Experiment 206

“F5.3: Gromark growth rules in bases 16-26 on the tables built from K1-K3's words and the 2025 letter (0054's 10,404 pairs), two- and three-term rules with lags to 13, exact, with scrambled copies and a planted Gromark text”

F5.3, found by the positive control C-F5-1d (#73): 0054 built 102 tables from the solved messages' words and the 2025 letter, found no pair admits a base of 15 or less, and so tested no growth rule; but bases 16-26 are admissible and were never tested on these tables (0046 tested them on the vocabulary's tables, 0076/0195 on a free cipher alphabet with the plain side standard). Here 0046's rule test, unchanged in substance, on 0054's pairs: every two-term rule k[i] = k[i-a] + k[i-b] and three-term rule k[i] = k[i-a] + k[i-b] + k[i-c], lags up to 13, every base 16-26 the pair admits, 3 forms, at least six checks inside the known runs, then the stream carried from EASTNORTHEAST to BERLINCLOCK; on K4, ten scrambled copies and a planted text.

revertedstatus
experiment 54parents
4 stime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

GromarkGromark A cipher whose secret is a short number that grows into a long stream of digits by adding pairs of earlier digits; each message letter is pushed along the alphabet by the next digit. grows a long number key from a few starting digits by addingVigenere The three rules of arithmetic a table can use: add the key letter to the message letter, subtract the message letter from the key letter, or subtract the key letter from the message letter. earlier digits. Experiment 54 built tables from the words of the solved messages and only checked small number bases, which the known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK. rule out; the larger bases, 16 to 26, were never checked on those tables. We check them now with every growth rule looking up to 13 digits back.

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.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARnumber bases, on 10,404 table pairs from the solved messages' words: 1-15 ruled out by 0054 (every pair forces a shift of 16 or more), 16-26 tested here1510162026364 rules (two and three terms, lags to 13), 3 forms, every base each pair allowsrules that fit six or more of the known steps, then carry from EASTNORTHEAST to BERLINCLOCK: K4, ten copies, the planted text PK410Pno rule fitsa rule fitsthe planted text (base 20, rule 7, 3, tables PART and THIRTY) is found, the only rule that fits itEASTNORTHEASTBERLINCLOCKIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENTOUT: NO READING; NO GROMARK RULE FITS K4 IN BASES 16-26 ON THESE TABLES
the idea

Experiment 54 built tables from the solved messages' words, saw that no pair allows a number base below 16, and stopped; bases 16-26 were never checked on those tables. A positive control found the gap.

the check

Every two- and three-term growth rule looking up to 13 digits back, in every base 16-26 a pair allows, three forms, needing six checks inside the known runs and then the stream carried to the second run; K4, ten copies, a planted text.

the bound

No rule fits K4 or any copy; the planted Gromark text is found. F5.3 closed.

2

Experiment lineage

What this experiment was built on, from the lineage page: 3 experiments before it, back to the root of its line. Its number is in bold.

kept reverted, in its family's colour ×error or timeout reverted under today's rules built on a parent in the same family built on a parent in another family
3

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 under Result and bounds below.

4

Walkthrough, by hand

Redo the method on a few letters with pencil and paper.

  1. Build a table from a solved-message word, say DESPARATLY, and use it for the plain or cipher side.
  2. Read off the shift each known letter needs: 13 shifts in a row over EASTNORTHEAST, 11 over BERLINCLOCK.
  3. Choose a base, say 20, and a rule, say each digit is the sum of those 5 and 2 back.
  4. Check: shift 6 must equal shift 1 + shift 4 mod 20, and so on along both runs.
  5. One failure kills the rule; repeat for every rule, base, table and form.
the worksheet: the first steps by hand, on squared paper
placeknowncarvedshift22EF823AL1724SR925TV326NQ727OQ628RP1229TR830HN1231EG932AK033SS1434TS13The largest shift is 17, so only basesabove it are possible. A rule such as'each digit is the sum of those 5 and 2back' must reproduce shift 6 from shifts1 and 4, and so on along the run: 11would be needed in base 20, the coppergives 6.THE SHIFTS EASTNORTHEAST FORCES, STANDARD PLAIN AND KRYPTOS CIPHER ALPHABET
5

Worked example, generated

The same steps run by the code on the real letters.

standard plain alphabet, KRYPTOS cipher alphabet, Vigenere: the forced shifts over EASTNORTHEAST

shifts: 8 17 9 3 7 6 12 8 12 9 0 14 13
largest 17: only bases 18-26 are possible
rule (5, 2) in base 20: shift 6 should be shift 1 + shift 4 = 11; it is 6
6

Hypothesis, for a cryptanalyst

Family, key space, the constraint under test, and the clues it reads.

C22(a) (Gromark; YAR as primer), Bean's Gromark case (knowledge/05-attacks.md). Model: c = C[P(p) + k_i] (or Beaufort and variant forms), plain and cipher alphabets keyword-mixed from K1-K3 plaintext words and the C13/C14 words (0054's pool: 102 alphabets incl. standard and KRYPTOS), key digits in base B with a lagged rule. Each known letter forces a shift; all must be below B; the rule is tested on the 13 and 11 consecutive forced shifts (13 - a and 11 - a checks), at least six (chance about 26^-6 per set), and survivors must carry their full stream from the first run to the second. Statistic: survivors with six or more checks, and survivors consistent with both runs, K4 against each copy.

7

Prediction

Written before the run; the result decides it.

No rule with six or more checks survives on K4 beyond the copies' count; none carries to the second run. The planted text is found. Zero candidates.

8

Method

  1. Rebuild 0054's alphabet pool.
  2. For each plain and cipher alphabet and form, the 24 forced shifts; the bases from max(16, largest + 1) to 26.
  3. Compiled: every rule (78 two-term, 286 three-term), checked on the consecutive shifts in each run; six or more checks to survive; then carry the stream from the first run to the second.
  4. K4, ten copies, a planted text; counts compared.
9

Result and bounds

The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.

0candidates returned
0passed every gate
0/24known letters, best
–lowest loss
nonechampion before

Survivors with >= 6 checks: K4 0 (both runs 0), copies 0-0 (both runs 0-0). Plant found: True.

What was searched, as the harness recorded it.

family
Gromark growth rules (two- and three-term, lags to 13) in bases 16-26 on 0054's K1-K3-word and 2025-letter tables
alphabets
102
pairs
10,404
forms
3
rules
364
bases
max(16, largest forced + 1) to 26
min checks
6
k4
survivors
0
survivors both runs
0
list
none
copies survivors
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
copies survivors both runs
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
plant
plain
PART/keyword
cipher
THIRTY/keyword
form
vig
base
20
rule
7, 3
found
yes
survivors
1
survivors both runs
1
spot check
8960 (table, base, rule) cases checked against Python
controls
10 shuffled copies (seed 5300)
seconds
3
exhaustive
yes

How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.

Rendered from the record on 2026-11-05 17:14 UTC; updated after every experiment.
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