After 671.0B+ configurations tested
What we’ve learned
No standard single-layer classical cipher has survived against K4 under the
project’s direct-positional, additive-key test frame. Large bounded slices of
two-layer and three-layer classical space are also saturated. A few anomaly
surfaces remain live, currently led by the CT-perturbation hypothesis (small
transcription differences between Sanborn’s archived coding charts and the
canonical 97-character text), with the W-delimiter interpretation
retained as a multi-layer-only component after its single-layer construction
saturated, and the local Stehle regularity still under follow-up. Several
earlier “signals” were retired after stricter controls.
The K4 Ciphertext (97 Characters)
Hover or tap a letter to see its position. Colors show known plaintext regions and the Stehle anomaly zone.
What 671.0B+ configurations told us
The site has accumulated a large negative map of bounded classical search space. Under direct positional correspondence (where ciphertext position N maps to plaintext position N), the current repo state supports the following:
- All repeating-key polyalphabetic ciphers (Vigenère, Beaufort, Variant Beaufort) at every key length 1–26: mathematically impossible within the direct-positional additive-key model.
- All autokey variants (PT-autokey, CT-autokey, both Vigenère and Beaufort): structurally impossible, even composed with arbitrary transposition.
- All fractionation families (Bifid, Trifid, Playfair, Four-Square, ADFGVX): eliminated by structural proofs (K4 uses all 26 letters; Bifid requires 25).
- Many structured transposition + periodic substitution combinations: exhaustively negative or algebraically blocked within their tested families.
- Running keys from 60,000+ public English texts combined with structured transposition: zero candidates across 106 billion position checks. A later check (April 2026) found that running-key combined with columnar transposition at widths 6/8/9 is also blocked by the current 242-inequality Bean constraint set regardless of which source text is used. This does not rule out running keys from non-English or non-standard texts under other transposition types.
- Two-layer and three-layer compositions tested so far: 105,692 two-layer branches (additive × transposition, transposition × periodic substitution, 6 stateful families) and 838,350 non-columnar three-layer branches. Max crib score 7/24 across the three-layer enumeration. All noise within the registered layer families and default keyword sets.
- Many bespoke or historical systems (VIC, RS44, Wheatstone, interrupted-key, DRYAD): all noise within tested scope.
These eliminations describe the scope of what we have tested under specific assumptions. They do not claim that K4 cannot be solved by classical cryptanalysis; classical cipher space has infinite variation, and any bespoke procedure, non-standard transposition, or combination outside our tested scope remains open. We document concrete negatives so the community does not have to re-test approaches that are already known to fail, not to suggest the problem is closed.
These eliminations do not rule out the same families as one layer of a multi-layer construction, nor do they apply if K4 uses a non-additive cipher mechanism. See the elimination database for the full inventory, and the open questions for what remains.
The entire codebase is open source. Every elimination includes a reproduction command.
The W-Delimiter Structural Lead
A live layout hypothesis, not a settled claim
The short version
The five carved Ws at positions 20, 36, 48, 58, and 74 explain the old
width-21 vertical-bigram anomaly: remove those five letters and the anomaly disappears.
As of April 2026 the single-layer construction is saturated: 80+ direct W-segmentation
hypotheses tested, no signal. W-segmentation is therefore no longer the primary anchor.
It remains admissible inside multi-layer hypotheses, and the public reading is still
“if K4 has a delimiter or row-end mechanism, the W positions are the cleanest
bounded place to test it,” not “the Ws are proven delimiters.”
What we know and don’t know
We know the width-21 effect is largely explained by W placement. We do
not know whether the Ws are ciphertext, nulls, row-end markers,
or some other procedural feature. The live value of this anomaly is that it creates a
finite structural test surface: six segments with fixed crib geometry, including only
two characters after EASTNORTHEAST and four before BERLINCLOCK.
One live interpretation worth testing is a punctuation or marker convention:
after decryption, some or all carved Ws may correspond to plaintext letters such
as X, Q, or Z used as separators or punctuation-like markers,
analogous to delimiter behavior seen elsewhere in Kryptos. The site treats that as a
bounded hypothesis surface, not as a recovered fact about the plaintext.
The Stehle Anomaly
A unique constant-difference pattern at positions 55–63
The short version
Every 4th character in one region of K4 (positions 55–63) differs from its predecessor by exactly 5 in the alphabet. This pattern appears nowhere else in the ciphertext. After correcting for 712 statistical tests, the odds of this happening by chance are about 1 in 642.
Technical detail
If you look at every 4th character in K4 starting from position 55, something unusual happens: each character is exactly 5 positions later in the alphabet than the one 4 spots before it. This holds for a run of 9 consecutive characters (positions 55–63).
We searched the entire ciphertext for this kind of pattern at every possible spacing and every possible difference value. This is the only one. After correcting for the 712 statistical tests we ran, the probability of seeing this by chance is about 1 in 642 (Bonferroni-corrected: 712 / 456,976).
The Constant-Difference Pattern
Every 4th character in this region differs from its predecessor by exactly 5 (mod 26).
What we know and don’t know
The pattern is real and survives multiple-testing correction. However, we have not been able to exploit it: no cipher mechanism we’ve tested produces this pattern as a consequence of its key schedule. It may be a local coincidence in the cipher structure, not a clue to the method. It remains a live local anomaly, but it is no longer the site’s sole or dominant public lead.
Retired Claims
Promising leads that did not survive matched controls
Science progresses by testing and discarding hypotheses. Several observations initially appeared statistically significant but were retired after more rigorous controls. We document them here because intellectual honesty matters more than looking right.
The Null Palette (retired April 2026)
The project previously centered a score-conditioned null-palette story as its strongest signal. That claim did not survive matched controls and is now retired. The underlying lesson is methodological rather than cryptographic: post-hoc anomaly selection can manufacture persuasive-looking structure unless the null model is explicit and adversarially checked. Full report.
Follow-up audit (2026-04-08): An adversarial internal review reclassified 19 additional “interesting” results as eliminated once their dependence on the retired palette or on structural disqualifiers (autokey family, VIC family, period underdetermination) was identified. We also ran a pre-registered checklist: Carter Vol 1 and Kahn Codebreakers as running-key sources against columnar widths 6/8/9, and a non-columnar three-layer enumeration of 838,350 compositions. All returned zero candidates under pre-committed conjunctive thresholds. Full records are in the internal status audit (which is deliberately adversarial about our own claims).
Summary
What we established
- 671.0B+ configurations evaluated across recorded experiments, with no solution-grade signal in the bounded classical slices tested so far
- Standard single-layer classical families are saturated within the project’s direct-positional additive-key frame
- A few anomaly surfaces remain live: the CT-perturbation hypothesis (currently primary), the Stehle local regularity, and the W-delimiter interpretation as a multi-layer-only component after its single-layer construction saturated
- Multiple earlier signals were retired when controls failed
- Every result is open source and independently reproducible
What remains unknown
- The cipher type and key. The site cannot claim to have exhausted non-standard or bespoke space.
- Whether the carved
Ws are ciphertext or delimiters, and whether any physical or procedural segmentation rule is real - Whether K4 contains null characters under any independently justified rule; the old statistical null palette is retired
- Running keys from non-public or non-English sources, or combined with monoalphabetic substitution + non-standard transposition
- Bespoke procedural mechanisms using Sanborn’s encoding charts or physical installation features
- Whether K5, archive photographs, or other primary-source evidence would reveal new constraints
- Anything we haven’t thought of. If you have an idea we haven’t tested, tell us — that is exactly why this site exists.