JSD ratio 1.373, p = 0.0000. Spectral clustering recovers O/R/α exactly — ARI = 1.000 across 8 seeds. The Astronomical section floats alone. Hover any node.
The void framework assigns each of the five Voynich sections to a position in (O, R, α) space. If that assignment is real — if the manuscript is actually encoding dimensional coordinates — then the vocabulary distributions between sections should be more separated than random.
We tested it. Shuffle the section labels 5,000 times, measure the spread of the JSD distance matrix each time, compare to the real manuscript. Zero of 5,000 shuffles matched or exceeded the observed spread. p = 0.0000.
Each cell is the Jensen-Shannon divergence between two sections' word frequency distributions. Lower = more similar vocabulary. Brighter = more distant (more different).
| Herbal_A | Astronomical | Biological | Pharmaceutical | Stars_Text | |
|---|---|---|---|---|---|
| Herbal_A | — | 0.596 | 0.586 | 0.529 | 0.552 |
| Astronomical | 0.596 | — | 0.664 ↑ max | 0.609 | 0.616 |
| Biological | 0.586 | 0.664 | — | 0.616 | 0.484 ↓ min |
| Pharmaceutical | 0.529 | 0.609 | 0.616 | — | 0.579 |
| Stars_Text | 0.552 | 0.616 | 0.484 | 0.579 | — |
The maximum gap (Astronomical↔Biological, 0.664) is between the R-axis and α-axis — cyclical responsiveness notation and coupling topology notation are maximally different. The minimum gap (Biological↔Stars_Text, 0.484) is between coupling topology and the constraint pole — the final specification is written in the language of coupling. Max/min ratio: 1.373. Permutation p: 0.0000.
Spectral clustering on the word co-occurrence matrix with k=3 recovers exactly the three dimensions the void framework predicted. Stable across 8 random seeds (ARI = 1.000 — identical assignments every time). k=4 is not better.
The void-object catalog. ch-, cth-, sh- prefix family. High-frequency opacity notation — the most basic cataloguing vocabulary.
Cyclical pattern notation. ote-, oke-, yke- prefix family. The R-axis morphological signature — each form encodes a periodic orbit configuration.
Flow topology notation. qo+k prefix family. The qol- subset (78% Biological) is the most section-specific prefix in the full manuscript.
No prior Voynich analysis has computed per-section conditional character entropy. When we did, we found something unexpected — a double dissociation between character-level and word-level entropy across the two most structurally distinct sections.
| Section | Pe | Char h₂ | Word h₂ |
|---|---|---|---|
| Biological | 10.0 | 1.990 LOWEST | 3.731 HIGHEST |
| Stars_Text | 0.1 | 2.175 | 3.357 |
| Pharmaceutical | 2.0 | 2.390 | 2.231 |
| Herbal_A | 25.0 | 2.398 | 3.309 |
| Astronomical | 0.8 | 2.440 HIGHEST | 1.764 LOWEST |
Biological (α-dimension): tightest character grammar (rigid coupling notation templates, h₂=1.990), most unpredictable word sequences (maximal configuration diversity, h₂=3.731). You know the formula. You cannot predict the content.
Astronomical (R-dimension): most expressive character sequences (diverse cyclical configurations, h₂=2.440), most predictable word sequences (zodiac labels follow fixed orbital order, h₂=1.764). You cannot predict the word-form. You can predict when it appears.
This double dissociation is not predicted by any prior Voynich theory. It falls directly out of the dimensional notation hypothesis — different axes require different information-theoretic strategies.
All three control texts fall below the Voynich JSD ratio: Dante 1.157, Douay-Rheims 1.297, Pride and Prejudice 1.085. Even the Bible's genre contrast (Pentateuch vs Epistles vs Poetry) doesn't reach 1.373. The Voynich structure is not genre — it's grammar.