Proposed Manuscript Chronology

[npcompl33t]

Could you please give more details on these experiments?  Especially

• Which statistics do you compute for each page, and how many are there?
  
• How do you compute the distances between the centroids?
  
• How did you generate the random clouds?
  

Meanwhile, here is my attempt to reproduce your experiment, without the "intrinsic order"premise.

Thanks for the response.

Statistics: 
I calculate two first order glyph transitions per page, essentially a 1st order markov representation, using the Zaterra 2022 slot alphabet. One is a pure word level , the second i concatenate all words in a line together. I did this because I noticed early herbal A in particular has low text, and using these different representations produces different but useful features to the top, so by combining them I get the unique distinctions each contains.

Distances:
I never compute centroid differences. The page-to-page distance is Jensen Shannon divergence between their transition matrices. I calculate the differences between each of the two independently, then average the distances together. JSD behaves like a squared Euclidean distance. D(X,Y) is the mean JSD over all page pairs across sections X and Y, and D(X,X) the mean over distinct pairs within X. D′(X,Y) = D(X,Y) − ½[D(X,X) + D(Y,Y)] is then an unbiased estimate of the squared distance between the two section centroids. For your S, use √D′.

Random Clouds
I compare best achievable orders. For a given ordering, a triplet fails if its two ends are not the farthest pair. I take the order with the fewest failures out of all, for the real sections and the random null draw. I didnt simulate fake word point clouds, I used the real 15 centroid distances shuffled among the network pairs, and six random centroids drawn from a standard gaussian distribution in 3, 5 and 50 dimensions, with those distances standing in for D′

Your Experiment
I was able to reproduce your numbers, however S measures straightness, not ordering, and it depends on the dimension. Random variance off the axis adds to every dimension equally. In 50d, the same x10 stretch gives S = 1.4, yet its best order leaves at most 1 triplet out of place 58% of the time. This is dramatically different from my results. My sections have S from 1.15-1.6. By pure S, they look like your random cube, but by order, they do not. 6 random centroid in 4 D leave two or more triplets out of place 96% of the time.

Your stretched cloud passes my test by construction, because it is only a 1 axis model. If that's the case, we agree on the overall geometry: sections differ mainly along one direction and the correlated character and digraph frequencies are that direction. I didn't tune a metric to pick this.

In your model, each section sits at a point on the axis, and pages scatter around it at random. So two leaves of one bifolio, with different plants, should be no closer on the axis than any two pages of that section. However, this is not the case. In Herbal A, they land in the same batch 85% of the time. Pure random placement would only give 30%. The position on the axis I've identified follows the sheet the page was written on. This is exactly what an order based on production would predict, and one that a fixed topic axis does not.

Happy to answer any additional questions.