Keith wrote:
"Is it step 7)?"

"7) From 6), the energy crossing quarter wave points is zero"

False, as are several other of Keith`s speculations.

Standing waves throughout a long transmission line with a hard short or
open-circuit at its end are proof enough that SWR nulls other than the
one at the actual discontinuity don`t bring the energy crossing 1/4-wave
points to zero. SWR nulls other than the one at the actual open or short
have no effect on traveling waves, absent an additional actual
discontinuity. SWR can`t exist without energy flow in both directions.
Energy flow is continuous. It doesn`t start and stop at SWR nulls. This
continuity is proved by measurements at the nulls, taken in one
direction at a time.

No speculation or even math is needed to observe this behavior on an
actual line. It is usless to try to conform the observable to some
theory. It is far more productive to conform theory to the observable.

Best regards, Richard Harrison, KB5WZI