This becomes exceedingly dishonest. It has repeatedly been pointed out to you that neither Darwin himself nor anyone after expected the fossil record to be continuous. This is for inevitable reasons of geology as much as biology.
All that said, there are certain known cases where millions of years of geological deposition have continued uninterrupted on certain areas of sea floor.
Cores from such deposists have been microscopically examined and, guess what? Very long and sweeping completely smooth transitions exist.
Smooth Change in the Fossil Record.
A Smooth Fossil Transition: Foraminifera.
So where we have a gap-free fossil record, we have found instances of gap free evolution. So what were you saying?
If the evolution of life can be shown to be "in fact" inherently discontinuous then Darwin is falsified.
Perhaps the out is that it doesn't matter how many continuous histories we find, any discontinuous process of evolution falsifies Darwin?
Not really. Such discontinuous events as speciations by hybridization and polyploidy (I can Google, you can Google) have been identified and, no, Darwin is not falsified. These are rather interesting special cases which Darwin, knowing nothing of genetics, did not anticipate but it's no big deal.
. Not the fossil record. The evolution of life. I'm sorry if I didn't make myself clear.
The fossil record is "severely discontinuous" as Darwin admitted. And that was his gravest concern.