The displayed gap list is bound to transition sources. 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 displayed list is not independent data

The upper-to-ground line is listed as 9 joules because its source transition has that gap.

ΔEupperground=9 J\Delta E_{upper\to ground}=9\ \mathrm{J}
Source-bound gapsThe gap list reads from transition sources.anchor=groundcount=3gap0=4 Jgap1=9 Jgap2=15 Jlowerupper4lowerupper9lowerupper15

A stale edited gap is not a renderable state

If that displayed gap were changed without changing its source transition, validation would stop the lesson.

valid list=4, 9, 15valid\ list=4,\ 9,\ 15
No stale listThe validator rejects stale line-series gap fields.anchor=groundcount=3gap0=4 Jgap1=9 Jgap2=15 Jlowerupper4lowerupper9lowerupper15