Experiment 107
0069 closed two-term Gromark rules on a free alphabet; 0046 tried three-term rules only on alphabets built from the puzzle's words. Here the digit rule is d[i] = d[i-a] + d[i-b] + d[i-c] mod 10 for every 1 <= a < b < c <= 6 (20 rules) and every primer of c digits, with the mixed alphabet left free, tested by 0069's exact digit-difference 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. makes a long stream of key digits from a short starting number, each new digit the sum of earlier ones, and uses a scrambled alphabet. Experiment 69 tried every rule that adds two earlier digits, with any scrambled alphabet, and found nothing. Here each digit is the sum of three earlier ones, every such rule and every starting number up to six digits, again with any scrambled alphabet.
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 grows a long stream of key digits from a short primer, each digit the sum of earlier ones, and enciphers on a mixed alphabet. Experiment 69 tried every two-term rule; here each digit sums three earlier ones.
With the alphabet free, the test is a clash: Q carved at 26 and 27 from N and O must sit in one slot, but this primer puts them in slots 19 and 15.
All 20 three-term rules, 10,631,000 primers of up to six digits, four ways of applying the digit: no primer survives on K4, nor on any of ten scrambled coppers.
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.
rule: each digit the sum of the digits 1, 3 and 5 places earlier, mod 10; primer 1 2 3 4 5
stream: 1 2 3 4 5 9 5 3 6 6 8 9 8 2 7 3 4 9 4 5 7 5 9 0 0 6 1 0 6 7 3 0 7 6
places 26 and 27 both carve Q, from known N and O; form M[P + d] = c:
N (13) + digit 6 = slot 19; O (14) + digit 1 = slot 15
two different slots of one alphabet cannot both hold Q
Family, key space, the constraint under test, and the clues it reads.
Family 5's open corner: 'three-term rules with a free alphabet' (families.md). Key digits base 10 from d[i] = d[i-a] + d[i-b] + d[i-c] mod 10, 1 <= a < b < c <= 6, every primer of c digits (10,631,000 primers in all). Four forms as in 0069 (M an unknown mixed alphabet, P and C standard indices): M[P + d] = c, M[P - d] = c, M[C - d] = p, M[C + d] = p. Pairs of known places with the same letter fix exact digit differences (digits are 0-9), then the full partial-bijection check. Exhaustive in base 10 for these rules. C22(a), C4(b). A planted text is recovered. Ten shuffled coppers.
Written before the run; the result decides it.
No primer under any of the 20 rules and 4 forms is consistent, on K4 or on any shuffled copper. Zero candidates.
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
20 of 20 rules, 10,631,000 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.