Ray,
You write, "I am not challenging the accuracy of Planck's Law."
That is not the issue! The real question is WHY Planck's Law is indistinguishable from the experimental data! The reason for this remarkable fact is because, as I show in my essay, Planck's Law is actually a mathematical tautology! This does not in any way take away any other 'truisms'. Rather provides more understanding of these. If such a mathematical fact brings to serious question other physical results, than in my humble opinion the physical results have to be more carefully reconsidered. Perhaps here lies more fruitful application of the Rosetta Stone in my essay!
Furthermore, it is a mistake to think that this results (re: Planck's Law) depends on any assumptions regarding the 'energy function', E(t). I show in my essay that Planck's Law taken as EXACT is mathematically equivalent to E(t) being a simple exponential function. However, if we take Planck's Law as a limit approximation (better than any experimental accuracy) then E(t) can be ANY integrable function. Thus, in all circumstances Planck's Law is a mathematical statement describing the interaction of measurement. And that explains why the 'measurements' are indistinguishable from the theory.
Ray, there are so many other results in my essay that neatly tie all together. Let me highlight three:
1)A relationship between entropy and time. This leads to a more intuitive interpretation of The Second Law of Thermodynamics to say that "all physical processes take some positive duration of time to occur".
2)Planck's Law and Boltzmann's entropy equation are mathematically equivalent.
3)The Photoelectric Effect can be explained without using photons. The photoelectric current obtained provides a better experimental fit that includes the 'asymptotic tail' to the data.
(I have not included this result in my essay, but details can be found at "The Photoelectric Effect Without Photons".
Best wishes,
Constantinos