“The copper off by one letter, through the two-word test on tables rebuilt from the puzzle's words”
Experiment 43 ran the exact two-word test on the carved text under 63 x 63 vocabulary alphabets and found nothing below a total length of 22. Experiment 31 ran the same test with one carved letter deleted or one unknown inserted anywhere, but only under the standard and KRYPTOS orders. Here the two parameters are combined: every one-letter variant of the copper, every vocabulary alphabet pair, total length up to 22, with a shuffled copper run through the same sweep as the control.
The second message on the sculpture has a carving mistake, so the fourth might too: one letter missing or one letter too many. That would throw off every test that counts positions. Experiment 31 tried every such slip on the sculpture's own table; experiment 43 tried two secret words on tables rebuilt 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. but with the copper taken as exact. Here both are allowed at once. A scrambled copy of the copper gets the same treatment so we know what luck alone produces.
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 slip
K2 has a carving error, so K4 may too. The experiment took the copper with one letter deleted or one inserted, at every place: 196 versions, 48 of them different where the known letters sit.
the two words
On each version it ran the exact two-word test: two secret words used in turn on the table, every pair of lengths up to a total of 22, every pair of tables built from puzzle words.
the bound
914 survivors at totals 21 and 22 on the copper, 878 on a shuffled copper run the same way: chance. No one-letter slip lets two short words explain the known letters.
2
Best candidate against the known letters
Laid out as the copper carries K4: OBKR ends the line that finishes K3, then three lines of 31. Left, as carved, the 24 known places in accent. Right, the candidate: a known place it gets right is an accent cell, one it misses is outlined. This is the candidate with most known letters right; none passed every gate.
in: the copper, always the same
as carved, 97 letters; the 24 known places in accent
ECDMRIPFEIMEHNLSSTTRTVDOHW?OBKR
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR
OBKR ends the line that finishes K3, then three lines of 31
out: the candidate
every place read; known places in accent, misses outlined
ECDMRIPFEIMEHNLSSTTRTVDOHW?DRQU
VOBEZACOPNWITCXML?ASTNORTHEASTJ
ZYUNCMFTTTJGEGOEBNVCVJJQTJZSBER
LINCLOCKNPAJSEMJYIDOCQTZQHJXPLU
checked: the known letters in place, and the reading turns back into the copper
3
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Suppose the carved letter at place 41 is spurious: delete it, so the copper letter under plaintext place 64 (B of BERLIN) is now the one carved at 65.
Rebuild the message alphabet from PALIMPSEST and the carved alphabet from ABSCISSA.
Lengths 7 and 8, Vigenere both passes: place 22 still needs the total that sends E to F, 5; place 64 now needs the total that sends B to the letter carved at 65.
Slots: place 22 uses slot 0 of the 7-word and slot 5 of the 8-word; place 29 uses slots 0 and 4; subtract and y5 - y4 is fixed.
Walk all 24 places; one loop that fails to close kills this variant, pair of lengths and pair of alphabets.
Do the same for every deletion, every insertion, every alphabet pair and every pair of lengths.
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.
variant: the carved letter at 41 deleted
plain PALIMSETBCDFGHJKNOQRUVWXYZ
cipher ABSCIDEFGHJKLMNOPQRTUVWXYZ
lengths 7 and 8, Vigenere: totals and slots
pos plain carved total x slot y slot
22 E F 1 0 5
23 A L 11 1 6
29 T R 11 0 4
30 H N 1 1 5
64 B Y 16 0 7
65 E P 10 1 0
places 64 and later now read the letter carved one place further along
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
K2 carries a known carving error (C14), so the K4 copper may be off by one letter, which shifts every later crib against a periodic key. The two-word composition t[i] = x[i mod a] + s y[i mod b] mod 26 (0014) is exact: 24 crib equations in a + b - 1 unknowns, so each (a, b) has 25 - a - b redundant checks at 1/26 each. Variants: the carved text, a letter deleted at each of 97 places, an unknown inserted before each of 98 places; variants that touch no crib collapse to the carved case, leaving about 50 distinct crib tuples, since every slip before the first crib shifts the cribs the same way. Under 63 x 63 keyword-mixed plain and cipher alphabets, both modes, both signs, length pairs with a < b, a + b <= 22 and lcm outside the dead periods: about 22 million union-find cases. Chance survival at a + b = 22 is 26^-3 per case, so a couple of hundred chance survivors at 22, a handful at 21, at most one at 20 and none below. A shuffled copper through the same sweep gives the control counts. Survivors with at most three free components are enumerated and their words matched against the vocabulary and K1-K3 windows. Bounds: complete for one error anywhere, these alphabets and these lengths.
6
Prediction
Written before the run; the result decides it.
No variant survives with a + b at or below 19 under any alphabet pair. Survivors at 20 to 22 appear in the same numbers on the copper and on its shuffle, and none yields a word from the vocabulary or K1-K3. Zero candidates pass.
7
Method
Build the variants and group them by the crib tuple they produce.
Build the alphabet pool.
For each distinct crib tuple, alphabet pair, mode, length pair and sign, add the crib equations to a weighted union-find; reject on contradiction.
Count survivors by a + b and by variant.
Enumerate survivors with at most three components and match the words.
Repeat on a shuffled copper with the same variants as the control.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.