Voynichese has a paradox at its centre.
It looks repetitive.
Words resemble one another constantly.
Families grow around familiar cores.
And yet an enormous fraction of the token types appear only once.
These one-off types are called hapax legomena—or simply hapaxes.
In August 2026, Rozanova and Temerev reported that about seventy percent of Voynich token types are singletons under their counting choices, substantially above the rates produced by two strong controls in the same study: a Voynich-imitating cipher and a self-citation generator.
That result is a preprint finding and needs independent replication.
But the underlying question is older and deeper than one percentage.
How can a writing system look so constrained and still keep inventing forms we never see twice?
Quick Read
- A hapax is a token type occurring exactly once in a corpus.
- Voynichese has long been known to contain many rare and unique token types.
- The August 2026 Rozanova–Temerev preprint reports about 70% singleton token types under its analysis, versus roughly 41% for its cipher control and about 59–60% for its self-citation control.
- The exact percentage depends on transcription, tokenisation, corpus scope and treatment of uncertain spaces.
- A high hapax rate does not prove natural language.
- It also does not prove random generation.
- High hapax rates can arise from productive morphology, open vocabularies, names, copying variation, abbreviation, cipher expansion, recursive generation or segmentation choices.
- The interesting Voynich combination is not hapaxes alone but hapaxes inside a system with unusually strong local constraints and word-family resemblance.
- A successful mechanism must explain both openness and constraint at the same time.
- Any hypothesis that generates too few unique forms or too many unconstrained forms fails one side of the paradox.
What Is a Hapax?
Suppose a corpus contains the token types:
apple, apple, tree, tree, leaf, branch, orchard.
Branch and orchard occur once.
They are hapaxes in that corpus.
In a large natural-language corpus, hapaxes are normal.
Names occur once.
Rare technical terms occur once.
Inflected forms occur once.
Spelling variation creates one-offs.
So “many hapaxes” is not mysterious by itself.
The Voynich problem begins when the one-off tokens remain visibly close to other token families.
The Paradox: Unique, but Not Unrelated
A random generator can create unique strings easily.
Pick ten characters at random and almost every result will be new.
But random uniqueness looks wild.
Voynich uniqueness often does not.
Many one-off tokens look like members of existing families with a small addition, deletion, substitution or rearrangement.
That creates a narrow corridor between two failures.
- Too much constraint: the generator keeps recycling a small vocabulary and produces too few hapaxes.
- Too little constraint: the generator creates many one-offs but they no longer look Voynich-like.
The manuscript appears to live between them.
Voynich is open enough to keep producing novelty and closed enough for that novelty to remain recognisably Voynich.
Why Transcription Matters
Before treating any singleton percentage as a physical property of the manuscript, ask how the corpus was built.
If one ambiguous bench is split into two EVA characters, one token type can become another.
If one uncertain space is retained, a long token becomes two shorter ones.
If that space is merged, two rare tokens can become one unique compound.
If rare allographs are normalised, several hapaxes disappear.
Therefore a robust hapax study should be repeated across:
- multiple transcriptions;
- different treatments of uncertain spaces;
- different compound-glyph policies;
- Currier A and B separately;
- labels versus running text separately.
The hapax problem lives downstream of the EVA and Segmentation Problem.
A Natural-Language Explanation
Natural language can produce many one-off forms through productive morphology.
A stem combines with prefixes and suffixes.
Rare combinations occur once.
Technical writing adds names, measurements and domain terms.
This makes high vocabulary openness compatible with meaning.
But a natural-language model must explain Voynich’s unusually strong internal constraints and narrow token architecture too.
“Language has hapaxes” is not enough.
The model needs the right amount of novelty under the right structural grammar.
A Cipher Explanation
A cipher can inflate vocabulary dramatically.
One plaintext word can map to several ciphertext forms.
Homophones, nulls, padding and verbose expansion can make repeated plaintext appear as many distinct visible tokens.
This is one reason ciphertext models remain serious.
But a cipher that creates too many forms too freely produces a vocabulary more chaotic than Voynich.
The challenge is to generate high apparent type diversity while preserving edge rules, word families, line effects and Currier variation.
A Self-Citation Explanation
Timm–Schinner self-citation generates new visible forms recursively from older ones.
That naturally produces a growing family tree.
It also produces singletons because many mutations are never reused.
The 2026 Rozanova–Temerev control is especially interesting because their self-citation output reaches a substantial singleton rate but still falls below the reported Voynich rate.
That does not disprove all self-citation models.
It creates a calibration target.
