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Darwin’s theory also asserts that there is an ancestry in the continuum leading from species to species and that is what I am saying requires a quantization of the continuum to assert.

The divergence of our understanding begins here. If I say that you are descended from your grandfather, it's true that there is an intermediate generation to be identified. I don't see how this requires "a quantization of the continuum to asset." We don't disagree that individuals are quantifiable. It's the chain of common descent that makes up the continuum. True, each generation is made up of individuals. That's not a contradiction, or an invocation of the fallacy.

Thank you for your reply!

The divergence of our understanding begins here.

Indeed. But Darwin's theory of a continuum of biological life was not based on any particular person's descent but rather the descent suggested by the geologic record. Of course, there is no written historical record to authenticate the descent and no mortal eyewitness survives.

So the theory of such a continuum is an interpretation of evidence which has been quantized by fossils along the geologic way. Which is why I said this:

IOW, if the evidence for a continuum is the quantization of it and the quantization of a continuum is a fallacy per se then ipso facto evolution is false.

If the quantization of a continuum is not a fallacy per se then we don't have a problem either with evolution or abiogenesis or seeking to answer the question, "in nature, what is life?"

It cuts both ways.