Experiment 150

“F1.6, second part: one carved letter wrong at a known place, or one letter missing or extra, through the exact free-alphabet Gromark verdicts (base 10 two- and three-term, other bases)”

F1.6, Gromark verdicts. 0069, 0076 and 0107 showed no primer of any two- or three-term Gromark rule gives a one-to-one alphabet consistent with the 24 known letters, in base 10 and bases 2-9, 11-16, 26. Here every single-letter error those tests can see: the carved letter at each known place changed to each other letter (600), and one letter missing or extra before EAST (every known place moves by one) or between the runs (BERLINCLOCK moves by one): 604 variants of K4. The Gromark key depends on absolute position, so the shifts matter here, unlike for periodic keys. K4's variants first; scrambled copies only if a variant fits.

revertedstatus
experiment 147parents
24 mintime, 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. is a cipher whose key is a stream of digits grown from a few starting digits, used with a scrambled alphabet; earlier experiments showed no starting digits and no alphabet fit 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.. If one carved letter is wrong, or one is missing or extra, that verdict might be unfair. We change each carved letter at the known places to every other letter, shift the known words by one place, and rerun the exact Gromark tests.

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 ACCENTfree-alphabet Gromark, base 10, two-term rules, lags up to 6 (0069): each cell one rule and base; does any of 605 one-letter variants fit?no variant fits15 settings, 0 with a fitting variantfree-alphabet Gromark, bases 2-9, 11-16 (lags up to 5) and 26 (up to 4) (0076): each cell one rule and base; does any of 605 one-letter variants fit?146 settings, 0 with a fitting variant (first 90 shown)free-alphabet Gromark, base 10, three-term rules, lags up to 6 (0107): each cell one rule and base; does any of 605 one-letter variants fit?20 settings, 0 with a fitting variantOUT: NO READING; GROMARK STAYS DEAD UNDER ANY SINGLE CARVING ERROREASTNORTHEASTBERLINCLOCK
the idea

Gromark grows a key of digits from a few starting digits and uses a scrambled alphabet; it was ruled out exactly. One wrong, missing or extra carved letter could have spoiled that verdict.

the check

605 versions of K4: each carved letter at the known places changed to every other letter, and the known words moved one place (a Gromark key depends on absolute position), through the three exact Gromark tests.

the bound

No version fits any rule, base or form: exact, so no scrambled copies are needed.

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. Take Rogers' rule (each digit the sum of the digits 5 and 4 places back, mod 10) and a primer.
  2. Suppose the carved Q at place 27 should have been another letter, say R.
  3. Places 26 and 27 no longer carve the same letter, so their digit difference is no longer forced; other equal pairs still are.
  4. Test every primer against the remaining pairs, then check that the slots and letters pair one to one.
  5. Repeat for every changed letter, every shift of the known words, every rule, base and form.
the worksheet: the first steps by hand, on squared paper
WHAT ONE SLIP CHANGES FOR GROMARK: A SUBSTITUTION TOUCHES ONE EQUATION, A SHIFT MOVES THE DIGITSvariantwhat changessub 27 Q->Rplaces 26 and 27 no longer carve the same letter; their digit pair is freedall known places +1every known letter reads the digit one place later in the streamBERLINCLOCK -1the second run reads digits one place earlier; EAST NORTHEAST unchangedas carved0069, 0076, 0107: no primer fits
4

Worked example, generated

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

the carved letters at the known places and the changes tried:

place 22: carved F under known E; tried the other 25 letters
place 26: carved Q under known N; tried the other 25 letters
place 27: carved Q under known O; tried the other 25 letters
place 33: carved S under known S; tried the other 25 letters
place 74: carved K under known K; tried the other 25 letters

plus every known place's carved letter moved one place left or right (a letter extra or missing before EAST),
and BERLINCLOCK's alone moved (a letter extra or missing between the two known words)
5

Hypothesis, for a cryptanalyst

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

Family G and C17 (a carving slip), C22(a) (the raised YAR as a Gromark primer), family E (Bean's Gromark case, knowledge/sources/bean-2021-cryptodiagnosis-of-k4.txt). Models and deciders unchanged from 0069 (base 10, two-term rules with lags up to 6, every primer, four forms), 0076 (bases 2-9 and 11-16 with lags up to 5, base 26 with lags up to 4) and 0107 (three-term rules, base 10, lags up to 6): equal-letter pairs fix exact digit differences, then a full one-to-one check. Exact. If no variant of K4 fits, the result is exact and needs no controls; any fit is compared with the same variants of ten scrambled copies in a follow-up.

6

Prediction

Written before the run; the result decides it.

No variant fits under any rule, base or form: Gromark stays dead with a single carving error. Zero candidates.

7

Method

  1. Load 0069, 0076 and 0107's deciders unchanged.
  2. For each rule and base: the digit stream at the known places for the copper's positions and for the four shifts.
  3. For each of 604 variants: the equal-letter pairs, then every primer, then the one-to-one check.
  4. List any variant that fits.
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

605 variants x 181 rule/base settings: settings with any fitting variant 0

What was searched, as the harness recorded it.

family
free-alphabet Gromark (0069, 0076, 0107) on 604 one-letter variants of K4
variants
605
settings
0069
settings
15
settings with a fit
0
0076
settings
146
settings with a fit
0
0107
settings
20
settings with a fit
0
fits
none
n settings with fit
0
seconds
1,359
exhaustive
yes
controls
none needed if nothing fits (exact); any fit is compared with the same variants of 10 scrambled copies in a follow-up

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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