Updated after the overnight gap-filling run: every red cell from the first version was tested, and all came back negative. K4 seen as an encryption pipeline. Each step can be built several ways, and every way we tested is marked with its status. The matrix below crosses key structure with alphabet type. Its empty cells are the gaps.
From plaintext to ciphertext, one possible step per column. Sanborn's "one-to-one" statement says no reordering step exists, so the last column is mostly moot.
No reordering, following Sanborn. Rows are how the key is generated; columns are where the alphabet comes from. Red cells are untested combinations.
| Key structure | A–Z / KRYPTOS2 alphabets | Clue words~138 keyed alphabets | Sanborn phrases613k keyed alphabets | Dictionary words842k keyed alphabets | Any alphabetsolved algebraically |
|---|---|---|---|---|---|
| Repeating keywordlength 1–26 | ruled outexact + 1–2 slips | ruled out13,456 pairs, 1–2 slips | ruled outexact | ruled outexact + 1 slip, 1.8M alphabets | partlymask out for L = 1–12, 14, 15, 17, 21, 22; independent alphabets impossible for 1–7, 9, 10, 14, 15, 17, 21, 25 |
| Long keywordlength 27–96 | partlyonly specific words and phrases as keys | partly | partlyphrase as its own key | partly8.9M-letter corpus by exact lookup, 81M configs | undecidable |
| Two combined keysScheidt "key splits" | ruled outunknown splits 2–26 each; QUAE + two splits | ruled out | ruled out | ruled out1.8M alphabets | undecidable |
| Grid keyrow key + column key | ruled outwidths 2–30, all offsets | ruled outwidths 2–30 | ruled out | ruled outwidths 2–30, all offsets, 1.8M alphabets | undecidable |
| Progressive keykey shifts each cycle | ruled out | ruled out | ruled out | ruled out1.8M alphabets, + 1 slip | not tested |
| Autokeyplaintext or ciphertext | ruled outall lags 1–96, forward and backward | ruled out | ruled out | ruled outexact; near-miss 10/24 vs shuffled 10–11/24 | ruled outarbitrary mask + autokey, all lags |
| Chain additionGromark / Vimark, 2 terms | ruled outcovered by the any-alphabet column: free alphabets include all of these | ruled outbases 3–26, primers ≤ 8 digits; 221k dictionary primers; none explains the width-21 rhythm | |||
| Chain addition3 terms | ruled outcovered by the any-alphabet column | ruled out2.27B primers, bases 3–26; 790k chance survivors, none explains the width-21 rhythm | |||
| Running textEnglish / German | ruled outscored vs shuffled | ruled out | ruled out | ruled outK4 −5.17 vs null −4.86…−5.21 | untestable |
| Specific textsK1–K3, tableau, Morse | ruled outexact, all offsets | ruled out | ruled out | ruled out+ 10 books, Carter's Tut vol. 1, interview; 81M configs | untestable |
| Digit keyGronsfeld, clock, dates | ruled outπ, e, √2, φ, coordinates, 1986/89 | ruled out | ruled outno alphabet gives digits ≤ 12 | ruled outnone < 16 | untestable |
| Formula keylinear, polynomial | ruled out1,544 linear rules | ruled out | ruled out | ruled outlinear and quadratic, 1.8M alphabets | n/a |
| Interrupted keysrestart/pause on triggers | ruled out | ruled outQuagmire IV, 116² pairs | not tested | ruled out11,077 models × 842k | undecidable |
| Clock / time streamsBerlin clock, zones, dates | ruled out | ruled outQuagmire IV, 116² pairs | not tested | ruled out1.35M streams × 8.4M vectors | untestable |
| Chaocipherself-modifying disks | ruled out | ruled out116² pairs | not tested | partlyclue × dictionary (10¹⁰ rows) and vs A–Z/KA closed; full dictionary × dictionary open | untestable |
| Two stagesdifferent tableaux | ruled outL1, L2 ≤ 26 | ruled outL ≤ 10 | not tested | partlyL ≤ 12, at shuffled baseline | undecidable |
| Keyword through a gridblock-constant, drift keys | ruled out | ruled out | not tested | ruled out3,366 models × 1.8M alphabets; 148 fits vs 197 chance, all gibberish | undecidable |
Ranked by plausibility for a 1989 hand cipher and by the cost of testing.
The 613k phrase alphabets are now closed for periodic, digit, running, linear and autokey structures. The three newest families were run with clue and dictionary alphabets only.
About 10¹³ rows. A 1M random sample and the whole clue × dictionary block are at the shuffled baseline, and Byrne's rule was unpublished in 1989.
Two tableaux with L1, L2 ≤ 12 sit at baseline. Longer periods are mostly undecidable with 24 cribs, and three stages are out of reach.
Strip-cipher sheets, arbitrary non-keyword alphabets, one-time key sheets. Nothing to search against.
Mask with key lengths 13, 16, 19, 20, 23, 24, 26; both alphabets free with long keys; mask + grid keys at widths above ~11. These need more known plaintext than 24 letters.