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Further, mutations will be passed on no matter what, favorable, benign or detrimental. That brings selection pressure to bear again.

This was my original point.

I think you have been studying too much mathematics and have had too few courses in the various biological-related sciences. My own coursework which is relevant here is in human races, and just in this one field I see real-world results differing from what you are postulating; that makes me distrust your model.

As I understand the basic premise of evolution, it is mutations that are favored by natural selection pressures will be passed on to succeeding generations (and the corollary that those detrimental will cause the demise of the individual and not be passed). The accumulation of enough of these “favorable” mutations leads to the emergences of a new species. On the other hand, the accumulation of enough “detrimental” mutations leads to the extinction of a species. Is this an incorrect statement of the basic premise of evolution?

On the other hand, the accumulation of enough “detrimental” mutations leads to the extinction of a species. Is this an incorrect statement of the basic premise of evolution?

This part isn't quite right. I don't think any species gradually mutates itself into extinction. Rather, due to environmental changes (climate, predators, whatever), it's unable to survive.

As I understand the basic premise of evolution, it is mutations that are favored by natural selection pressures will be passed on to succeeding generations (and the corollary that those detrimental will cause the demise of the individual and not be passed). The accumulation of enough of these “favorable” mutations leads to the emergences of a new species. On the other hand, the accumulation of enough “detrimental” mutations leads to the extinction of a species. Is this an incorrect statement of the basic premise of evolution?

Yes, it is an incorrect statement of the basic premise of evolution. Perhaps it would be easier for you to actually study the theory of evolution rather than trying to shoehorn it into your desired strawman?

As I understand the basic premise of evolution, it is mutations that are favored by natural selection pressures will be passed on to succeeding generations (and the corollary that those detrimental will cause the demise of the individual and not be passed). The accumulation of enough of these “favorable” mutations leads to the emergences of a new species. On the other hand, the accumulation of enough “detrimental” mutations leads to the extinction of a species. Is this an incorrect statement of the basic premise of evolution?

Yes, this is an oversimplification on the order of "See Spot run!"

There is no one "favorable" or "detrimental" in most individuals. There are thousands of benign (here and now), slightly detrimental (here and now), slightly beneficial (here and now), etc. The range is huge. That seems to be the point you are missing.

Try a close look at sickle-cell anemia. One single trait. Bad news, right? Right, except that it provides some resistance to malaria. So, the efficacy of this particular trait (out of millions) depends on--is there malaria here? If there is malaria here, then you have a slight advantage in that one area, while still maintaining the disadvantage of the anemia. If there is no malaria, the slight advantage of malaria resistance does no good, and the anemia is still detrimental.

Multiply this by thousands of traits. The folks with the best overall adaptations for here and now (and here and now is always changing) survive and reproduce a little better than those who do not. Toss in a few million years and stir well.

But forget the mathematical models until you have a handle on the variables. If you can't figure out all the variables, and correctly model them, your mathematical models don't mean much in the real world.