“Two quarter turns in mixed directions (clockwise then anticlockwise, and the reverse), with a repeating key”
0080-0083 composed quarter turns in one direction only (clockwise, twice or three times). K3's rotations and Sanborn's 'double matrixes' do not fix the sense of each turn. Here every pair of widths 2-96 is turned clockwise then anticlockwise, anticlockwise then clockwise, and anticlockwise twice, forward and inverse, deduplicated against each other and against the clockwise pairs already tested, with a repeating key of length 1-26 before or after.
K3the earlier messages The three solved parts of the sculpture. was made by writing the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. in a grida grid Writing the message into rows of some width and reading it out in another order, column by column for instance, which shuffles the letters without changing them., turning the grida quarter turn Writing the text in rows of a given width and reading the columns out, each from the bottom up, left column first, as if the grid had been turned on its side. a quarter turn, writing it out, and doing that again with a grid of another width. Experiments 80 and 83 always turned the same way. Here the two turns go in opposite directions, or both the other way, at every pair of widths, followed or preceded by a short repeating secret word, and each combination is checked against 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..
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.
the move
Experiment 83 turned the grid clockwise twice. Here one turn goes each way, or both anticlockwise, at every pair of widths from 2 to 96: 53,743 new scrambles.
the check
After the two turns a repeating secret word on the table must give the copper's letters where the known letters landed; two known letters in one slot of the word must agree.
the bound
No word shorter than 22 letters fits, on the copper or the scrambled coppers, and from 22 up K4 sits inside their range, counted as settings or as distinct check sets.
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.
Write the 97 letters in rows of 9; read the columns bottom to top, left column first (a clockwise quarter turn).
Write the result in rows of 12; read the columns top to bottom, right column first (an anticlockwise quarter turn).
Each known letter, say E at place 22, now sits at a new place j.
With a key of length p after the move, its key letter is slot j mod p and must turn E into the carved letter at j; letters sharing a slot must agree.
Repeat for every pair of widths, the three mixed senses, key lengths 1-26 and table rules, and with the key before the move.
the worksheet: the first steps by hand, on squared paper
4
Worked example, generated
The same steps run by the code on the real letters.
clockwise turn in rows of 9, then anticlockwise in rows of 12: where the first known letters go
place letter after cw 9 after ccw 12 copper there
22 E 42 52 J
23 A 53 61 N
24 S 64 70 M
25 T 75 79 Z
64 B 4 65 Y
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Type 1 of directions.md, closing a gap in 0080 and 0083: the two-turn library held only clockwise-clockwise pairs. Sanborn: 'double matrixes and triple matrixes... then went back to this table' (C1); K3 is two rotations of 14 x 24 and 8 x 42 grids (01-facts.md; the Stehle formula). A turn on a ragged grid is not the reverse of the other turn, so mixed senses give new routes. Routes: turn(w1, d1) then turn(w2, d2), (d1, d2) in {(cw, ccw), (ccw, cw), (ccw, ccw)}, w1, w2 = 2-96, forward and inverse, minus repeats and minus the cw-cw set. Key: periodic 1-26 after the move (slot = carved place mod p) or before it, 8 tableau classes, exact by slot agreement; the excess check counts distinct check sets (the lesson of 0086 and 0092). Ten shuffled coppers.
6
Prediction
Written before the run; the result decides it.
Nothing consistent below period 20; at every period the number of distinct consistent check sets on K4 lies inside the ten coppers' range, give or take one period. Zero candidates.
For each sense pair and widths, compose the two turns and its inverse; drop repeats.
For each route and class, compute the key values at the known letters and test periods 1-26 in both orders.
Count settings and distinct check sets per period on K4 and ten shuffled coppers.
List K4's settings below period 20.
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
53,743 new mixed-sense two-turn routes (407 repeats and cw-cw routes skipped) x 8 classes x 2 orders, periods 1-26. K4 live below 20: 0. Outside the control range by settings: {'A': [], 'B': []}; by distinct check sets (periods up to 24): {'A': [], 'B': []}.
What was searched, as the harness recorded it.
family
two quarter turns in mixed senses at widths 2-96, then or before a periodic tableau key