“The map reference at the end of K2, used as the number table of a Hill cipher”
Experiments 24 and 38 used the K2 coordinates as a repeating string of digits added to the letters. A Hill cipher needs a small table of numbers instead, and the coordinates are exactly a short list of numbers, so here they fill the table directly, in every reading, and the 24 known letters judge it.
K2the earlier messages The three solved parts of the sculpture. ends with a map reference: 38 degrees 57 minutes 6.5 seconds north, 77 degrees 8 minutes 44 seconds west. A Hill ciphera Hill cipher A cipher that turns letters into numbers, takes them two, three or four at a time, and mixes each group with a fixed table of numbers. mixes letters two or three at a time using a small square of numbers, and the map reference is a ready-made list of numbers. So we pour those numbers into the square in every sensible order, use it to unmix the copper, and count how many of 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. come out right. Random squares of numbers show what luck alone scores.
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
K2 ends with map coordinates. The experiment read their numbers as the table of a Hill cipher, which mixes letters in blocks, in every order and window, as 2 x 2 and 3 x 3 tables.
the table
Drawn for the first four numbers: 38, 57, 6, 5 become 12, 5, 6, 5. Its determinant is even, so it has no inverse and can only be used to encipher.
the bound
72 coordinate tables: the best lands 4 of 24 known letters, below random tables tried the same way (best 7, average 2.72).
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?YRWH
CIRXUXKLJNGHSJLEKBBMTLONHUMUQUC
ZQNGKLDQUCKPWGGTIMNOTOOCYRIFSCB
LILFZQFNQAXFDYTICHYIOEZPQGCKKKR
checked: the known letters in place, and the reading turns back into the copper
3
How the score is made
The loss of the best candidate, part by part. Zero is solved.
Known letters missed
20 of 24, ten points each
200.00
English
the 73 free letters score -7.96; English text scores -3.6
4.36
Key
32 bits to write it down (key words are cheap, arbitrary letters 4.7 bits each); each 60 beyond 60 costs a point
0.00
Loss
of 240, the worst possible
204.36 85.1%
4
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Take the first four numbers 38, 57, 6, 5 and reduce them mod 26: 12, 5, 6, 5.
Fill a 2x2 table by rows: top row 12 5, bottom row 6 5.
Number the letters A=0 to Z=25 and cut the copper into pairs from place 1.
Multiply each pair by the inverse of the table, mod 26, if the table has one (its determinant 12x5 - 5x6 = 30 = 4 mod 26 is even, so it has none and this reading can only encrypt).
Using the table to encrypt instead, look for the pair it would send to each carved pair.
Count how many of the 24 known letters land right.
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.
first window 38 57 6 5 mod 26 = 12 5 6 5; by rows [[12, 5], [6, 5]]; determinant 4; inverse None
6
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C23(b): the K2 coordinates 38 57 6.5 N, 77 8 44 W as a matrix. Hill encryption (C21) with a key matrix filled from the coordinates: 2x2 from every window of four in the number lists [38, 57, 6, 5, 77, 8, 44] and [38, 57, 65, 77, 8, 44] and the digit list 3 8 5 7 6 5 7 7 8 4 4, each forward and reversed, filled by rows or by columns; 3x3 from every window of nine; entries mod 26. Numberings A=0 and A=1 on the standard and KRYPTOS orders; every alignment; the matrix encrypting or decrypting (singular matrices skipped where an inverse is needed). Each setting decrypts K4 and the 24 cribs are counted. Control: the same count for 2,000 random invertible matrices per size under the same settings. Bounds: exact for these readings.
7
Prediction
Written before the run; the result decides it.
No coordinate matrix recovers more than four of the 24 known letters, the same as the best random matrices. Zero candidates pass.
8
Method
List the coordinate readings.
Fill 2x2 and 3x3 matrices from every window, forward and reversed, by rows and columns.
For each numbering, alignment and direction, decrypt K4 and count crib hits.
Do the same with random invertible matrices.
Compare the best counts.
9
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
Hill from K2 coordinates, digits window 0 by rows, std0, offset 0, matrix encrypts
2failed at cribs4/24 known lettersloss 85.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?YRWH
CIRXUXKLJNGHSJLEKBBMTLONHUMUQUC
ZQNGKLDQUCKPWGGTIMNOTOOCYRIFSCB
LILFZQFNQAXFDYTICHYIOEZPQGCKKKR
Hill from K2 coordinates, numbers window 1 by rows, std0, offset 0, matrix decrypts
3failed at cribs4/24 known lettersloss 85.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?OMPM
NZCGEKDHXYEYNLREJNZHTYOLTYDSUYE
SBWRXAOAWWJKOHLQYXQHMFWIBOLRMHR
RHJZMTXYSJEJKNNMBMFAUXQGAMYUCVE
Hill from K2 coordinates, numbers window 2 by rows, std1, offset 1, matrix encrypts
4failed at cribs4/24 known lettersloss 85.4%
ECDMRIPFEIMEHNLSSTTRTVDOHW?YZWZ
CCRXUZKNJTGXSDLMKXBGTTOFHCMOQIC
LQPGULNQICAPOGYTWMVOZOECMRMFUCJ
LILLZSFZQCXTDETWCDYIOOZTQWCAKOR
Hill from K2 coordinates, digits window 2 by columns, std0, offset 0, matrix decrypts
72 coordinate matrices; best 4/24 known letters (numbers window 1 by rows). Random invertible matrices under the same settings: 2x2 best 7 (mean 2.72), 3x3 best 7 (mean 3.06).
What was searched, as the harness recorded it.
family
Hill with the key matrix filled from the K2 coordinates
matrices
72
numberings
std0, std1, kry0, kry1
directions
2
best hits
4
best reading
numbers window 1 by rows
top
hits
4
reading
numbers window 1 by rows
hits
4
reading
numbers window 2 by rows
hits
4
reading
numbers reversed window 3 by rows
hits
4
reading
digits window 0 by rows
hits
4
reading
digits window 2 by columns
hits
4
reading
digits window 3 by rows
hits
4
reading
digits window 7 by rows
hits
4
reading
digits reversed window 4 by columns
control best 2x2
7
control best 3x3
7
control mean 2x2
2.72
control mean 3x3
3.06
control matrices
2
2,000
3
2,000
How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.
Rendered from the record on 2026-10-18 12:26 UTC; updated after every experiment.