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

Proposition: C2b with zero slack

Euclidean cone convergence and microscopic compatibility · lines 1233–1246 · proof included or linked

En06-A@1#prop:C2b

For the increasing-stencil family,

ℓ_{n} = sup {∥ x - y ∥_{2} : d_{n} (x, y) \leq 1} \leq ε_{n} = c Δ t_{n} .

Every scheduled dependency path of $k$ ticks has Euclidean displacement at most $c k Δ t_{n}$ .

Proof. A distance-one displacement is a generator displacement. Sum the one-step bounds and use the triangle inequality.

Displayed formulas in this passage

unlabeled · line 1235
$ℓ_{n} = sup {∥ x - y ∥_{2} : d_{n} (x, y) \leq 1} \leq ε_{n} = c Δ t_{n} .$