Measuring Long-Range Structure in the Voynich Manuscript

[quimqu]

There is one more step that completes the picture.

If the gap is not generated inside lines, and not inside paragraphs, what about pages?

So I ran the same type of test again, but this time at the page level. First, I shuffled words only inside each page. Then I kept each page intact and shuffled the order of entire pages. Here is the summary (Currier, punctuation removed, normalized by H1):

Shuffle scheme	Tail gap	Normalized gap
Global token shuffle	0.00250	0.00094
Shuffle within lines	≈ 0	≈ 0
Shuffle within paragraphs	≈ 0	≈ 0
Shuffle within pages	≈ 0	≈ 0
Shuffle order of lines	0.00251	0.00094
Shuffle order of paragraphs	0.00062	0.00023
Shuffle order of pages	≈ 0.00205	≈ 0.00077

Now the structure becomes much clearer.

If we shuffle words inside lines, the gap disappears.
If we shuffle words inside paragraphs, the gap disappears.
If we shuffle words inside pages, the gap disappears.

So the anomaly is not produced inside lines.
It is not produced inside paragraphs.
It is not even produced inside pages.

But when we shuffle the order of entire lines, nothing changes.
When we shuffle the order of paragraphs, the gap drops sharply.
When we shuffle the order of pages, the gap drops slightly, but remains large.

This combination is important. It means the long-range gap depends on two things at the same time:

1. Internal coherence inside large blocks (pages and paragraphs).
   
2. Systematic differences between those blocks across the manuscript.
   

If we destroy the internal coherence of a page by shuffling its words, the effect vanishes.
If we keep pages intact but rearrange them, the effect survives.

That tells us the main driver is not simply the linear order of pages. It is the fact that different parts of the manuscript have different statistical profiles, and that those profiles are preserved inside pages.

In other words, the manuscript behaves like a set of statistically distinct blocks. When we globally shuffle all words, we destroy that block structure and the contrast becomes visible as a long-range MI gap.

Inside a page, however, the behavior is much closer to stationary. The anomaly only emerges when we treat the whole manuscript as one homogeneous string and then break that structure.

So if we put everything together:

• The gap is not a line-level effect.
  
• It is not a paragraph-level word-order effect.
  
• It is not caused by punctuation.
  
• It is not removable by simply reordering pages.
  
• It reflects large-scale structural segmentation of the manuscript.
  

This strongly points toward macro-level organization rather than local sequential constraints. The long-range anomaly appears to be a property of how the manuscript is partitioned and organized globally, not of how words are arranged inside sentences or paragraphs.

That is a very different picture from a purely local generative mechanism.