A One-Page Ledger Method for Generating Voynich-Like Text

[Dunsel]

If you compute the correlation between S2 Herbal B and S2 Quire 13, I expect it will be lower than your S2 vs S3 correlation of 0.948 — despite being the same "scribe." That would mean the within-scribe variation exceeds the between-scribe variation, which is hard to reconcile with a multiple-scribe model but follows naturally from a continuous evolutionary gradient.

I ran the comparison you suggested, and yes, your prediction is technically correct — but the separation is not large.

Using Zandbergen/Landini:

comparison	Pearson	cosine
S2 Herbal B vs S2 Quire 13	0.918	0.928
S2 Herbal B vs S3 Quire 20	0.942	0.949
S2 Quire 13 vs S3 Quire 20	0.926	0.934

Using Takahashi, where my other computations are from:

comparison	Pearson	cosine
S2 Herbal B vs S2 Quire 13	0.887	0.898
S2 Herbal B vs S3 Quire 20	0.945	0.951
S2 Quire 13 vs S3 Quire 20	0.925	0.931

So, yes: S2 Herbal B is closer to S3 Quire 20 than to S2 Quire 13 in both transcriptions.

But the size of the effect matters. In Zandbergen/Landini, the Pearson gap is only 0.024 and S2 Quire 13 vs S3 Quire 20 is 0.926, only 0.001 higher than the same comparison in Takahashi at 0.925. So this is not a large collapse of scribal structure. It is a small but real sign that section/regime can cut across scribal hand.

That is actually compatible with what I am arguing: scribal hand, section, and production weighting are separable variables. All of my modeling to this point has focused on Scribe 1.  To clarify that method before looking into the <ed> heavy later scribes.  The chart below shows the same point visually. That <ed> does not divide perfectly by Davis scribe, but it does separate Scribe 1 very cleanly from the later <ed>-heavy sections.  And, aside from the Herbal section which has scribe 2 sheets mixed into quires with scribe 1 sheets, you can almost pick out each section by scribe and <ed> density.

   

[Jorge_Stolfi]

• You need a seed text (a "visible source") to start the process. (1)

• The modify step must respect the complex word structure. (2)

I think we can tie 1 and 2 together and say that if there is some template that all words should conform to (something like curve-line system + or one of your grammars), then 1 could be just generating a set of random seed words according to the template (seems easy, I did something like this in You are not allowed to view links. Register or Login to view. in this thread) and 2 is just making sure modifications still conform to the template.

Word templates like mine do not capture all the constraints we see in the actual Voynichese lexicon.  No matter how we define prefix, core, and suffix, these three parts are not independent.  My model specifies a couple of constraints (the counts of benches and dealers) but there are more.  Your own color tables show that, for one particular core, there are prefix-suffix pairs that are twice as common as expected, or half as common. I gave a couple of more dramatic examples of "skew squares" were Fr(AKX):Fr(BKX) is very different from Fr(AKY):Fr(BKY).

There is still no explanation for how the Author could have created words with those hidden statistical anomalies, both for the seed text and during modification.

The suggestion above does not seem to be very different from

1. Generate a lexicon of a couple thousand words with the required structure.
   
2. Create a seed text by picking among those words with a Zipf-like distrib.
   
3. Run self-copy, but instead of modifying a word, pick a similar one from the lexicon.
   

This variant would solve one of my objections by keeping the lexicon stable.  But it still does not ensure that the word frequencies would be stable and Zipfian.  And why the word-pair distribution has "skew squares".

All the best, --stolfi

[oshfdk]

Word templates like mine do not capture all the constraints we see in the actual Voynichese lexicon.  No matter how we define prefix, core, and suffix, these three parts are not independent.  My model specifies a couple of constraints (the counts of benches and dealers) but there are more.  Your own color tables show that, for one particular core, there are prefix-suffix pairs that are twice as common as expected, or half as common. I gave a couple of more dramatic examples of "skew squares" were Fr(AKX):Fr(BKX) is very different from Fr(AKY):Fr(BKY).

