I don't have much time right this second, but a couple of comments:
I deliberately asked the redshift/distance question because I know your program cannot derive it. It is inherently non-linear.
It is useless to say the distance in a 'static' space because we are not in a static space. So any distance you derive is based on a linear Doppler shift approximation which is good only for very small redshifts.
Most people forget that the better interpretation of redshift is that of the expansion of the space itself which is inherently non-linear. Hence we have redshifts greater than 1 which classically implies recession velocities greater than c. This paradox is the consequence of applying special relativity to a situation where it does not apply. That is the metric of spacetime we need to use on the largest scales is that of a curved spacetime and not an asymptotically flat Minkowski metric. I cannot use the same coordinate system to represent myself and the distant (high z) galaxy. This is also borne out of the fact that energy conservation in general relativity is a local law that applies only with the said flat (Minkowskian) metric. When using a dynamic FRW metric it is not possible to formulate a 'conservation of energy' rule - You cannot make a meaningful statement of the total energy and hence derive a conservation. This is because energy conservation is dependent on the arrow of time and the problem becomes which (or whose) time do you use. For example the total energy of the Universe in a Hamiltonian approach is zero, in other calculations you get other values (pseudotensor methods.)
Thus there is no way HLT can handle this.
It will automatically give wrong values because it uses the wrong physics. To me that means it is worthless in these questions.
I'm still unclear by what your 'energy' is in the Boyle's law example.
Also how did you get a 'mass' for the photon. Please show me the HLT calculation.
The reason I pointed this out is that it is already known to have an UPPER limit way less than this. In fact the value is almost undoubtedly ZERO. Any value you have determined is almost undoubtedly WRONG. There are big consequences of a photon mass that are not observed, hence the very small upper limits from astrophysical observations. Any non zero value that HLT determines (and I'd love to see how you did it) is based upon WRONG physics, period. If you show me how, I'll show you why it's wrong.
AND to address the basic issue of what you are doing
Your tool might reduce everything down to a simple relationship as you say - BUT IN DOING SO IT DOES THE WRONG PHYSICS IF IT DOES THIS REDUCTION.
Sure it works for a simple f=x/y relationship but my God I can do that in my head already. HLT gains me nothing and obscures if anything.
I can show you get the wrong redshift/distance.
I can show your photon mass calc. (if you show it) is wrong.
I also would like to see your black hole calculation. I am still puzzled why you mentioned a UV photon? That seemed to me to hint you don't know any GR. Please expound - i.e. show the HLT calculation to derive this.
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