Experiment 196

“F5.1: Gromark with multiplicative feedback (each digit the product of two earlier ones) on a free mixed alphabet, bases 2-16 and 26, every primer: exact; YAR as a primer by subsumption”

F5.1. Every Gromark rule tested so far adds earlier digits. Here d[i] = d[i-a] * d[i-b] mod B, 1 <= a < b <= 6, every primer, bases 2-16 (base 26 with b <= 5: lag 6 is 1.5 billion primers), four forms, a free mixed alphabet, with 0195's compiled decider in product mode. YAR as a primer (Y A R as 24 0 17 in base 26, or any digits) is one of the primers every exhaustive sweep already enumerates (0076 two-term base 26, 0195 three-term base 26), so it is closed by subsumption.

revertedstatus
experiment 195parents
56 stime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

A variation of the 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. key: each new digit is the product, not the sum, of two earlier digits. We try every base from 2 to 16 and 26, every pair of earlier positions up to six back, every set of starting digits, with any mixed alphabet.

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.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENTGromark, each digit the product of two earlier digits, on a mixed alphabet in any order: each cell one number base; does any rule and starting run fit the 24 known letters?24681012141626no starting run fits K4some dobase not triedK4 fits in 0 of 16 basesrules per base: 15 (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16), 10 (26)starting runs of digits tried in each base, each in four forms (bar height: log of the count)24681012141626299,394,061 starting runs in allfrom 516 in base 2 to 88,285,440 in base 16settings the 24 known letters allow, all bases togetherK410PPK4 0, ten scrambled copies 0, the two planted texts (P) 1 and 32OUT: NO READING; GROMARK WITH MULTIPLIED DIGITS FITS K4 IN NO BASEEASTNORTHEASTBERLINCLOCK
the idea

Every Gromark rule tried so far adds earlier digits. Multiplying them is the other simple rule, and the raised YAR has been read as starting digits.

the check

Every pair of earlier positions up to six back, every base from 2 to 16 and 26, every starting run, four ways of applying the digit, any mixed alphabet.

the bound

Nothing fits K4 or a scrambled copy; planted texts are found. F5.1 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.

  1. Base 10, rule 'multiply the digits 2 and 5 places back', primer of 5 digits.
  2. The digit stream often collapses to zeros; then the key is constant and K4's three different carved letters under the known E rule it out at once.
  3. Otherwise the same checks as the additive Gromark: equal known letters must land on equal slots.
  4. Every primer, rule, base and form; then scrambled copies.
the worksheet: the first steps by hand, on squared paper
MULTIPLIED DIGITS OFTEN DIE OUTBase 10, each digit the product of those2 and 5 back, starting 3 7 9 1 4: 3 7 91 4 3 8 7 8 8 4 4 8 2 4 8 6 4 ... Once a0 or an even run appears, the digitsstay even or collapse to 0.A key of zeros is one plain mixedalphabet, which K4's three differentcarved letters under the known E ruleout at once. The rest fail the samechecks as the added Gromark.
4

Worked example, generated

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

base 10, each digit the product of the digits 2 and 5 places back, primer 3 7 9 1 4:
3 7 9 1 4 3 8 7 8 8 4 4 8 2 4 8 6 4 2 6 6 6 4 2 4 2 4 8 8 2 6 8 8 4 6 4 8 2 2 2
5

Hypothesis, for a cryptanalyst

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

F5.1 (low value: no creator remark points here), C22(a) (YAR as a primer). Model as 0107/0195 with the recurrence multiplicative. Statistic: consistent (rule, primer, form) settings, K4 against 10 copies; plants.

6

Prediction

Written before the run; the result decides it.

No setting consistent on K4 or the copies. Zero candidates.

7

Method

  1. For each base, rule and form: equal-letter pairs fix digit differences (or kill the form).
  2. Every primer (compiled, 4 processes), product recurrence, pair checks, then the one-to-one check.
  3. K4, 10 shuffled copies, 2 planted texts.
8

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

299,394,061 primers x 4 forms; consistent K4 0 (copies 0-0); plants [1, 32]

What was searched, as the harness recorded it.

family
Gromark with multiplicative feedback d[i] = d[i-a] d[i-b] mod B, free mixed alphabet, bases 2-16 (lags to 6) and 26 (lags to 5), four forms, exact
rule jobs
235
primers
299,394,061
per base
2
rules
15
primers
516
k4
0
3
rules
15
primers
4,923
k4
0
4
rules
15
primers
25,488
k4
0
5
rules
15
primers
92,775
k4
0
6
rules
15
primers
268,740
k4
0
7
rules
15
primers
663,411
k4
0
8
rules
15
primers
1,455,168
k4
0
9
rules
15
primers
2,914,623
k4
0
10
rules
15
primers
5,432,100
k4
0
11
rules
15
primers
9,548,715
k4
0
12
rules
15
primers
15,991,056
k4
0
13
rules
15
primers
25,709,463
k4
0
14
rules
15
primers
39,919,908
k4
0
15
rules
15
primers
60,149,475
k4
0
16
rules
15
primers
88,285,440
k4
0
26
rules
10
primers
48,932,260
k4
0
consistent
k4
0
copies
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
plants
1, 32
plants
  1. base
    13
    lags
    1, 4
    primer
    1, 5, 2, 3
  2. base
    26
    lags
    2, 5
    primer
    16, 18, 10, 20, 19
k4 consistent
none
blocked
base 26 with lag 6 (1.5 billion primers)
yar primer
subsumed: every primer enumerated in 0076 and 0195
copies
10 shuffled copies (seed 1970)
seconds
56
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 2026-10-18 12:26 UTC; updated after every experiment.
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