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It IS a fact that the allele frequencies of the gene pools of populations of organisms change over time. That is the definition of the term evolution. Therefore evolution is a fact.

If one accepts your posit that the definition of evolution is only “change,” then I can hardly take exception to your assertion. However, below is a definition of the term quoted from a dictionary, which you can see includes a primary element of the “theory”:

ev·o·lu·tion: Biology. Change in the genetic composition of a population during successive generations, as a result of natural selection acting on the genetic variation among individuals, and resulting in the development of new species. [emphasis mine]

The inclusion of the element of theory (indicated by the emphasis above) in the dictionary definition of the word is what causes me to challenge assertions that “evolution is fact.” Removal of that theory element would eliminate my objections to use of the word as a descriptor. However, its inclusion remains the source of my objection.

As my reading has indicated, as well as some of the posters on this thread have observed, there is not even a consensus in the scientific community as to what constitutes a “species” and differentiates one from another. Consequently, it becomes extremely difficult to take exception to what an advocate of evolution (as noted by the above definition) could chose to call a “new” species.

Nonetheless, please do not come to the conclusion that I abjure the theory of evolution. I do not. However, I do not accept it as “fact,” merely a potentially plausible explanation of observations that is subject to challenge, modification and even revocation.

Please allow me to skip the remaining portion of your explanation as I find very little, if any fault (except as previously noted) with it, to your last sentence:

The changes are in the details, however, and thus far nobody has successfully challenged the basic principles of evolution.

You may consider the following postulates and reasoning as a challenge to the principles of evolution, or merely a questioning observation. (Please accept my apologies for being unable to get superscript number to appear. I have resorted to italics to indicate a superscript) Perhaps, you could respond to this sequence from your perspective.

1. Assume the following time line (source: http://pubs.usgs.gov/gip/geotime/ ):

Phanerozoic Eon (570-544 million years ago to present)

Cenozoic Era (65 million years ago to present)
Quaternary Period (1.8 million years ago to present)
Holocene Epoch (8,000 years ago to present)
Pleistocene Epoch (1.8 million to 8,000 years ago)
Tertiary Period (65 to 1.8 million years ago)
Pliocene Epoch (5.3 to 1.8 million years ago)
Miocene Epoch (23.8 to 5.3 million years ago)
Oligocene Epoch (33.7 to 23.8 million years ago)
Eocene Epoch (55.5 to 33.7 million years ago)
Paleocene Epoch (65 to 55.5 million years ago)

Mesozoic Era (248 to 65 million years ago)
Cretaceous Period (145 to 65 million years ago)
Jurassic Period (213 to 145 million years ago)
Triassic Period (248 to 213 million years ago)

Paleozoic Era (544 to 248 million years ago)
Permian Period (286 to 248 million years ago)
Carboniferous Period (360 to 286 million years ago)
Pennsylvanian Period (325 to 286 million years ago)
Mississippian Period (360 to 325 million years ago)
Devonian Period (410 to 360 million years ago)
Silurian Period (440 to 410 million years ago)
Ordovician Period (505 to 440 million years ago)
Cambrian Period (544 to 505 million years ago)

The Pre-Cambrian encompasses nearly 90% of the Earth's history, postulated as stretching from 4.5 billion years ago, to 570 million years ago when the fossil evidence first suggests living cells.

The most complex of Pre-Cambrian period life forms can be grouped into three categories: sponge-like animals, cnidarians, and worms. The sponges, and cnidarians (corals and sea anemones), are the most primitive with about 11 specialized cell types. Worms and higher metazoa have approximately 55 specialized cells.

Following the Pre-Cambrian period simple life forms, other, more complex forms of life are postulated to have appeared based upon fossil records. According to authorities the Paleozoic period includes the “Cambrian explosion” (so-called because of the appearance of all living animal phyla within a few millions of [for discussion, say, 5 million] years).

2. Assume a mutation rate for a single chromosome of 2.5 X 10-4 (estimated from Genetic Sampling Error of Distance (òµ)2 and Variation in Mutation Rate Among Microsatellite Loci by Lev A. Zhivotovsky, David B. Goldstein and Marcus W. Feldman)

3. Assume a beneficial mutation at a rate of 3 sigma (2.7 X 10-3). (Note: this estimate is exceptionally generous in complex animals to the evolution assumption… a more realistic beneficial mutation rate would be in the 10-6 or greater range.)