While existing templates don't capture all words and the existing words only, hypothetically, if someone finds a relatively simple set of rules that would cover >95% of existing word types and would only produce < 5% of unregistered word types, is there a possibility to resolve all of this? Since I think many people have been focusing on glyph-based manipulations only, what if the right set of rules is more like "match the number of left and right semicircular curves in each word", "make sure the number of vertical lines matches the number of crossed strokes", "make sure the number of upwards flourishes per word is the same as the number of mimims"? I'm just inventing those, but given that individual characters appear to be designed by combining a few simple strokes in (almost) all possible ways, I think it wouldn't be reasonable to assume the rules, if any, can be formulated in terms of strokes and not in terms of glyphs.

[Jorge_Stolfi]

Your constructed language scenario ... makes predictions the VMS doesn't satisfy:

A constructed language dictionary produces consistent usage. If "daiin" means "heat," it should appear in consistent semantic contexts. In the VMS, "daiin" appears everywhere — in every section, next to every kind of word. No semantic clustering is detectable.

You are not allowed to view links. Register or Login to view. that, by pure coincidence, is statistically similar in some aspects (like word structure and size distribution) to the VMS text.  The text was not created by me; it was taken from a published and heavily used manual.  It is not encrypted, merely written in a simple but intentionally obfuscated spelling system, using a Latin letter or digraph for each sound.  The word spaces are as in the original.  <%> and <$> delimit parags.  The line breaks, other than parag breaks, were created by "fmt -s -w 50".   

Can you detect any "semantic clustering" of a kind that is not detectable in the VMS? 

A constructed language doesn't show a continuous evolutionary gradient.

I have yet to see evidence that there is a "continuous evolutionary gradient" along the VMS.  Sure, if one sorts the pages of a document in a way that minimizes the distances between consecutive pages in any document, the result will tend to show a continuous gradient.  

On the contrary, all tests that I have seen show that, if one merely separates the pages by section (treating Herbal-A and Herbal-B as two separate sections), what one sees instead is abrupt changes in word frequencies between sections. Like those one sees in any natural language text between sections on very different topics. Or even between sections on the same topic but written by different authors in a different style.

And (as you noted) if the word frequencies change, so will the frequencies of glyphs and digraphs. 

A constructed language doesn't show line-boundary production effects. If words have fixed meanings, their form shouldn't depend on line position. But some words appear almost exclusively at line starts or line ends.

These alleged "line-boundary production effects" have been discussed extensively in the LAAFU thread.  One fact that has been recently pointed out is that in fact one should expect different word frequencies at line-start and line-end, because the probability of breaking a line before any given word greater for longer words, and because in a manuscript document the scribe will be more likely to use abbreviations (like, apparently, m -> iin) near line-end.  

We do not know yet whether these two content-insensitive processes can account for all anomalies seen around line breaks.  And we do not know either whether these are the only content-insensitive processes that can produce those anomalies.  Until these questions are resolved, the line-break anomalies cannot be used as evidence that the VMS text is not natural language.

A constructed language with semantic prefixes doesn't show prefix-suffix independence.

 

And neither does Voynichese: 

  56 otedy 56 oteedy
   2 ytedy 12 yteedy

  12 ched  11 ches               
  10 shed   0 shes

 119 chey  11 ches           
  77 shey   0 shes

  50 dain  30 dair               
  12 rain   2 rair

All the best, --stolfi

[ReneZ]

There is still no explanation for how the Author could have created words with those hidden statistical anomalies, both for the seed text and during modification.

Let alone why a great majority of possible modifications are never made.

[Jorge_Stolfi]

However the flow of the writing suggests that the writer did not pause after each word to think of what ought to come next.

You are assuming that the VMS was written directly "from brain to vellum". But that is extremely unlikely.  

The Author surely composed the text as a draft on paper, which then was clean-copied to vellum.  So the flow of writing does not tell how quickly the text was composed.

(And many clues, as well as common sense, suggest that the copying to vellum was done by a Scribe who did not understand the text. 

All the best, --stolfi

[Jorge_Stolfi]

While existing templates don't capture all words and the existing words only, hypothetically, if someone finds a relatively simple set of rules that would cover >95% of existing word types and would only produce < 5% of unregistered word types, is there a possibility to resolve all of this?

