“F3.1: a puzzle word and a dictionary word joined by a combiner other than plain addition: through a table on a third, keyword-mixed alphabet, or by multiplication”
F3.1. 0115 tested two key words added letter by letter, with letters numbered on the standard or KRYPTOS order. Here the combiner changes: (a) the two words are joined through a table built on a third alphabet, the keyword-mixed alphabet of any of the 62 vocabulary words, which numbers both words' letters (so the combined key is a + b on that numbering); (b) the two words' numbers are multiplied mod 26, on the standard, KRYPTOS or any vocabulary numbering. Everything else as 0115: first word any puzzle word from every start, second word any dictionary word of 3-24 letters in every rotation, 12 table rules, exact, ten scrambled coppers.
revertedstatus
a new rootparents
5 stime, all phases
0candidates
0/24known letters
unclocked
1
The experiment method
What the method does with the 24 known letters.
Scheidt's professional habit is a key built from two parts joined by a rule. We already tried two secret words added together letter by letter. Here the rule for joining them changes: the words are combined through a table made from a third word's alphabet, or their letter numbers are multiplied. For each first word from the puzzle, the 24 known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK. then dictate the second word letter by letter; we check whether any real English word fits, and compare with scrambled copies of the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page..
Words in the margin are defined on the glossary page.
1.1
The method at work
The carved letters go in at the top; the reading comes out at the bottom.
the idea
Scheidt's habit is a key made of parts joined by a rule. Two words added letter by letter was tried before (0115). Here the rule changes: the words are numbered by an alphabet mixed from a third word, or their numbers are multiplied.
the check
For every first word from the puzzle, at every start, the 24 known letters dictate the second word's letters; any consistent second word is looked up in the dictionary in every rotation. Exact; ten scrambled copies; two planted texts.
the bound
Not one pair of first word and length survives on K4 or on any copy; both planted texts come back word for word. F3.1 closed.
2
Best candidate against the known letters
This experiment produced no candidate: the search ruled everything out before a full text was built. Its product is the bounded negative in section 7.
3
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Take the sculpture's table (KRYPTOS alphabet, Vigenere) and number letters by the alphabet mixed from the word BERLIN: B=0, E=1, R=2, L=3, I=4, N=5, A=6 and so on.
At each known place, the table gives the key value: carved place minus known place.
Write the first word, say PALIMPSEST, under the message from some letter, and number its letters the same way.
The second word's number at that place is the key value minus the first word's number (or, for multiplication, the number that times the first word's number gives the key value).
If the second word repeats every n letters, places n apart must ask for the same letter.
When every letter of the second word is forced, look it up in the dictionary, in every rotation.
Do the same on scrambled copies of the carved text.
the worksheet: the first steps by hand, on squared paper
4
Worked example, generated
The same steps run by the code on the real letters.
numbering by the alphabet mixed from BERLIN: BERLINACDFGHJKMOPQSTUVWXYZ
sculpture's table (KRYPTOS alphabet, Vigenere); first word PALIMPSEST from its P at place 1; second word of length 8
place known carved key value first letter (number) second word's number slot (mod 8)
22 E F 1 A (6) 21 5
23 A L 10 L (3) 7 6
24 S R 21 I (4) 17 7
25 T V 18 M (14) 4 0
30 H N 5 T (19) 12 5
31 E G 2 P (16) 12 6
64 B N 11 I (4) 7 7
slots asked for two different numbers: [0, 1, 2, 3, 4, 5, 6, 7]: this pair is dead
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C5(b) ('executed years later when used with the correct key word/s', Scheidt 2011 via Bean, knowledge/sources/bean-2021-cryptodiagnosis-of-k4.txt and 03-scheidt-said.md), C6 (Scheidt's constructive key management: a working key built from splits through a combiner, knowledge/07-people.md), F3 family. Model: carved = T(plain, k_i) for one of 12 table rules (Vigenere, Beaufort, variant; plain and cipher alphabets standard or KRYPTOS), key value k_i = g(N(a[(i + o) mod m]), N(b[i mod n])) with N a numbering of letters (standard, KRYPTOS, or the keyword-mixed alphabet of a vocabulary word: 64) and g in {addition (new only for the 62 mixed numberings), multiplication mod 26}. a: every puzzle word (0115's list: vocabulary, K1-K3 plaintext words, theme words), every start o. The 24 known letters force k at their places; g^-1 gives b's number (multiplication: all solutions of a x = k mod 26, none when gcd fails); b repeating with period n must agree within each slot; a fully forced b (or, for multiplication, every b allowed by the slot sets) is looked up among the rotations of dictionary words of length n (kryptos/data/words.txt). Exact.
6
Prediction
Written before the run; the result decides it.
No pair fits on K4 under either combiner; the coppers give no or almost no dictionary hits either (0115 had none on K4). Multiplication leaves more consistent cases than addition (zero divisors make b ambiguous), at the coppers' rate. Zero candidates, or only candidates inside the coppers' hit counts.
7
Method
Build the puzzle word list (0115's) and the 64 numberings.
For each text (K4, ten coppers), table rule, numbering, combiner, first word and start: the forced key value at each known place, then the second word's number (or numbers) there.
For each length 3-24: slot agreement; fully forced second words looked up among dictionary rotations; for multiplication with ambiguous slots, dictionary rotations matched against the slot sets.
Count consistent cases and hits per text; decrypt K4's hits.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.