A complete vocabulary, bounded and checksummed

Every DNA word through tenin Ensembl 116 GRCh38 primary assembly

No A/C/G/T word of length 1 through 10 is absent from the pinned Ensembl release 116 GRCh38 primary assembly. Multiply the vocabulary by four once more, to length 11, and holes appear.

The honesty line. This is a fact about one versioned reference assembly at one checksum. A reference assembly is a mosaic construct, not a person. This page does not describe every human genome, any individual person's DNA, or unknown bases hidden by assembly gaps.

The certificate

VERIFYING LOCAL DATA

The claim: No canonical A/C/G/T word of length 1 through 10 is absent from Ensembl release 116 Homo sapiens GRCh38 primary assembly, GCA_000001405.29.
Domain swept: All computing words in Σ 4^k, k = 1…10, against every maximal A/C/G/T run in the pinned FASTA.
Method: Rolling two-bit codes mark exact words within records and canonical runs; the browser inspects every vector slot and also tests reverse complements.
Positive control: At k = 11 the same search must find published nullomer CGCTCGACGTA and reverse complement TACGTCGAGCG.
Planted witness: Suppress every observed AAAAAAAAAA and TTTTTTTTTT window, then the same k = 10 search must report exactly that pair absent.
Result: verifying local vectors
Bound: The certified empty domain ends at k = 10. At k = 11 it is non-empty. Shipped exact vectors stop at 11, and the interface refuses longer queries.

01 · The operable base

Move the frontier

The field below is not a picture of an answer. Your browser reads the shipped bit vector, enumerates every word at the selected length, tests the exact presence rule, and draws the holes it finds.

Vocabulary map · prefix bins

LOADING

no absent word in binone or more absent words

words tested…

absent…

Loading the pinned presence vectors...

Absent words, lexical order

Waiting for verified data.

Word length, k

110

Assembly scope

Occurrence rule

Record boundaries and every non-ACGT symbol break a run. Words never cross them. “Either strand” asks whether the word or its reverse complement appears in the displayed FASTA sequence.

Interrogate one word

Use 1 to 11 letters from A, C, G and T.

02 · Make absence possible

Two ways the same search succeeds

An empty answer from a searcher that cannot find anything is worthless. One control moves to the first real holes. The other changes the real input by suppressing every occurrence of a known 10-mer pair, then removes that intervention.

Positive control · the world at 11

CGCTCGACGTA ↔ TACGTCGAGCG

Hampikian and Andersen printed the first sequence in Table 3 in 2007. Their older snapshot is internally inconsistent about its own total: Table 1 reports 80 human 11-mer nullomers, while the results text describes 43 sequences together with their complements. A 2021 hg38 analysis counted 104. This page computes the release-116 count anew and takes neither figure as an expected value.

Not run yet.

Planted witness · subtract a word

AAAAAAAAAA ↔ TTTTTTTTTT

The generator counts every displayed-strand occurrence of both words. The plant operation suppresses all those observed windows before passing the modified presence vector to the unchanged exhaustive search. Nothing is added to DNA, because adding sequence cannot create an absence.

0 absent. Unmasked release-116 data.

03 · The depth layer

Is the frontier just CpG depletion?

Many early nullomers are rich in CpG dinucleotides. That observation does not by itself establish negative selection. Mutation bias, sequence composition, reference scope and assembly representation remain possible explanations.

Run the second census. It sorts all 4¹¹ possible words by their exact CpG count, then repeats the absence test for the primary assembly and the direct release-116 toplevel FASTA. The build also proves that vector equals the union of primary with the separately distributed alternate and patch records.

04 · The check

What was actually counted

Verifying local artifacts before asserting a result.

FASTA records, primary: computing
Canonical A/C/G/T bases: computing
Noncanonical symbols: computing
Added records for toplevel: computing
Direct toplevel records: computing
Direct toplevel A/C/G/T bases: computing
Generator version: computing
Generated UTC: computing
Primary bytes: computing
Primary SHA-256: computing
Alt bytes: computing
Alt SHA-256: computing
Direct toplevel bytes: computing
Direct toplevel SHA-256: computing
Primary vector SHA-256: computing

Uncertainty and free choices

The assembly, release, primary-versus-toplevel scope, exact matching, A/C/G/T alphabet, ambiguity handling and either-strand convention are choices, named here because changing them can change the answer. Assembly gaps are unknown sequence, not observed absence. The generator treats lowercase A/C/G/T as canonical, ignores FASTA layout whitespace, and breaks at records or other symbols.

The page ships derived presence vectors, not the multi-gigabyte expanded assembly. Its browser check proves those vectors have not changed and re-enumerates their full word domain. The research verifier independently checks the vectors, controls, refusal paths and source manifest. Regenerating the vectors from the source FASTA is a separate, documented heavy step.

Sources retrieved for this check

Ensembl release 116 Homo sapiens FASTA README, assembly accession, file semantics and primary/toplevel scope.
Ensembl Data and Software Disclaimer, unrestricted access and use for Ensembl-generated data, with an explicit warning that third-party constraints may apply.
Greg Hampikian and Tim Andersen, “Absent Sequences: Nullomers and Primes”, Pacific Symposium on Biocomputing 12 (2007), 355–366. Table 1 reports 80 human 11-mer nullomers while the results text describes 43 sequences and their complements, so the paper is internally inconsistent; Table 3 includes CGCTCGACGTA.
Ilias Georgakopoulos-Soares and colleagues, “Absent from DNA and protein”, Genome Biology 22, 245 (2021). The hg38 analysis reports 104 shortest human nullomers at 11 bp.