There may be, but until one is found, that remains a problem for all "gibberish" theories.   Is there a simple enough model that generates the Voynichese words with the observed frequencies?  Even if it is not the kind of model that a Medieval author could have devised and used? 

For any lexicon and any probability distribution of the words, can build a tree-like automaton with probabilities on the transitions that generates precisely those words with precisely those probabilities.  But that model is as complex as a table with the frequency of each word.   

To reduce the complexity one could merge sub-trees, creating an automaton which is not a tree but a directed acyclic graph (a DAG).  In that model, any state S that can be reached from the root by M different paths and leads to N final states represents a subset of the lexicon whose words consist of M prefixes combined with N suffixes, chosen with various probabilities but independently of each other.  How many such subsets can we find in the VMS lexicon?  Even allowing for, say, spelling and transcription errors on 15% of the words?  I don't expect that such a model can approximate the whole lexicon with the observed frequencies.

Maybe a model that is not a finite state automaton can do better.  In my word model, the constraints on the total counts of dealers and benches can be implemented by keeping counters, reducing the size of the corresponding automaton by  a large factor.  But my model does not predict the word probabilities, only whether words are "valid" or not; and it still allows many "valid" words that don't occur at all.

All the best, --stolfi

[Torsten]

I have yet to see evidence that there is a "continuous evolutionary gradient" along the VMS.

It is documented here: You are not allowed to view links. Register or Login to view. and You are not allowed to view links. Register or Login to view. 

The gradient follows a specific path through specific intermediate forms — chol → cheol → cheo → chey → chedy — each attested with specific frequencies in a specific section order. The first step from <chol> to <cheol> even happens within Currier A.

  56 otedy 56 oteedy
  2 ytedy 12 yteedy

  12 ched  11 ches             
  10 shed  0 shes

119 chey  11 ches         
  77 shey  0 shes

  50 dain  30 dair             
  12 rain  2 rair

The frequency-connectivity correlation arises through a feedback loop inherent in the  copying process. Frequent words are more likely to be selected as copying templates, generating more variants; the existence of more variants increases the probability that members of that word family are selected in subsequent copying events. This self-reinforcing cycle ensures that the most frequently used words accumulate the most similar neighbors—precisely the pattern you document.

[Dunsel]

There is still no explanation for how the Author could have created words with those hidden statistical anomalies, both for the seed text and during modification.

I am hesitant to define any Voynich statistics as “hidden anomalies.” Some may simply be emergent structure.  Some of the Voynich statistics are likely the Texas sharpshooter fallacy. Fire bullets at a barn and then paint a target around the tightest cluster afterward.

In my own tests, the Zipf-like curve and word-length distribution were not programmed in directly; they arose from the copy/mutate process itself.  Word-length.  Hapax count.  Vocabulary size.  All arose without any effort to specifically code for them. I would expect the same with other statistical patterns. If you dig deeply enough into natural language, or into generated text from a constrained local process, you will find uneven pairings, family clusters, missing combinations, and odd-looking skews.  So the question is not whether anomalies exist. Of course they do. The question is whether they require a hidden semantic lexicon, or whether they can emerge from constrained local copying, reuse, and mutation.

Let alone why a great majority of possible modifications are never made.

No, the manuscript never explored every possible word combination. A realistic copy-mutate system would stay conservative, reusing active word families and nearby variants instead of wandering randomly through all legal forms.  Natural languages work the same way. English could produce far more legal letter combinations than it actually does. And if someone really was trying to create a convincing hoax, making the text feel language-like would be the goal, not splattering every theoretically possible word across the page.  That's gibberish.  Even the ledger I demonstrate shows that thousands of never used combinations could exist. Constraint is why they don't exist. 

These words look English but don't exist.  Humans could have created them, but never did.  In our cases, the necessity wasn't there.  In the Voynich, that same constraint applies whether you think it has meaning or not.

• brathen
  
• cloryn
  
• fenwall
  
• dravick
  

[Dunsel]

I reworked one of my comparison tests to operate at the sheet level. What this appears to show is that the manuscript is not behaving like a collection of unrelated pages. Certain sheets are much more similar to specific other sheets than to the manuscript as a whole, especially in Quire 13 and Quire 20.

