You are correct up to but excluding the para beginning "Dear Sir". Thank you for persevering.
Para beginning "Dear Sir":
My Table 1 shows three objects have the same location parameter: -0.18. If the objects were 1D fermions this would already have broken Pauli's Exclusion Principle so that that particular metric would have exceeded its maximum content for holding fermions. Also Table 1 uses a finite and small number of different location parameters and that is the feature which I claim prevents intervals between fermions being zero on such a metric, assuming only one fermion per location. I realise that argument could be deemed circular. [My contest paper uses a preon model, with strings, so I do not have singularites for Standard model point particles, as they are divisible in my model. So I do not worry about the location parameters being points.]
I apologise for my lack of clarity. What I need to do is re-write my Rasch paper to bring in the new physics contexts. And I would understand if you deferred until I finished that paper. There is hardly any discussion in my Rasch paper because of the nature of origin of the paper. In a late use of Rasch in psychometrics before I retired an issue arose over whether one should use standard statistical tests of significance on the rasch results from a particlular experiment, ignoring that the results came from a Rasch analysis. Or could one squeeze more error out of the findings by using extra information from the fact that a Rasch analysis was used. And the paper was written for that psychometric purpose. But I realised that I could try to mimic the effects of GR compressing metrics near masses. So, as I was retired and could do as I pleased, I added that in without any discussion. I have since realised that the same data can be extended to try to show why the metric beaks down near a CCC node but I have not amended the discussion to explain how. It is not fair of me to explain on the hoof but maybe just one more para might help.
The part of your post that I agreed you had correct was emphasising that uncertainty was equivalent to homogeneity. That is for nearby space. The opposite is true for far flung space approaching a CCC node. That is, lack of homogeneity is equivalent to no error. And 'no error' implies a Guttman structure of data. And a Guttman structure of data plays havoc when constructing metrics. And not just the Rasch metric but any kind of metric, in my opinion. So the metric collapses at the CCC node.
Best wishes
Austin