4. Assume a success rate of reproduction (i.e., surviving to reproductive maturity, finding a non-sterile mate or one which would be compatible with the mutated chromosome, passing the chromosome and survival of the succeeding generation) of 80% (8.0 X 10-1). (Note: this estimate is also generous in complex animals to the evolution assumption given disease, food scarcity, predation, natural disasters, etc.)

5. Intuitively, it is obvious that all of these conditions (and some others not even discussed) must exist simultaneously. Therefore, just multiplying the numbers, the probability of a single beneficial mutation trait being passed is a number with between 6 and 10 zeroes in front of it.

6. In conclusion, even though the “Cambrian explosion” period may have been millions of years long, the likelihood of enough beneficial mutation-generated traits being created to generate a single new species appears very remote. The odds against the appearance of all living animal phyla due to this mechanism are even greater. This is especially so since the current theory of evolution requires a hierarchy of development, i.e., certain complex animals had to exist and experience enough mutations to create the next branch of complexity.

Obviously, the numbers used as estimates can be manipulated to increase showing the probability of emergence of a single beneficial trait, and indeed, the actual numbers may be different. However, the fact remains that even millions of years is not long enough for a purely random change mechanism such as mutation to generate all of the change, both in the number of traits (multiple chromosome mutations simultaneously) and increased complexity (increased number of chromosomes) attributed to the “Cambrian explosion” period.

Is the above posit a sufficient challenge to the current theory of evolution in your estimate?

"Is the above posit a sufficient challenge to the current theory of evolution in your estimate?"

No. You can't just pull numbers out of your posterior and think it is science.

During the precambrian, as life was evolving, it took a good long time for one celled animules to turn into primitive organisms (involving multicellular organization).
We don't have much evidence because of the nature of the animules and the very old age of the rock you have to find to get any fossils. Also, we can't assume that life was all that widespread for a good length of time. If fumeroles under the ocean, as some postulate, were where life first formed, it might have taken eons to spread from there.

But when you do falsify evolution, let me know. I will be your press agent for a 10% cut.

Evolution is defined as I have stated by scientists. The definition in your dictionary is more along the lines of what scientists refer to as the theory of evolution. Whether or not "species" can be adequately defined (or whether it is even a fundamentally important concept) isn't particularly relevant. "Different species are formed by the process of evolution" is equivalent to saying that the changing allele frequencies in the gene pools of populations of organisms are sufficient to produce the diversity of life observed today and in the fossil record. As far as your challenge to evolution goes, it is a legitimate challenge, but it falls short. Any argument based on probabilities, no matter how good, is only sufficient to show that an occurrance is unlikely, not that it didn't happen. Analogously, I can show that the particular sequence of the last 50 powerball drawings was even more unlikely than what your argument shows the precambrian explosion to be. I don't think that anyone will argue that the last 50 powerball drawings didn't happen, though. Given enough trials of a probabilistic occurrance and some very unlikely things will happen. I once had a statistics professor assign the class to flip a coin 10000 times and record the results. He could always tell who did it and who just made up results. How? Most people think that flipping a coin and having heads come up 10 times in a row is pretty unlikely. However the probability of this happening is 1 in 1024. So in 10000 real coin flips, it's actually pretty likely to happen. People who make up the results very rarely write down sequences of heads (or tails) longer than 3 or 4 in a row. It would be exceedingly unlikely that there would not be sequences of at least 7 or 8 in a row in a series of 10000 flips. The point is that you shouldn't discount randomness when looking at an event. People think they know what random processes look like intuitively, but their intuition is usually faulty. I am not an expert on precambrian (or any other type) of biology, so I don't know if the numbers you use are reasonable or not. However, I don't think that they rule out an evolutionary process.

Re #2: Not all genes have the same mutatation rate.

Re #3: Beneficial cannot be determined ex ante, only ex post. Most mutations are neutral and thus not selected for or against.

Re #4: False premises again. Bacteria need not find mates. Even with sexual reproduction, chromosomes with mutated genes work fine (in general) with the original from the mate.

Re #5: This claim is just false, even if it fits your intuition. The math is wrong too, there are more than 10**14 bacteria just hanging around in your gut thus something with a 10**(-10) chance of happening will happen to you about 10000 times.

Re #6: Millions of years gives 10**10 times for things like #5 to happen, and that's only in your gut.

You need to get the mechanisms and arithmetic correct.

...there is not even a consensus in the scientific community as to what constitutes a “species” and differentiates one from another...

Actually there is perfect consensus in science of what a species is. It just doesn't conform to the box that creationists want to put it in. Species are frequently in transition as we observe them, with many gradations of separation from each other. As we would expect from the theory of evolution.