That is consistent with what I would expect from a copy-and-modify process, where words and word families are repeatedly reused and gradually altered over time, creating clusters of closely related sheets instead of uniformly random text.

This alone does not prove a copy-and-modify system. A natural language text could also produce local clustering through shared topics, scribal habits, or repeated terminology. At the same time, not all sheets correlate most strongly with their immediate neighbors. Some show stronger affinity to more distant sheets, which is also consistent with my broader analyzer results suggesting that sheets may draw from small recurring source pools rather than strictly adjacent pages alone.

Sheet	Closest Match	Pearson	Cosine	Mean
Quire 1 Sheet 1 (q1s1)
	Quire 6 Sheet 2 (q6s2)	0.738570	0.785728	0.762149
	Quire 1 Sheet 2 (q1s2)	0.612324	0.701843	0.657084
	Quire 7 Sheet 1 (q7s1)	0.619659	0.693897	0.656778
Quire 1 Sheet 2 (q1s2)
	Quire 7 Sheet 1 (q7s1)	0.666632	0.744950	0.705791
	Quire 2 Sheet 2 (q2s2)	0.667659	0.742020	0.704840
	Quire 3 Sheet 4 (q3s4)	0.638953	0.736955	0.687954
Quire 1 Sheet 3 (q1s3)
	Quire 3 Sheet 1 (q3s1)	0.528717	0.656501	0.592609
	Quire 2 Sheet 2 (q2s2)	0.531632	0.626589	0.579111
	Quire 1 Sheet 1 (q1s1)	0.496705	0.606720	0.551712
Quire 1 Sheet 4 (q1s4)
	Quire 3 Sheet 4 (q3s4)	0.638768	0.733743	0.686256
	Quire 2 Sheet 2 (q2s2)	0.639366	0.723205	0.681285
	Quire 4 Sheet 1 (q4s1)	0.648412	0.709008	0.678710
Quire 2 Sheet 1 (q2s1)
	Quire 2 Sheet 2 (q2s2)	0.711392	0.773835	0.742613
	Quire 3 Sheet 3 (q3s3)	0.639688	0.710703	0.675196
	Quire 5 Sheet 4 (q5s4)	0.607467	0.679974	0.643720
Quire 2 Sheet 2 (q2s2)
	Quire 2 Sheet 1 (q2s1)	0.711392	0.773835	0.742613
	Quire 3 Sheet 3 (q3s3)	0.686641	0.747322	0.716982
	Quire 5 Sheet 4 (q5s4)	0.683149	0.740385	0.711767
Quire 2 Sheet 3 (q2s3)
	Quire 5 Sheet 4 (q5s4)	0.639470	0.706742	0.673106
	Quire 2 Sheet 2 (q2s2)	0.610292	0.697264	0.653778
	Quire 3 Sheet 3 (q3s3)	0.613912	0.693052	0.653482
Quire 2 Sheet 4 (q2s4)
	Quire 7 Sheet 1 (q7s1)	0.430707	0.573375	0.502041
	Quire 3 Sheet 3 (q3s3)	0.424867	0.574041	0.499454
	Quire 2 Sheet 3 (q2s3)	0.395196	0.577715	0.486455
Quire 3 Sheet 1 (q3s1)
	Quire 1 Sheet 3 (q1s3)	0.528717	0.656501	0.592609
	Quire 19 Sheet 2 (q19s2)	0.498225	0.621177	0.559701
	Quire 1 Sheet 1 (q1s1)	0.494887	0.621925	0.558406
Quire 3 Sheet 2 (q3s2)
	Quire 3 Sheet 3 (q3s3)	0.509947	0.613904	0.561926
