A joke, followed until it broke.

A hackathon toy turned a FASTA file into a PNG and noticed the PNG came out smaller. The idea underneath was real: an image codec's row filters are two-dimensional predictors, so the width you pick is a free parameter, and sweeping it detects tandem repeats. Following that all the way removed the codec from the answer.

Read the results Repository Full write-up Play the puzzle

68%

of annotated chr21 windows agree with TRF

the compressed version manages 4%

indel rate the statistic survives

the compressed version dies by 0.5%

17×

faster than the version with a compressor in it

and it is the only one that can go in a proof

One

What the statistic is looking at

Write a sequence into an image row by row. A PNG can subtract each row from the row above before compressing — the Up filter. Choose a width equal to the period of a tandem repeat and every row becomes a near-copy of the row above, so the subtraction leaves almost nothing.

The same sequence laid out at two widths, with the row difference below each — **Top: the same bytes at two widths. Bottom: each row minus the row above, black where they differ.** At width 140 the rows are unrelated and 77% of bytes differ. At width 171 — the period — the monomers stack into vertical stripes and only 9% differ. That gap is the entire signal.

Read this before the next section

Notice what does not change. The raw stream deflates to 0.86 bits per base at one width and 0.86 at the other. Deflate finds this repeat from one dimension without any help from the layout. The 2-D arrangement changes the row difference, not the file size — and that turns out to be the whole story.

Two

The reversal

Three ways to measure the same sweep. png writes a real PNG at each width. up fixes the Up filter and deflates the residual. match throws the compressor away and counts positions where a byte equals the byte w earlier.

Sweep curves under three statistics across four planted arrays — **One row per statistic, one column per planted array; the dashed line marks the true period.** **match** and up agree closely (r = 0.78–0.92) and spike only at the period and its multiples. **png** correlates with neither (r = -0.26 to 0.02); its dips grow with width because a wider image has fewer rows, which has nothing to do with any repeat.

The finding

The compressor was never doing the work. It was the lens that found the statistic. The framing this project is named after turns out to be scaffolding — and taking it away made the method faster, twenty times more tolerant of indels, and the only version that works on a real genome.

Three

Where it works, and where it stops

Planted arrays, 400 kb per cell, substitutions only. The boundary is a horizontal line: every period from 5 bp to 5000 bp is found at 65% divergence and none at 80%. Period does not enter into it.

Phase diagram of detection over repeat period and divergence — **36 of 72 cells; × marks a cell where the detector's first answer was not the planted period.** Two independently mutated copies agree at 0.34 of positions at 65% divergence and 0.28 at 80%, against a chance baseline of 0.25 for four letters. So detection holds down to about a five-point excess over chance, and not below.

Indels, not substitutions, are the real limit

Detection under substitutions and indels for both statistics — **Hollow markers: the detector's first answer was no longer the planted period.** Both statistics compare a position to the position w earlier, so an indel should hurt both. It does not hurt them equally: **match** survives to 5% and fails by 10%, up fails by 0.5%. A compressed size is one number over a whole window, so out-of-phase stretches add entropy that swamps the in-phase ones; a match rate is a mean over positions, so the stretches still in phase keep contributing.

Four

Real genomes

45 windows of 200 kb across T2T-CHM13v2 chr21:5–14 Mb — the acrocentric short arm and the centromere — scored against UCSC's simpleRepeat (Tandem Repeats Finder) and censat, neither of which knows anything about this method.

statistic	windows calling a period	agreement (25 annotated)	agreement (period ≥ 20 bp)
`match`	19/45	17/25 (68%)	6/11
`png`	4/45	1/25 (4%)	1/11
`up`	0/45	0/25 (0%)	0/11

Reported period against TRF annotation along chr21 — **Grey rings are TRF's dominant consensus size per window; green is what the sweep reported.** Green sits on grey where they agree: 68 bp in the two windows `censat` labels `bsat_21_7` (beta satellite), 171 bp in the `mon_21_*` windows (alpha-satellite monomer), and multiples of 170 in `hor_21_3`, the higher-order array. `up` appears only in the legend — it calls nothing at all.

A plant satellite, and a control that has to stay quiet

2/92

A. thaliana chr4 windows calling a period

both of them 178 bp — pAL1, the centromeric satellite

0/23

E. coli windows calling a period

the negative control; reporting nothing is the right answer

Period calls across Arabidopsis chr4 and E. coli — **Green: the statistic. Blue: the unconfirmed adaptive-PNG version, shown for contrast.** Unconfirmed, the statistic also calls period 3 in 10 of 23 E. coli windows. That is not a false positive — it is codon structure in a dense bacterial genome — and harmonic confirmation removes it, because 6 and 9 do not dip.

Five

What it is not

Most of what was learned here is negative, so it gets its own section rather than a footnote.

