“Routes beyond columns: spirals, snakes and diagonals through a grid, tested in both orders”
The route set is the one gap the columnar experiments left: writing in rows and reading out along a spiral, a snake (alternate rows reversed), or diagonals, at every width. Each route is tested before the tableau, as in experiments 6 and 16, and after a substitution, as in experiment 19.
So far the grids were read out by columns. The old manuals also read them out in a spiral from a corner, in a snake that turns at the end of each row, or along diagonals. We try all of those, at every width, and ask the two questions as before: if the scramble came first, could a short secret word on the tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS. then explain the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.; and if the letters were swapped first and scrambled after, do 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. ever land without clashing.
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 routes
Spirals, snakes and diagonals over grids of width 2 to 48, read forwards or backwards: 1,128 ways of shuffling the 97 letters before the sculpture's table.
the arcs
Drawn for one route, a clockwise spiral on rows of 10. Each known letter moves to a new place; the carved letter there must be its enciphered form.
the bound
No route lets a secret word shorter than 23 letters explain the known letters, and the best forced key run, GLEBRIM at -4.937, is no more English than on shuffled coppers. After a letter swap instead of the table, no route passes at all.
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.
Width 10: write the 97 positions in rows of 10.
Spiral: start at the top left, read along the top row, down the right edge, back along the bottom, up the left edge, then inward.
Note where position 22, the E of EAST, comes out, and where each of the other known letters comes out.
Before-the-table test: the carved letter at each landing place and the known letter force a key letter; landing places a multiple of p apart must agree.
After-a-swap test: if the carved letter at E's landing place also sits at the landing place of a different known letter, the route is dead for any letter swap.
Snake and diagonals the same way, at every width.
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.
route: rows of 10, read out in a clockwise spiral from the top left
first twelve positions read out: 1 2 3 4 5 6 7 8 9 10 20 30
plain pos letter lands at carved there
22 E 61 N
23 A 62 F
24 S 63 B
64 B 91 A
65 E 90 U
66 R 89 H
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Experiments 6, 8, 16, 26 and 37 covered columnar, keyed columnar, rotation and affine routes; 19 covered substitution then those routes. The classical route transpositions of the manuals, spiral inward and outward from each corner in either turn, boustrophedon by rows and by columns, and the two diagonal zigzags, at widths 2-48 (about 700 routes), remain. Two tests per route. Before a periodic tableau: the forced key letters at the crib landing places give the live periods by the divisor rule and the forced key at live periods up to 40 is scored as English, 8 conventions, with ten full-size shuffled controls. After any one-to-one substitution: the 24 crib images must never put two different plaintext letters on one carved letter, as in experiment 19, with ten shuffles. Bounds: complete for these route families at these widths, both orders.
6
Prediction
Written before the run; the result decides it.
Before the tableau: smallest live period 22 to 24, forced keys inside the range of the shuffled controls. After a substitution: no route passes the one-to-one test, and no shuffle does either. No candidate.
7
Method
Build the routes as permutations of 97 positions: for each width, spirals from four corners in two turns inward, boustrophedon by rows and by columns, and the two diagonal zigzags; each also inverted.
Test one, before the tableau: send the cribs through, force key letters under 8 conventions, live periods by the divisor rule, score the forced key at live periods up to 40.
Test two, after a substitution: check the crib images for clashes.
Ten shuffles for each test.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
1128 routes. Before the tableau: smallest live period 23, best forced key -4.937 vs shuffled [-5.305, -4.473, -4.909, -4.614, -4.791, -5.019, -5.015, -4.968, -4.85, -4.858]. After a substitution: 0 routes pass the one-to-one test vs shuffled [0, 0, 0, 0, 0, 0, 0, 0, 0, 0].
What was searched, as the harness recorded it.
family
route transpositions (spiral, snake, diagonal), widths 2-48, forward and inverse; before a periodic tableau and after a substitution