lies on

p ∣ x ∣ - q ∣ y ∣ = Δ s

and extends from a central triple junction to the exterior. The only remaining pairs are $E W$ and $N S$ , already calculated.

Displayed formulas in this passage

En03-A@1#eq:transversality · line 1610
$ℓ ˙_{-} (0^{-}) = - 2Δ/ q < 0, ℓ ˙_{+} (0^{+}) = 2Δ/ p > 0.$
unlabeled · line 1622
$p ∣ x ∣ - q ∣ y ∣ = Δ s$