Manuscript En06-A@1 · En06-A.tex · corollary · e04c9892

Corollary: Sharp coarse signalling speed

A precise coarse relational outcome-law theory › Sharp speed and nondegenerate relays · lines 1439–1454 · proof included or linked

En06-A@1#cor:coarsespeed

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Define $c_{coarse}$ as the supremum of $∥ x_{B} - x_{A} ∥_{2} / (t_{B} - t_{A})$ , $t_{B} > t_{A}$ , over matched modification signalling pairs localized arbitrarily near $A, B$ . Then

c_{coarse} = c .

Proof. For a ratio greater than $c$ , sufficiently small neighborhoods of $A$ have positive distance from the past of neighborhoods of $B$ . Theorem thm:coarseDOD excludes a law difference. Theorem thm:relays attains the limiting boundary.

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unlabeled · line 1444
$c_{coarse} = c .$

Nearby in this section

theorem: Theorem: Directional geometric and coarse relays
section: Sharp speed and nondegenerate relays