	Quire 2 Sheet 2 (q2s2)	0.470679	0.596163	0.533421
	Quire 4 Sheet 1 (q4s1)	0.472432	0.562973	0.517703
Quire 3 Sheet 3 (q3s3)
	Quire 5 Sheet 4 (q5s4)	0.790320	0.825820	0.808070
	Quire 4 Sheet 1 (q4s1)	0.785575	0.817966	0.801770
	Quire 5 Sheet 3 (q5s3)	0.696172	0.752013	0.724092
Quire 3 Sheet 4 (q3s4)
	Quire 7 Sheet 1 (q7s1)	0.718656	0.782494	0.750575
	Quire 2 Sheet 2 (q2s2)	0.660336	0.737009	0.698673
	Quire 1 Sheet 2 (q1s2)	0.638953	0.736955	0.687954
Quire 4 Sheet 1 (q4s1)
	Quire 5 Sheet 4 (q5s4)	0.817946	0.843787	0.830866
	Quire 5 Sheet 3 (q5s3)	0.803942	0.832919	0.818431
	Quire 3 Sheet 3 (q3s3)	0.785575	0.817966	0.801770
Quire 4 Sheet 2 (q4s2)
	Quire 13 Sheet 1 (q13s1)	0.503905	0.586732	0.545318
	Quire 5 Sheet 2 (q5s2)	0.464865	0.603391	0.534128
	Quire 6 Sheet 3 (q6s3)	0.461342	0.603957	0.532650
Quire 4 Sheet 3 (q4s3)
	Quire 7 Sheet 1 (q7s1)	0.604012	0.697502	0.650757
	Quire 6 Sheet 2 (q6s2)	0.569787	0.666633	0.618210
	Quire 3 Sheet 4 (q3s4)	0.549608	0.671661	0.610635
Quire 4 Sheet 4 (q4s4)
	Quire 2 Sheet 2 (q2s2)	0.639485	0.725273	0.682379
	Quire 3 Sheet 4 (q3s4)	0.611928	0.719979	0.665954
	Quire 7 Sheet 1 (q7s1)	0.617309	0.704995	0.661152
Quire 5 Sheet 1 (q5s1)
	Quire 5 Sheet 2 (q5s2)	0.675752	0.752361	0.714057
	Quire 7 Sheet 2 (q7s2)	0.633491	0.729379	0.681435
	Quire 20 Sheet 4 (q20s4)	0.520811	0.583510	0.552161
Quire 5 Sheet 2 (q5s2)
	Quire 5 Sheet 1 (q5s1)	0.675752	0.752361	0.714057
	Quire 6 Sheet 3 (q6s3)	0.619137	0.714398	0.666768
	Quire 7 Sheet 2 (q7s2)	0.569341	0.674544	0.621943
Quire 5 Sheet 3 (q5s3)
	Quire 4 Sheet 1 (q4s1)	0.803942	0.832919	0.818431
	Quire 5 Sheet 4 (q5s4)	0.726317	0.772944	0.749630
	Quire 3 Sheet 3 (q3s3)	0.696172	0.752013	0.724092
Quire 5 Sheet 4 (q5s4)
	Quire 4 Sheet 1 (q4s1)	0.817946	0.843787	0.830866
	Quire 3 Sheet 3 (q3s3)	0.790320	0.825820	0.808070
	Quire 5 Sheet 3 (q5s3)	0.726317	0.772944	0.749630
Quire 6 Sheet 1 (q6s1)
	Quire 6 Sheet 3 (q6s3)	0.412365	0.597777	0.505071
	Quire 20 Sheet 6 (q20s6)	0.453805	0.543655	0.498730
	Quire 13 Sheet 1 (q13s1)	0.444410	0.548235	0.496322
Quire 6 Sheet 2 (q6s2)
	Quire 1 Sheet 1 (q1s1)	0.738570	0.785728	0.762149
	Quire 7 Sheet 1 (q7s1)	0.701692	0.759352	0.730522
	Quire 3 Sheet 4 (q3s4)	0.644373	0.720588	0.682481
Quire 6 Sheet 3 (q6s3)
	Quire 5 Sheet 2 (q5s2)	0.619137	0.714398	0.666768
	Quire 20 Sheet 3 (q20s3)	0.489479	0.580730	0.535104
	Quire 4 Sheet 2 (q4s2)	0.461342	0.603957	0.532650
Quire 6 Sheet 4 (q6s4)
