“A progressive key: the key word steps forward on every repeat, which revives the short periods”
The periodic key gains a progression: on each repeat, or on each letter, every key letter moves a fixed number of places along the key alphabet. Periods 1 to 26 and 30 to 52, dead under a plain periodic key, are back in play.
A repeating secret wordthe secret word The word or string a cipher needs besides the method. was ruled outdead Said of a period, grid or method when the known letters contradict it: no secret word of that kind can produce the carved letters. at most lengths because two known letters that would share the same letter of the word disagreed. But an old trick fixes that: each time the secret word repeats, every letter of it slides forward by a fixed amount. Then the two known letters no longer need to agree, they need to differ by that slide. We try every word length and every slide and ask which combinations 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. allow, and whether any of 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. fits what they force.
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 fold
A progressive key shifts the whole secret word one step further on each repeat. Folding the message into rows of 13 puts the places that share a key slot in one column.
slot 8
Places 22 and 74 share slot 8. Undoing one and five steps, they need base letters K and U: a contradiction, so period 13, step 1, is dead on the sculpture's table.
the verdict
Over 121,056 combinations, periods 1 to 25 and 31 to 51 die at every step. Only 26 to 30 and 52 upwards survive, as without the steps, and no puzzle word fits.
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.
Choose period 13 and step 1, per-repeat form, with the sculpture's alphabet throughout and Vigenere.
Position 22 is in repeat 1 (positions 14 to 26), slot 8. Its forced key letter, from E and F, is R, index 1 in KRYPTOS; subtract one step for repeat 1: index 0, K.
Position 35 would be slot 8 of repeat 2, but it is not a crib. Position 74, the K of CLOCK, is repeat 5, slot 8: its forced key letter K against ciphertext K is index 0; subtract 5 steps: index 21.
Slot 8 is now forced to two different letters, so period 13 with step 1 is dead under this convention.
Try the other 25 steps and the other 23 conventions.
A survivor gives a pattern of forced base letters with blanks; slide the puzzle's words across it.
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.
period 13, step 1, per-repeat; plain/cipher/key all on the KRYPTOS alphabet, Vigenere
pos plain cipher forced key index repeat minus step base slot
22 E F R 1 1 0 (K) 8
23 A L D 10 1 9 (C) 9
24 S R U 21 1 20 (Q) 10
25 T V M 18 1 17 (L) 11
26 N Q R 1 1 0 (K) 12
64 B N E 11 4 7 (A) 11
65 E Y L 17 4 13 (G) 12
74 K K K 0 5 21 (U) 8
positions 22 and 74 share slot 8; their base letters must agree for period 13 step 1 to live.
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Progressive-key Vigenere is in every hand-cipher manual Scheidt taught from (Friedman's Military Cryptanalysis, Part II; C5, C6): key index at position i is base[i mod P] plus d times the repeat number, or plus d times i for the letter-wise form. 0005 excluded periods 1-26 and 30-52 for d = 0 only. Here d runs 0-25, P 1-97, both progression forms, under the 24 conventions. For each combination the crib at position i forces base[(i mod P)] after the progression is subtracted; a conflict kills it. Survivors at P up to 30 get their forced base fragment matched against the vocabulary and K1-K3 windows; each match is decrypted and submitted. Stein's I.C. peak at 13 (C28) is a specific target: period 13 with any step. Bounds: complete for progressive periodic tableau systems under the stated conventions, periods and steps.
6
Prediction
Written before the run; the result decides it.
Most (period, step) pairs below 27 still die, because the cribs collide many times and a single step cannot reconcile them all. A scatter of survivors appears at periods 13 to 26 for some step under some convention, consistent with chance. No forced fragment matches a vocabulary word or K1-K3 window; zero candidates pass.
7
Method
For each convention, period P, step d and progression form, compute for each crib the forced key index, subtract the progression, and reduce to the base slot.
A slot forced to two different letters kills the combination.
Count survivors per period.
For survivors with P up to 30, match the forced base fragment against the vocabulary and all K1-K3 windows of length P; decrypt and submit any match.
Record the survivor map by period and step.
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
121056 (form, period, step, convention) combinations; 0 fragment matches submitted.
What was searched, as the harness recorded it.
family
progressive-key periodic tableau, separate alphabets