After 671.0B+ configurations tested
What we’ve learned
No single classical cipher decrypts K4. Every standard cipher family has been eliminated under direct positional correspondence. One statistical anomaly survived correction. Several promising leads were rigorously tested and retired. This page documents both.
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
Every standard classical cipher family has been tested against K4 under direct positional correspondence (where ciphertext position N maps to plaintext position N). The results:
- All periodic polyalphabetic ciphers (Vigenère, Beaufort, Variant Beaufort) at every key length 1–26: mathematically impossible (Bean constraint proof).
- 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).
- All simple transposition families combined with periodic substitution: maximum 13/24 crib matches (noise).
- Running keys from 60,000+ English texts combined with structured transposition: zero candidates across 106 billion position checks.
- Bespoke systems (VIC, RS44, Wheatstone, interrupted-key, DRYAD): all noise within tested scope.
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 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 the only statistically significant anomaly in K4 that survived rigorous correction.
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)
Under a KA-autokey Vigenère model, simulated annealing identified 17 candidate filler positions that used only 7 letters (B, G, I, K, O, W, Z), with odds of roughly 1 in 16,000. This was our strongest statistical claim for months. However, a score-conditioned null experiment showed that the SA process produces 11 distinct letters on real K4, indistinguishable from shuffled controls (p = 0.30). The original “7 distinct” observation was traced to post-hoc selection from positions already containing palette letters, a circular observation. All downstream claims (BCL keystream enrichment, KA mod-5 column structure, arithmetic progression patterns, KRYPTOS × SEVEN lookup table) were also retired. Full report.
Summary
What we established
- 671.0B++ configurations tested with zero signal above noise across all classical single-layer cipher families
- One surviving anomaly: the Stehle constant-difference pattern (p ≈ 1/642)
- Multiple promising leads rigorously tested and retired when controls failed
- Every result is open source and independently reproducible
What remains unknown
- The cipher type and key (every standard single-layer classical cipher eliminated under direct correspondence)
- Whether K4 contains null characters (plausible but unproven; the statistical evidence was retired)
- The source text for a running-key cipher, if that model is correct
- Whether the answer requires external evidence (physical investigation, unreleased documents, K5) rather than further computation