I've been successful via my search math. For your claim, as far as I know, you are correct, but actually that does not make my search engine and its math impossible.
> That will produce a set of techniques that are observed to increase the ranking.
Ranking? I can't resist, to borrow from one of the most famous scenes in all of movies: "Ranking? What ranking? We don't need no stink'n ranking".
Nowhere in my search engine is anything like a ranking.
People pay tens or even hundreds of thousands of dollars to move their result from #2 to #1 in the list of Google results.
My user interface is very different from Google's, so different there's no real issue of #1 or #2.
Actually that #1 or #2, etc. is apparently such a big issue for Google, SEO, etc. that it suggests a weakness in Google, one that my work avoids.
You will see when you play a few minutes with my site after I announce the alpha test.
Google often works well; when Google works well, my site is not better. But the post I responded to mentions some ways Google doesn't work well, and for those and some others my site stands to work much better. I'm not really in direct competition with Google.
Yes, but capturing meaning mathematically is somewhat an unsolved problem in both mathematics, linguistics and semiotics. Your post claims you have some mathematics but (obviously as it's a secret) doesn't explain what.
SEO currently relies on keywords, but SEO as a practice is humans learning. There is a feedback loop between "write page", "user types string into search engine" and "page appears at certain rank in search listing". Humans are going to iteratively mutate their content and see where it appears in the listing. That will produce a set of techniques that are observed to increase the ranking.