Lattice Spacing Is A Checked Repeat

Larger Spacing Has Smaller Reciprocal

Changing the repeat changes the reciprocal spacing. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A wider spacing has a smaller reciprocal spacing

With spacing 4 meters, the checked reciprocal is one-fourth inverse meters.

a=4 m,b=1/4 per ma=4\ \mathrm{m},\quad b=1/4\ \mathrm{per\ m}
Wider repeatThe reciprocal label changed with the source spacing.a=4 mb=1/4 1/ma*b=1

The old reciprocal would not be allowed

The product still closes to 1; a stale one-half label is not a renderable state.

ab=4⋅1/4=1a b=4\cdot 1/4=1
No stale labelThe validator binds the reciprocal to the lattice source.a=4 mb=1/4 1/ma*b=1