Differences between SGP8 and the standard SGP4? Is it ever used in practice?

Question

The Wikipedia article Two Line Element Set says:

The SGP4 model was later extended with corrections for deep space objects, creating SDP4, which used the same TLE input data. Over the years a number of more advanced prediction models have been created, but these have not seen widespread use. This is due to the TLE not containing the additional information needed by some of these formats, which makes it difficult to find the elements needed to take advantages of the improved model. More subtly, the TLE data is massaged in a fashion to improve the results when used with the SGP series models, which may cause the predictions of other models to be less accurate than SGP when used with common TLEs. The only new model to see widespread use is SGP8/SDP8, which were designed to use the same data inputs and are relatively minor corrections to the SGP4 model.

Then the Wikipedia article Simplified Perturbations Models says:

SGP8/SDP8 introduced additional improvements for handling orbital decay.

Note that the current usage of the term SGP4 tends to refer to implementations that contain both SGP4 proper and SDP4, the switchover being at a period of 225 minutes.

The reference for the above quote is Revisiting Spacetrack Report #3: Rev 2 which says:

Spacetrack Report Number 3 officially introduced five orbital propagation models to the user community—SGP, SGP4, SDP4, SGP8 and SDP8—all “generally” compatible with the TLE data. At the time, SGP had just been replaced by SGP4/SDP4 (the latter having included deep-space perturbations). The SGP8/SDP8 model was developed to alleviate deficiencies of SGP4/SDP4 for the special cases of orbital decay and reentry. The approach provided a closed-form solution based on the general trends of orbital elements as they neared reentry, and was quite successful. However, there is no evidence to suggest that SGP8/SDP8 was implemented for operational TLE formation.

1. Is this "closed-form solution based on the general trends of orbital elements as they neared reentry" the only significant difference between SGP8 and SGP4?
2. What is this closed-form solution? Is there a reference for further reading?
3. What does "...there is no evidence to suggest that SGP8/SDP8 was implemented for operational TLE formation..." mean exactly? A "forensic" examination of TLEs shows no sign that they are being generated for SPG8? Or no evidence that people are using SPG8? Something else?
4. Is SGP8 ever used in practice?

Answer 1

About fifteen years ago, I very carefully implemented SGP8 and SDP8 (and the 'original' SGP) into my software (see https://github.com/Bill-Gray/sat_code ). It is hard to prove a negative -- i.e., that the 8 versions never saw any use -- but I've since seen SDP4/SGP4 get an incredible amount of use, and have seen the 8 variants get absolutely zero use and have never seen a reference to them being used.

I should note that I work almost exclusively with objects in multi-day to multi-month orbits, rather than those about to re-enter. Still, people using my code (of whom there are many) do use it for a lot of purposes; I think if they were using the 8 variants, I'd have heard about it.

But the convincer, to me, would be the 'Revisiting Spacetrack Report #3' comments. Those of us outside Space-Track/JSpOC/etc. have to do a certain amount of reverse-engineering; details on how SGP4/SDP4 are implemented internally, for example, have never been publicly released. The authors of 'Revisiting' are not only experts in this field; they also have some inside knowledge and access to historical data which I lack. If they can't come up with a case where the 8 versions were used, I'd be reasonably confident such use never occurred.