Experiment 69
Experiments 13, 28, 46 and 54 tested the Gromark running-number key only on alphabets built from the puzzle's words. Here the mixed alphabet is left completely free: the 24 known letters must fit some one-to-one alphabet, which the run checks exactly for every starting number and every two-term rule up to six digits back.
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 secret is a short starting number that grows into a long stream of digits, each digit the sum of two earlier ones, plus a scrambled alphabet. Earlier experiments only tried scrambled alphabets built from the puzzle's wordsthe puzzle's words A list of 62 words tied to the sculpture: the earlier secret words, place names, the names of the people involved, the words in the Morse code, and the themes Sanborn has named.. Here the alphabet can be any scramble at all. That sounds hopeless to search, but it is not: the same plain letter must always land on the same carved letter when the digit is the same, which pins the digits down so tightly that every starting number can be checked in a fraction of a second.
Words in the margin are defined on the glossary page.
The carved letters go in at the top; the reading comes out at the bottom.
Gromark adds a running stream of digits to the message on a mixed alphabet. The stream starts from a short primer and grows by adding earlier digits.
With the primer 12345, places 26 and 27 both carve Q but land in two different slots of the alphabet: impossible, so this primer is dead whatever the alphabet.
All 15 two-term rules up to 6 back, every 5-digit primer, four forms, a completely free alphabet: no fit on K4 or on any shuffled copper.
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.
Redo the method on a few letters with pencil and paper.
The same steps run by the code on the real letters.
Rogers' rule (5 and 4 back), primer 12345
stream 1234535798826760833681694975336286
place known carved digit slot (M[P+d]=c)
22 E F 1 5
23 A L 6 6
26 N Q 9 22
27 O Q 7 21
31 E G 6 10
Family, key space, the constraint under test, and the clues it reads.
Family 5, free-alphabet Gromark (the open corner named in families.md after 0028 and 0046). Key digits base 10 from a lagged-Fibonacci rule d[i] = d[i-a] + d[i-b] mod 10, 1 <= a < b <= 6 (15 rules, including Rogers' Gromark a = 4, b = 5), every primer of b digits (5,432,200 primers in all). Four forms, with P, C the standard-alphabet indices and M an unknown mixed alphabet: M[P + d] = c, M[P - d] = c, M[C - d] = p, M[C + d] = p (mod 26). For each primer the 24 cribs give slot-letter pairs that must be a partial bijection: equal slots need equal letters and equal letters need equal slots. Because the digits lie in 0-9, every pair of cribs with the same letter fixes an exact digit difference, so most primers die on the first two such pairs; survivors get the full bijection check. Exhaustive for these rules and forms in base 10. Run on K4 and ten shuffled coppers. Clue entries: C22(a) (the raised YAR / DYAHR as a Gromark primer), C4(b) (Scheidt: 'base', a non-standard number system), C5 ('not mathematical' argues against it, recorded).
Written before the run; the result decides it.
No primer under any of the 15 rules and 4 forms gives a consistent alphabet, on K4 or on any of the ten shuffled coppers. Zero candidates pass.
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
15 of 15 rules, 5,432,100 primers x 4 forms: K4 consistent primers 0; ten shuffled coppers [0, 0, 0, 0, 0, 0, 0, 0, 0, 0].
What was searched, as the harness recorded it.
How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.