	Quire 2 Sheet 2 (q2s2)	0.484621	0.609233	0.546927
	Quire 2 Sheet 1 (q2s1)	0.426874	0.612524	0.519699
	Quire 2 Sheet 3 (q2s3)	0.445476	0.588755	0.517115
Quire 7 Sheet 1 (q7s1)
	Quire 3 Sheet 4 (q3s4)	0.718656	0.782494	0.750575
	Quire 6 Sheet 2 (q6s2)	0.701692	0.759352	0.730522
	Quire 1 Sheet 2 (q1s2)	0.666632	0.744950	0.705791
Quire 7 Sheet 2 (q7s2)
	Quire 5 Sheet 1 (q5s1)	0.633491	0.729379	0.681435
	Quire 5 Sheet 2 (q5s2)	0.569341	0.674544	0.621943
	Quire 20 Sheet 3 (q20s3)	0.545362	0.613511	0.579437
Quire 7 Sheet 3 (q7s3)
	Quire 19 Sheet 2 (q19s2)	0.494754	0.615074	0.554914
	Quire 17 Sheet 1 (q17s1)	0.472687	0.630905	0.551796
	Quire 3 Sheet 1 (q3s1)	0.425250	0.600156	0.512703
Quire 7 Sheet 4 (q7s4)
	Quire 5 Sheet 4 (q5s4)	0.499364	0.594524	0.546944
	Quire 3 Sheet 3 (q3s3)	0.488857	0.597364	0.543111
	Quire 2 Sheet 2 (q2s2)	0.458215	0.590065	0.524140
Quire 8 Sheet 1 (q8s1)
	Quire 6 Sheet 3 (q6s3)	0.257227	0.436389	0.346808
	Quire 13 Sheet 1 (q13s1)	0.287917	0.398632	0.343275
	Quire 20 Sheet 3 (q20s3)	0.270727	0.404701	0.337714
Quire 8 Sheet 2 (q8s2)
	Quire 20 Sheet 4 (q20s4)	0.443076	0.551508	0.497292
	Quire 20 Sheet 5 (q20s5)	0.436977	0.547381	0.492179
	Quire 5 Sheet 1 (q5s1)	0.413948	0.540531	0.477239
Quire 10 Sheet 1 (q10s1)
	Quire 8 Sheet 2 (q8s2)	0.360871	0.520528	0.440699
	Quire 20 Sheet 4 (q20s4)	0.332859	0.437859	0.385359
	Quire 11 Sheet 1 (q11s1)	0.250932	0.508714	0.379823
Quire 11 Sheet 1 (q11s1)
	Quire 20 Sheet 4 (q20s4)	0.428510	0.507518	0.468014
	Quire 20 Sheet 5 (q20s5)	0.381054	0.477716	0.429385
	Quire 20 Sheet 3 (q20s3)	0.334403	0.437608	0.386005
Quire 12 Sheet 1 (q12s1)
	Quire 10 Sheet 1 (q10s1)	0.091711	0.429769	0.260740
	Quire 20 Sheet 4 (q20s4)	0.167399	0.307395	0.237397
	Quire 8 Sheet 2 (q8s2)	0.107132	0.353295	0.230213
Quire 13 Sheet 1 (q13s1)
	Quire 13 Sheet 4 (q13s4)	0.876554	0.891779	0.884166
	Quire 13 Sheet 2 (q13s2)	0.794608	0.818532	0.806570
	Quire 13 Sheet 5 (q13s5)	0.790289	0.817012	0.803650
Quire 13 Sheet 2 (q13s2)
	Quire 13 Sheet 3 (q13s3)	0.870040	0.884687	0.877364
	Quire 13 Sheet 1 (q13s1)	0.794608	0.818532	0.806570
	Quire 20 Sheet 1 (q20s1)	0.735346	0.768024	0.751685
Quire 13 Sheet 3 (q13s3)
	Quire 13 Sheet 2 (q13s2)	0.870040	0.884687	0.877364
	Quire 13 Sheet 1 (q13s1)	0.770537	0.797586	0.784062
	Quire 13 Sheet 5 (q13s5)	0.721673	0.756828	0.739250
Quire 13 Sheet 4 (q13s4)
	Quire 13 Sheet 1 (q13s1)	0.876554	0.891779	0.884166
	Quire 13 Sheet 5 (q13s5)	0.794138	0.818786	0.806462
