Cecil, W5DXP wrote:
"Seems to me, canceled waves must "cease to exist" at a point in space
time if they exhibit zero measurable evidence of their existence forever
after---."

A union of two waves can make them both disappear if they are exact
opposites, but elimination of just one of the two produces the the
other. Were the two waves actually annhilated by their coexistence on
the path together, they would not be exhibitable on demand by
turning-off one or the other constituent.

Best regards, Richard Harrison, KB5WZI