1. The mapping between DOM content and Visible content should be well-behaved.
As a simple example, take document (a) consisting of the words 'an axiom' styled white on a white background, and document (b) an empty document with default styling of black text on a white background. Both would appear blank.
Now apply an edit, say inserting the text 'a fallacy' into both documents. After the edit, document (a) can be expected to remain blank while document (b) can be expected to show 'a fallacy'.
I think if you want #1, you need an isomorphism between documents and their appearance. This article only asks for a homomorphism, where different documents are allowed to produce the same result.