Lattice Spacing Is A Checked Repeat

Reciprocal Spacing Is the Inverse Repeat

The reciprocal spacing is source-bound to the repeat. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The toy reciprocal spacing is the exact inverse

The real-space spacing is 2 meters, so the toy reciprocal spacing is one-half inverse meters.

a=2 m,b=1/2 per ma=2\ \mathrm{m},\quad b=1/2\ \mathrm{per\ m}
Toy reciprocal spacingThis uses b equals one over a, not two pi over a.a=2 mb=1/2 1/ma*b=1

The product closes to one

The source-bound product is 1.

ab=2⋅1/2=1a b=2\cdot 1/2=1
Inverse checkA stale reciprocal label would fail validation.a=2 mb=1/2 1/ma*b=1