I sympathise and empathise fully with you and hope you are now getting some sleep. I am in my fourth week of flu. I sent in my contest essay when the flu was at its worst. I went to bed tonight but was too ill to sleep and so am typing this three hours after midnight.
I think I am not explaining myself well. I am possibly the only person who sees any relevance of Rasch analysis to Penrose's CCC. There are no Rasch papers written, as far as I know, pertaining to cosmology. Rasch analysis is used for tasks such as item analysis in examinations and analysing questionnaire scales. Quite often measurements or ratings get added and averaged etc without much care about the nature of the rating scale. The Rasch analysis aims to improve the quality of the scale of the results, for example by adding or averaging modified ratings rather than adding the raw ratings.
Forget the previous links that I listed.
Try the wiki website:
https://en.wikipedia.org/wiki/Rasch_model
for an overview of the Rasch model.
However, the only Rasch paper that I can show you which is not using Rasch in a standard psychometric context is my own paper at
http://vixra.org/abs/1609.0329
In that paper you can see a number of metrics made by the Rasch model. Some of these metrics break down. I am suggesting that these metrics break down possibly for the same reason that the metric breaks down at the end of a Penrose CCC cycle. And that reason is the nature of the data is too perfectly Guttman, with too little error in the data. This idea does make a bold assumption that the universe's space metric can somehow be constructed and destructed in a similar manner to running a Rasch analysis! And maybe this is too off-beat a step for you to want to follow it further? If so, that would be understandable.
Best wishes
Austin