A recursive generator must remain open enough to match Voynich without losing the other structures it already matches.
See The Self-Citation Problem.
Could Rare Tokens Be Names?
Names are naturally hapax-rich.
A list of people, stars, plants or places can contain many unique labels.
This is particularly relevant to the zodiac and diagrammatic labels.
But the manuscript’s one-off vocabulary extends beyond obvious label populations.
A name hypothesis therefore needs document-role separation.
Labels may legitimately be more singleton-heavy than prose.
The whole corpus should not inherit that explanation automatically.
Could Hapaxes Be Scribal Error?
Some can.
Copying errors produce one-offs.
Hesitations produce one-offs.
Rare ligatures produce one-offs.
Transcriber uncertainty produces one-offs.
But the manuscript’s visible writing is too regular for “most unique types are mistakes” to be a satisfying default.
A serious error model should predict where singleton forms cluster:
- difficult parchment;
- rare glyph contexts;
- line endings;
- specific hands;
- damaged folios.
If hapaxes remain distributed systematically after those controls, they belong to the system more deeply.
Vocabulary Growth Is the Better Question
A single hapax percentage is only one snapshot.
A stronger question is:
As we read more Voynich, how quickly do new token types keep appearing?
If the vocabulary saturates quickly, the system behaves like a closed codebook.
If it keeps growing, the system is open.
If growth differs sharply by section, the openness may be topic-, scribe- or state-dependent.
This is the link to Heaps-like vocabulary growth discussed in Frequency Laws.
The hapax problem owns the tail of that growth: the forms that appear once and never return.
A Closed System With Productive Surface Forms?
There is a useful middle possibility.
The underlying system may contain a small number of functional units while the visible surface combines them productively.
That would create:
- strong internal constraints;
- recurrent subtoken units;
- many unique complete tokens;
- families of near-neighbours.
This is exactly why the next owner, The Unit-Scale Problem, matters.
The visible token can be open even if its underlying building blocks are highly stable.
The Hapax Distribution Should Be Mapped, Not Merely Counted
Where do the singletons live?
- Which sections?
- Which hands?
- Which Currier regime?
- Which line positions?
- Which labels?
- Which diagrams?
- Which token lengths?
- Which word families?
A manuscript-wide percentage can hide several mechanisms.
One section may be closed and repetitive.
Another may be label-rich and unique.
One scribe may regularise more aggressively.
Another may generate more variants.
The map matters more than the headline number.
The Rarest Tokens May Be the Best Discriminators
Common tokens can be imitated easily.
A model learns frequent forms first.
The difficult test is whether it produces the right rare forms.
Not merely enough rare forms.
The right kind of rarity.
- Do unique tokens sit one edit away from common families?
- Do they obey the same edge restrictions?
- Do they use rare glyphs disproportionately?
- Are they concentrated in labels or prose?
- Do they respect line-position grammar?
This is where a generator stops being visually convincing and starts being scientifically testable.
What the Hapax Problem Does Not Prove
- It does not prove Voynichese is natural language.
- It does not prove the manuscript contains names.
- It does not prove every singleton is meaningful.
- It does not prove self-citation is wrong.
- It does not prove a cipher.
- It does not make one 2026 singleton percentage timeless ground truth.
- It does not erase transcription and segmentation uncertainty.
What It Can Give Us
- A direct measure of vocabulary openness.
- A stress test for closed-codebook generators.
- A stress test for unconstrained random generators.
- A bridge between word families and vocabulary growth.
- A place where natural language, cipher, abbreviation and recursive-generation models make different quantitative predictions.
Reader Checklist
- Which transcription is used?
- How are uncertain spaces treated?
- What counts as the same token type?
- Are labels and prose pooled?
- What is the singleton rate by Currier regime?
- What is the rate by quire and hand?
- How does vocabulary growth behave as the corpus expands?
- Do singleton forms obey ordinary word-family constraints?
- Do candidate generators reproduce both hapax rate and other manuscript properties?
- Is the headline percentage being treated as more precise than the representation warrants?
Research Foundations
- Rozanova & Temerev — A Glyph Is Not a Letter, a Token Is Not a Word, a Space Is Not a Space (2026 preprint).
- Frequency Laws.
- Word Families.
- The Self-Citation Problem.
The Final Idea
The strange thing about Voynich is not that it contains rare words.
It is that rarity itself looks disciplined.
The manuscript keeps producing forms we may never see again.
Yet those forms rarely look as though they came from another universe.
The Voynich vocabulary behaves like a system that knows how to create novelty without forgetting what counts as Voynich.