Thanks.
And you know that these derivations (etc) are rigorous because:
a) you personally checked them out
b) you asked someone you know is unaffiliated with Mills et al. and who you independently know has deep knowledge and experience
c) you trust Mills implicitly (i.e. you never consider independent checking to be relevant)
d) something else?

Re this: "the (1 + 1/n) factor multiplying the spherical harmonic term arises from the trapped photon in the excited electron"
How does a free electron know how many transitions it will undergo, before it reaches the ground state? As I'm sure you know, an electron may "jump" directly to the ground state, or undergo potentially a (countable) infinite number of jumps (a cascade). As each transition results in the emission of a photon, the free electron must have from one to a (countable) infinite number of "trapped photons", right?
My hilite.Please see Appendix I of the GUTCP. Per Haus's derivation, the electric field E perpendicular to the current field J is found from analysis of the space time Fourier components in (k, omega) space. Haus shows that radiation in the perpendicular requires components of J(omega/c * n, omega). Mills extends this analysis to the bound electron and the orbitsphere and shows the condition under which radiation is not allowed.
In case of the excited state, a simplified explanation is provided starting on page 28 of the GUTCP of how the internal electric field leads to instability. In equation I.113, the (1 + 1/n) factor multiplying the spherical harmonic term arises from the trapped photon in the excited electron. With n = 2, 3, 4 . . . of the excited states, a fractional charge is felt by the electron. This creates a radial doublet function, which as a result (see the discussion starting around equation 2.30) creates components in the Fourier transform that lead to radiation.
And you know that these derivations (etc) are rigorous because:
a) you personally checked them out
b) you asked someone you know is unaffiliated with Mills et al. and who you independently know has deep knowledge and experience
c) you trust Mills implicitly (i.e. you never consider independent checking to be relevant)
d) something else?
Re this: "the (1 + 1/n) factor multiplying the spherical harmonic term arises from the trapped photon in the excited electron"
How does a free electron know how many transitions it will undergo, before it reaches the ground state? As I'm sure you know, an electron may "jump" directly to the ground state, or undergo potentially a (countable) infinite number of jumps (a cascade). As each transition results in the emission of a photon, the free electron must have from one to a (countable) infinite number of "trapped photons", right?
What makes it obey fick's laws? Lacking any buoyancy it will sink to the center of the gravity well. You know what happens when you concentrate hydrinos at the center of a deep gravity well?