	Quire 13 Sheet 2 (q13s2)	0.685743	0.722164	0.703953
Quire 13 Sheet 5 (q13s5)
	Quire 13 Sheet 4 (q13s4)	0.794138	0.818786	0.806462
	Quire 13 Sheet 1 (q13s1)	0.790289	0.817012	0.803650
	Quire 20 Sheet 1 (q20s1)	0.731929	0.768713	0.750321
Quire 15 Sheet 1 (q15s1)
	Quire 19 Sheet 2 (q19s2)	0.195890	0.415680	0.305785
	Quire 4 Sheet 1 (q4s1)	0.193468	0.377629	0.285549
	Quire 3 Sheet 3 (q3s3)	0.152643	0.372895	0.262769
Quire 15 Sheet 2 (q15s2)
	Quire 19 Sheet 2 (q19s2)	0.480138	0.614009	0.547073
	Quire 7 Sheet 3 (q7s3)	0.359650	0.566087	0.462868
	Quire 3 Sheet 1 (q3s1)	0.268906	0.510035	0.389471
Quire 17 Sheet 1 (q17s1)
	Quire 7 Sheet 3 (q7s3)	0.472687	0.630905	0.551796
	Quire 19 Sheet 2 (q19s2)	0.400173	0.545924	0.473049
	Quire 1 Sheet 3 (q1s3)	0.388305	0.547121	0.467713
Quire 17 Sheet 2 (q17s2)
	Quire 5 Sheet 1 (q5s1)	0.415730	0.605162	0.510446
	Quire 20 Sheet 3 (q20s3)	0.458740	0.550560	0.504650
	Quire 5 Sheet 2 (q5s2)	0.412126	0.586891	0.499508
Quire 19 Sheet 1 (q19s1)
	Quire 19 Sheet 2 (q19s2)	0.478109	0.610468	0.544288
	Quire 7 Sheet 3 (q7s3)	0.297804	0.520092	0.408948
	Quire 3 Sheet 3 (q3s3)	0.280833	0.434393	0.357613
Quire 19 Sheet 2 (q19s2)
	Quire 7 Sheet 1 (q7s1)	0.541257	0.627063	0.584160
	Quire 3 Sheet 4 (q3s4)	0.523183	0.623006	0.573094
	Quire 3 Sheet 1 (q3s1)	0.498225	0.621177	0.559701
Quire 20 Sheet 1 (q20s1)
	Quire 20 Sheet 6 (q20s6)	0.765874	0.793804	0.779839
	Quire 13 Sheet 2 (q13s2)	0.735346	0.768024	0.751685
	Quire 13 Sheet 5 (q13s5)	0.731929	0.768713	0.750321
Quire 20 Sheet 2 (q20s2)
	Quire 20 Sheet 4 (q20s4)	0.723869	0.774492	0.749180
	Quire 20 Sheet 5 (q20s5)	0.700254	0.749052	0.724653
	Quire 20 Sheet 3 (q20s3)	0.658746	0.725649	0.692198
Quire 20 Sheet 3 (q20s3)
	Quire 20 Sheet 4 (q20s4)	0.740062	0.784679	0.762371
	Quire 20 Sheet 5 (q20s5)	0.690327	0.740376	0.715352
	Quire 20 Sheet 2 (q20s2)	0.658746	0.725649	0.692198
Quire 20 Sheet 4 (q20s4)
	Quire 20 Sheet 5 (q20s5)	0.812893	0.840823	0.826858
	Quire 20 Sheet 3 (q20s3)	0.740062	0.784679	0.762371
	Quire 20 Sheet 2 (q20s2)	0.723869	0.774492	0.749180
Quire 20 Sheet 5 (q20s5)
	Quire 20 Sheet 4 (q20s4)	0.812893	0.840823	0.826858
	Quire 20 Sheet 6 (q20s6)	0.770385	0.799424	0.784904
	Quire 20 Sheet 2 (q20s2)	0.700254	0.749052	0.724653
Quire 20 Sheet 6 (q20s6)
	Quire 20 Sheet 5 (q20s5)	0.770385	0.799424	0.784904
	Quire 20 Sheet 1 (q20s1)	0.765874	0.793804	0.779839
	Quire 13 Sheet 2 (q13s2)	0.735210	0.762953	0.749082