One way I like to analyze these things is in real-world examples. Usually all these cognitive processes have analogies or metaphors or results in the real world. For example, about Si you said:
The traditional example of Se was an athlete practicing a jump shot in basketball or a pitch in baseball over and over, comparing the feel and results of each repetition, until he can pin down the absolute perfect way to make that shot or pitch.
As for Si, I gave the example of a scientist working up a taxonomy, i.e., taking a jumble of objects and analyzing their features with the goal of categorizing the elements of that jumble into a coherent system. And the more elements they can analyze, the tighter they can make the system.
Or think of an accountant going through a company’s books, taking disordered records and creating order from them and standardized financial statements.
And I said that this resembles Ni and Ne in that it involves holding a set of items in one’s mind and contrasting among and between those items with the goal of extracting data.
Now here you talk about Ni:
For what it’s worth, I talked in my previous post about how I experience my Ne and noted that I don’t notice any such archetypes/algorithms in using it. My Ne just tends to use whatever's at hand to generate new combinations and new spins on things; but it's a haphazard process, at least until it suddenly stumbles in the right direction and gets close to a desired solution. To back that up, here’s an old post I wrote about my real-world experience of Ne. It’s kind of “cutesy” in the way that I presented it, but hopefully it will convey the sense: Se wants to develop Ne
In turn, it would be good if you could spell out the Ni process a little more tangibly than you’ve done so far. I realize it’s tougher for introverted functions than for extraverted functions. But I’m not getting much understanding from your explanation so far, and I really am curious about this. Or even if you could quote some Jung or something.