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

Proposition: Spacelike capped slices

External conical geometry and certified local moves › Compact collar and frozen exterior · lines 1746–1766 · proof included or linked

En03-A@1#prop:cap

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The capped graph is continuous, piecewise flat, and $p$ -Lipschitz. It agrees with $T = H + s$ near $\partial K$ , and retains the lower time increment $a (s_{2} - s_{1})$ . Both central edge laws remain unchanged in the window.

Proof. Minimum and maximum preserve a common Lipschitz bound and a common lower time increment. Strict collar margins give the resting boundary neighbourhood. The incoming central height margin is

H + s - a s = 2 + s /5 \geq 9/5;

the outgoing margin is

H + s - b s = 2 + s /13 \geq 25/13.

Thus the cap does not clip the central edges.

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unlabeled · line 1758
$H + s - a s = 2 + s /5 \geq 9/5;$
unlabeled · line 1762
$H + s - b s = 2 + s /13 \geq 25/13.$

Proposition: Spacelike capped slices

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