It is not a compressor

input	v0.1 (base64)	v0.2	gzip -9	xz -6	2-bit + xz
sample.fasta, 611 B	0.452×	0.666×	0.111×	0.183×	0.183×
CHM13 chr21 5–14 Mb	—	0.214×	0.253×	0.184×	0.172×

The rewritten container beats gzip on the megabase inputs, but that is the two-bit packing, not the layout — the same packer into xz beats the PNG every time. And the 2-D layout never beat gzip on the same bytes, at any width, for any period tested.

Things that looked like results and were not

A phase diagram with no phase boundary. The first grid ran to 30% divergence and 900 bp and every one of its 70 cells was a hit. That is not a result, it is an under-ranged axis. It had to be re-ranged twice before anything failed.
A global baseline made every short width periodic. Four letters mean a byte matches the byte two positions back about a quarter of the time, so every sequence “dips” below a global average at small widths. The detector had been scoring against a rolling local baseline all along; nobody noticed that was load-bearing until the statistic was ported to a browser and every puzzle level was solvable with the answer “2”.
The smallest member of a harmonic family is not the fundamental. A noise-level dip at p/2 gets full harmonic support, because 2p, 3p and 4p are the real period and its harmonics. A 340 bp array was reported as 170 with a dip of 0.07 while 340 dipped 0.90.
A finder detector that matched a template. It failed silently past ten degrees of rotation, because a rotated square fills less of its own bounding box — 0.49 straight, 0.32 at 17°, 0.25 at 45°. A topological test (one hole, 25/49 of the filled shape) is rotation-invariant by construction and took recovery to 12/12 across a full turn.
A container detector that catches containers. It catches high-entropy containers. A satellite array two-bit-packed into a PNG comes out at 0.13× and its pixels are nowhere near random, so the rule never fires. Portrait mode evades it too, by looking like a picture.

Six

The rest of what was built

A container that is a container

No base64, two-bit DNA packing with lossless side streams for headers, newlines, N runs and soft-masking case, length and SHA-256 in a tEXt chunk, strict decoding. 0.214× on chr21.

Details →

A portrait that still decodes

Payload in the low nibble of every channel, a GC-and-compressibility rendering in the high nibble, Hilbert-ordered so neighbouring pixels are neighbouring sequence. Costs 1.16–1.48× the plain container.

Details →

Provenance inside a figure

The git commit, the command line and the input checksums, hidden in a plot's low bits, so a figure carries its own provenance through the one channel that always survives — somebody pasting it into a slide.

Details →

A detector for both

40/40 containers flagged, 0/119 real figures falsely flagged. A manifest-sized LSB payload is invisible (AUC 0.41); a full cover is not (AUC 0.92).

Details →

A FASTA you can print

Reed–Solomon over GF(256) with interleaving and four finder squares. 73 of 108 photographed trials recovered; the boundary is roughly blur σ ≲ 0.3 × module pitch, and rotation is not a factor.

Details →

Proving a repeat without showing the genome

A match count is one equality per base, so unlike a compressed size it can be arithmetised. The relation, a Merkle commitment and a sampling audit are implemented and tested; the SNARK is written and unproven.

Details →

CHM13 chr21 5-14 Mb rendered as a Hilbert-ordered portrait — **9.1 MB of chr21 in one 2048×2048 PNG that decodes byte-for-byte.** Hue is GC content, brightness is local compressibility, and position on the curve is position in the file — so satellite arrays glow and unique sequence stays dark.

The claim the proof would make

I know a sequence S of n bases whose Merkle root is R,
such that at least k positions satisfy S[i] = S[i − w].

For a satellite array that is a statement about repeat structure. At w = 3 it is a statement about a trinucleotide expansion.

0.899

audited lower bound on the match rate

against a claim of 0.835

7.7%

of the sequence the audit discloses

which is exactly why the audit is not the real thing

39310k

circuit constraints

only 1799k of them are the statistic; the commitment is the cost

Not built

The SNARK. The circom circuit is written and its constraints counted, and it has not been compiled or proven — this machine has no circom. And a proof that some sequence with root R has k matches says nothing about where that sequence came from; the commitment has to be bound to a sequencer signature or a lab attestation. The cryptography is the easy half.

Seven

Play it

The same statistic as a puzzle. You get a sequence and a budget of probes; each probe lays the sequence out at a width you choose and tells you what it compressed to. Find the period. It runs on the browser's own CompressionStream, so a width that snaps in the game snaps in the Python.

Open the puzzle

Building it is what exposed the global-baseline bug above — every level was solvable with the answer “2”, and it took a second implementation to see it.

Eight

Method

Every number on this page is read out of results/ by site/build_site.py, which generates the page. None of it is typed by hand, so it cannot drift from the experiments. Colour tokens are contrast-checked at build time by site/palette.py, which refuses to build if a token that carries meaning falls below its WCAG floor.

Eleven experiments, each one file, each writing a TSV or JSON that these figures and numbers come from. 107 tests, including a suite that ports the puzzle's random number generator into Python so its levels cannot silently become unsolvable.

Experiments Raw results Tests Write-up