“Replication: two unknown alphabets fit K4 at key length 19, where 3 of 100 scrambled coppers fit; against 1,000 fresh coppers, corrected for looking at every length, and against copies that keep the known places' letters”
F1.2, replication (order-of-work rule 5). 0123 found K4 consistent with Quagmire IV at key length 19 while only 3% of 100 coppers were. Here: (a) 1,000 fresh shuffles (seed 124), all lengths 1-26, give the share fitting at 19 and a look-elsewhere p: the share of shuffles whose rarest fitting length is as rare as K4's; (b) 1,000 copies that keep the 24 carved letters at the known places and shuffle only the other 73 (null B), which isolates whether the fit comes from the known places themselves.
In the last run, two unknown alphabets with a 19-letter key could produce 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., which happened for only 3 of 100 scrambled copies. One reason may be a coincidence in the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.: two known R's, 38 places apart, both sit under a carved P. Here we try 1,000 new scrambled copies and ask how often any key length looks as rare as 19 did, since we looked at 26 lengths and something rare turns up by chance.
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
0123 found two unknown alphabets fitting K4 at key length 19, which only 3 of 100 scrambled coppers did. Rule 5 of the order of work: replicate against fresh controls before anything else.
the check
At length 19 the known places pair 38 apart; the R at 28 and the R at 66 both sit under P, a check that holds for free. 1,000 fresh scrambles show how often that kind of luck happens.
the bound
26 of 1,000 fit at 19 (p 0.026); lengths 15 and 17 are as rare, so a copper lands on such a length often enough. Not a signal; F1.2 goes on.
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 K4 in rows of 19; places 38 apart fall in the same column.
Pair the known places that share a column: 26 with 64, 27 with 65, and so on up to 34 with 72.
Places 28 and 66 are both R under carved P: whatever the alphabets, that pair agrees by itself.
The other eight pairs must each satisfy carved-place minus known-place equal in both, and some pair of alphabets does.
Scramble the carved letters, repeat, and count how often a scramble fits at 19, or at any length as rarely.
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.
Family, key space, the constraint under test, and the clues it reads.
Follow-up of 0123 (C27(c), C1(b)). Mechanism to test: at length 19 the known places pair up 38 apart (26-34 with 64-72), nine checks; places 28 and 66 are both R under P, so one check holds for free, and the other eight leave two free alphabets room to fit. Under null A (letters shuffled) that coincidence is rare. Under null B the carved letters at the 24 known places are those of K4, so the exact test, which reads only those letters, returns K4's verdict on every copy: null B is a check that the test depends only on the known places, and the honest null is A. Prediction is about A with the look-elsewhere correction. Same exact decider as 0123 (two independent alphabets, CRT mod 13 and mod 2, witness re-checked).
6
Prediction
Written before the run; the result decides it.
At length 19 about 2-5% of the 1,000 fresh coppers fit (K4's p near 0.03), but corrected for looking at every length the p is above 0.2: a copper usually fits at some length that few coppers fit at. So the length-19 fit is not a signal and F1.2 continues. If the corrected p is below 0.01, stop and report.
7
Method
Draw 1,000 shuffles of K4 (seed 124).
For each, decide Quagmire IV consistency at lengths 1-26 exactly.
Share fitting per length; K4's p at 19.
For K4 and each shuffle, the rarest fitting length's share (shares estimated from the other shuffles); corrected p = share of shuffles at least as rare as K4.
Null B: 200 copies keeping the known places' carved letters, to confirm the verdict depends only on those.
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
Length 19: 26 of 1000 fresh coppers fit (p 0.026). K4's rarest fitting length share 0.026; look-elsewhere p 0.026. Null B: 200/200 copies give K4's verdict at every length.
What was searched, as the harness recorded it.
family
two unknown alphabets (Quagmire IV), periodic key 1-26, no move: replication of the length-19 fit