“A1.3: running keys from the named texts (K1-K3, the sculpture's texts, Carter, Sanborn's letters) on the standard, KRYPTOS and keyword tables, with up to seven of the 24 known letters carved wrong, exact, against scrambled copies, with planted slipped messages”
A1.3 (Stage 2, step 2, issue #76). 0004, 0017, 0021, 0045, 0047 and 0078 slid running keys from the named texts along K4 and asked for 0, at most 2 (0021, 0045, 0047) or at most 3 (0017) mismatches at the 24 known places; 0004 and 0078 reported best 16 and 15. Here every one of those searches is rerun in one pass allowing up to 7 slips, exact, by a pigeonhole index (with 7 or fewer slips, one of 8 blocks of 3 known places matches exactly), K4 against 20 scrambled copies, with three planted running-key messages carrying 2-3 slips. The item asks for k = 1-3; k up to 7 costs nothing more and shows how far the test reaches.
A running keya running key A secret word as long as the message, taken from a book or another text. uses a long text, a page of a book or the sculpture's own letters, as the secret wordthe secret word The word or string a cipher needs besides the method., one letter of the text for each letter of the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered.. Earlier experiments slid every text we could think of along the carving and found none that gives 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.. If Sanborn slipped at two or three of those places, the right text would have been thrown away. Here we let up to seven of them be wrong, on the carving and on scrambled copiesa shuffled control The same experiment run on the carved letters shuffled into a random order., and we hide three messages of our own, with slipsa slip A mistake made while enciphering by hand: a wrong row or column of the table at one letter, so the carved letter is not the one the method gives there., to check they are found.
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 idea
A running key takes the secret letters from a long text. Every text we could name was slid along the carving before, and none gave all 24 known letters; a few hand slips at those places would have hidden the right one.
the check
Every named text (K1-K3, the sculpture's texts, Carter's book, Sanborn's letters), every offset both ways, on standard, KRYPTOS and keyword tables, allowing up to 7 of the 24 known letters to disagree; K4, 20 scrambled copies, three planted messages with slips.
the bound
No setting with 7 or fewer slips on K4 or any copy (chance about 10^-10); the three plants are found at their own text and offset, judged 96, 90, 93.
2
Experiment lineage
What this experiment was built on, from the lineage page: 5 experiments before it, back to the root of its line. Its number is in bold.
keptreverted, in its family's colour×error or timeoutreverted under today's rulesbuilt on a parent in the same familybuilt on a parent in another family
3
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 under Result and bounds below.
4
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Write the key text (say Carter's book) under K4 from some starting letter.
At each of the 24 known places, look up on the table which carved letter the known letter and the key letter give.
Count the places where it is not the carved letter: those would be Sanborn's slips.
Keep the starting letter if 3 or fewer places disagree, and read the whole message with it.
Move the key text one letter and repeat, for every starting letter, both directions, every table.
Do the same on scrambled copies of the carving.
the worksheet: the first steps by hand, on squared paper
5
Worked example, generated
The same steps run by the code on the real letters.
Carter's book as the key, from letter 1000, standard plain and KRYPTOS cipher alphabet, key letters on KRYPTOS, Vigenere
place known key gives carved
22 E Y S F slip?
23 A P P L slip?
24 S R N R slip?
25 T E T V slip?
64 B N Q N slip?
65 E A E Y slip?
66 R T U P slip?
places that disagree, of 24: 24 (7 or fewer would be kept)
6
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
A1 (knowledge/12-assumptions.md); C7(a) and C6(a) (keys from the earlier texts and the sculpture: Sanborn 2005 'instructions in the earlier text that refer to later text', Scheidt 2003 'the keys were concealed at the sculpture'), C17 (a copper not as intended), C27(a) (the PALIMPCEST slip). A running key fixes every key letter from the text and the offset, so each setting gives one full reading and 24 checks. Setups: plain and cipher alphabets standard, KRYPTOS or keyword-mixed from the 61 vocabulary words (0045's pool of 63); K1-K3 sources with every pair (as 0045); Carter's Tomb of Tut-ankh-Amen vol. 1, the carved tableau (rows, rows with the index column, columns), the Morse (as carved, reversed order), the four ciphertexts as one panel and Sanborn's 1989 letter, the 1991 dedication texts and the 2025 open letter with one side standard or KRYPTOS or both sides the same keyword alphabet (as 0047, 0017, 0078); key letters on the standard or KRYPTOS order (or the keyword alphabet itself when both sides share it, as 0078); Vigenere, Beaufort, variant; every cyclic offset, forward and backward. A slip at a known place is one failed check; settings with 24 - k checks matched are counted for k = 0-7. Chance of one setting with k <= 3 among the ~1.2 x 10^9 trials: about 10^-17; with k <= 7 about 10^-9, so the 24 checks decide the running key at every k <= 7 (the key costs a source name and an offset, about 25 bits; the slips 4.7 k + log2 C(24, k) bits). Readings of any setting found go to quadgrams and the blind judge with the copies'.
7
Prediction
Written before the run; the result decides it.
No setting with 7 or fewer slips on K4 or on any copy (chance about 10^-9). The three planted messages are found at their own source, offset and table, each with exactly its planted slips, and their readings judged as English. Zero candidates on K4.
8
Method
Build the sources and the alphabet pool as 0045, 0047, 0017, 0078.
For every source and key alphabet, index each offset by the key letters it puts on each of 8 blocks of 3 known places.
For every setup, compute the key letter each known place needs; look up the offsets that match a whole block; check those offsets on all 24 places.
Keep every setting with 7 or fewer mismatches, by count.
K4, 20 copies and three planted messages (with 10 copies each); readings of any setting found to quadgrams and the judge in one call.
9
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
running keys from the named texts on standard, KRYPTOS and keyword tables, 0-7 known letters slipped (A1.3)
alphabet pool
63
setups
A (K1-K3, every pair)
23,997
B (other sources, one side std/kry or both the same word)
2,037
sources
K1 plain fwd
63
K1 plain bwd
63
K2 plain fwd
369
K2 plain bwd
369
K3 plain fwd
336
K3 plain bwd
336
K1+K2+K3 plain fwd
768
K1+K2+K3 plain bwd
768
K1 cipher fwd
63
K1 cipher bwd
63
K2 cipher fwd
369
K2 cipher bwd
369
K3 cipher fwd
336
K3 cipher bwd
336
K1+K2+K3 cipher fwd
768
K1+K2+K3 cipher bwd
768
K2 plain corrected ending fwd
13
K2 plain corrected ending bwd
13
carter vol1 fwd
284,914
carter vol1 bwd
284,914
tableau rows fwd
781
tableau rows bwd
781
tableau rows with index column fwd
807
tableau rows with index column bwd
807
tableau columns fwd
781
tableau columns bwd
781
morse as carved fwd
80
morse as carved bwd
80
morse reversed order fwd
80
morse reversed order bwd
80
right panel K1-K4 fwd
865
right panel K1-K4 bwd
865
letter 1989 fwd
2,176
letter 1989 bwd
2,176
Cryptogram 1991 fwd
4,880
Cryptogram 1991 bwd
4,880
open letter 2025 fwd
2,228
open letter 2025 bwd
2,228
trials
1,360,451,298
offsets
every cyclic offset, forward and backward
max slips
7
method
pigeonhole index: 8 blocks of 3 known places, offsets bucketed by their key letters; every offset matching a whole block checked on all 24 (exact for <= 7)