“F1.8: Carter's book as a running key on one unknown alphabet (both directions, every offset, three forms), solved exactly; and how many checks two unknown alphabets would leave for each running-key source”
F1.8, rerun of 0153, which hit the harness's time limit in its second pass (no clock check there; record kept as an error). Same test; the second pass now stops at the deadline and reports what it left, at a node limit of 100,000. 0098 solved the sculpture's running keys on an unknown alphabet exactly but left Carter's book out; 0021 and 0047 ran Carter only on fixed and keyword tables. Here every offset of Carter's Tomb of Tut-ankh-Amen vol. 1 (284,914 letters as scanned), forwards and backwards, under one unknown alphabet on both sides, three forms: each known letter gives an equation in alphabet places only, decided by a compiled propagation search (checked against a Python solver on 300 random offsets and on a planted text), node limit 20,000, then 100,000 for the undecided. Ten scrambled coppers. Second part, counted not searched: for two unknown alphabets, the checks the 24 equations leave (24 minus their rank mod 13) at sampled offsets of each running-key source.
revertedstatus
a new rootparents
24 mintime, all phases
0candidates
0/24known letters
unclocked
1
The experiment method
What the method does with the 24 known letters.
A running keya running key A secret word as long as the message, taken from a book or another text. takes a long text, here Carter's book about opening Tutankhamun's tomb, which K3the earlier messages The three solved parts of the sculpture. quotes, and uses its letters one after another as the keythe secret word The word or string a cipher needs besides the method.. With an alphabet in an unknown ordera free alphabet A table whose rows are one scrambled alphabet that we do not know, any of the 26 x 25 x ..., each known letter gives an equation about the alphabet alone. For every starting point in the book, forwards and backwardsa mirror Reading or writing the text from the end to the start., a search decides whether any alphabet satisfies all 24, on the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. and on scrambled copies. We also count whether, with two unknown alphabets, the known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK. could ever rule anything out.
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
K3 quotes Carter's account of opening Tutankhamun's tomb. His book, letter after letter from some starting point, could be K4's key, with the alphabet in any order.
the check
At every starting letter, forwards and backwards, each known letter gives an equation about the alphabet alone; a compiled search decides all 24 exactly, on K4 and ten scrambled copies.
the bound
No starting letter fits K4 or any copy; 953 of about 1.7 million stay undecided. With two unknown alphabets the equations leave almost no checks, for any book: the known letters cannot decide that case.
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.
Write Carter's book as one long string of letters and lay it under K4 from some letter onwards.
At known place 22 (E under F) the book's letter there, say T, gives: place(F) = place(E) + place(T) in the unknown alphabet.
The 24 known places give 24 such equations in the 26 unknown places.
Search for one alphabet order that satisfies them all; none means this starting point is dead.
Repeat from every letter of the book, with the book reversed, for the three ways of using the table, and on scrambled copies.
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.
Carter's book from letter 1001, under K4; one unknown alphabet, added form
place 22: place(F) = place(E) + place(Y)
place 23: place(L) = place(A) + place(P)
place 24: place(R) = place(S) + place(R)
place 25: place(V) = place(T) + place(E)
place 64: place(N) = place(B) + place(N)
place 65: place(Y) = place(E) + place(A)
...
24 equations in the unknown places, decided exactly at every starting letter
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C7(d) (K3 is Carter's text; 'instructions in the earlier text that refer to later text', knowledge/02-sanborn-said.md), C13, C27(c), C5 ('a named text and a place in it' is a short key description). Model: x a bijection letters -> Z26 on both sides; key letter k_i = Carter[o + i] (forward) or the reversed book; forms V x(c) = x(p) + x(k), B x(c) = x(k) - x(p), R x(c) = x(p) - x(k). Source: knowledge/sources/carter-1923-tomb-of-tutankhamen-vol1.txt, letters only. Exact per offset (undecided counted). Statistic fixed before the run: fitting offsets per (direction, form) on K4 against the ten coppers' range. Two-alphabet count: C(c) = P(p) + N(k) with the key numbered on P or on C; rank of the 24 equations mod 13 over the place variables, checks = 24 - rank, at 2,000 offsets per source (Carter, K1-K3 plaintexts, the sculpture's ciphertext panel).
6
Prediction
Written before the run; the result decides it.
No offset fits K4 in any form or direction; the coppers give 0 or a handful; undecided offsets resolve to dead at the higher limit. Two unknown alphabets leave no checks at any offset of any source (the equations' unknowns outnumber them), so that cell is blocked by structure. Zero candidates.
7
Method
Compile the solver; check it against Python on 300 random Carter offsets on K4 and on a planted text.
For K4 and 10 coppers, both directions: every offset, three forms, limit 20,000; re-decide the undecided at 100,000 while time allows.
Count fits per (direction, form); decrypt K4's fits.
Two alphabets: rank mod 13 at 2,000 offsets of each source.
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
K4 fitting offsets 0 (coppers 0-0), undecided left 953; two alphabets, checks by source: carter 4/2 max, k2 1/1 max, k3 2/1 max, cipher_panel 2/2 max
What was searched, as the harness recorded it.
family
running key from Carter's book (both directions, every offset) on one unknown alphabet, three forms; two-alphabet check counts for every running-key source
carter letters
284,914
offsets per direction
284,818
solver
compiled propagation search, limit 20,000 then 100,000; agrees with a Python solver on 300 random offsets; a planted text fits