“F1.4: every hand key schedule K4 fits on one free alphabet (2,093 settings, both forms), each decided by D1's one-run decider against copies climbed one at a time”
F1.4, the one-alphabet residue reopened by D2 (0252). 0252 measured the one-run decider's power on F1.4's schedules (37 of 48 per group against 6 own copies) and costed the residue at about 41 core-hours. Here every one of the 2,093 (schedule, slot count, form) settings K4 fits is decided: K4 is climbed once, then shuffles that the exact decider also fits at that setting are climbed one at a time until one reaches K4's score, up to 12; where K4 beats all 12 the copies go on to 100. 24 plants (12 clean, 12 Sanborn-style) on settings K4 fits go through the same decision in the same run.
Sanborn may have used the cipher table with a twist in how he stepped through the keythe secret word The word or string a cipher needs besides the method. word (skipping a letter now and then, going back and forth) and with his own scrambled alphabet. About two thousand such twists are consistent with 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., so those letters cannot tell them apart. For each one we search for the most English-looking reading of K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. and do the same on scrambled copiesa shuffled control The same experiment run on the carved letters shuffled into a random order. of K4 that fit the same twist equally well; a real answer should read better than all its copies.
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
F1.4: the cipher table with a scrambled alphabet and a key stepped by a hand rule (skip a key letter every m letters, back and forth); 2,093 such rules agree with the 24 known letters.
the check
Each rule: one search on K4, then scrambled copies fitting the same rule until one reads as well; 21,878 searches in all. Planted messages found 17 of 24.
the surprise
K4 beats all 12 copies in 299 rules where chance gives 161, and all 100 in 66 where chance gives 21, yet every reading is gibberish: the next run checks the test itself (0254).
2
Experiment lineage
What this experiment was built on, from the lineage page: 18 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.
Pick a schedule, say: key of 11 letters, skip one key letter after every 7 carved letters.
Write the key slot under each of the 97 carved letters.
Check with the 24 known letters that some alphabet makes them agree (two known places in one slot must differ by the same amount on the alphabet).
Search alphabets and keys for the most English-looking reading of K4 under that slot map.
Shuffle K4's letters until the shuffle also passes step 3, and search it the same way.
If the shuffle reads as well as K4, stop: K4 is ordinary there. Otherwise shuffle again, up to 12 times (100 if K4 keeps winning).
Count how often K4 won all 12; chance alone gives about one setting in 13.
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.
F1.4: one free alphabet under a hand key schedule, decided setting by setting.
setting skip one key letter every 7 letters, 11 key letters
slot map place 1 2 3 4 5 6 7 8 9 ...
key letter 1 2 3 4 5 6 8 9 10 ... (letter 7 skipped)
K4 gets one tempering search under that slot map; then scrambled copies that fit the same 24 checks
get one each, one at a time, until a copy reads as well as K4 (at most 12, or 100 if K4 keeps winning).
Chance alone lets K4 win all 12 in about 1 setting of 13.
6
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
F1.4: a keyed table with a hand key schedule other than a plain repeat (C20(d): tableau rows as keys; the schedules of 0126-0128: one key letter skipped every m letters, stutter, back and forth, triangle, square, a restart per carved line), with one free alphabet on both sides (Quagmire III with an unknown order, Sanborn's 'slightly different' tableau, C27(c)), Beaufort or added form. 0127/0128 closed the standard and KRYPTOS tables exactly; on a free alphabet K4 fits 2,093 settings at the copies' rate (0252's exact recount: 2,016 skip schedules, 77 others), each with its 24 known letters satisfied by some alphabet, so the known letters cannot decide them and English must. The decider is 0140's tempering climb (one run, 16 x 625 x 1000) generalised to any slot map (0252, identical to 0140 on plain periodic keys), with copies drawn as shuffles the exact decider fits at the same setting, so K4 and its copies have the same freedom. Clue entries: C20(d), C27(c), C5(a).
7
Prediction
Written before the run; the result decides it.
No setting stands out: the number of settings where K4 beats all 12 copies is within the binomial range for 1/13 (about 161 of 2,093, sd about 12; anything above 186 is an excess to chase), and the settings where K4 beats 100 copies are about 1 in 101 (about 21, at most about 30). Plants found (above all 12 own copies) about 16 of 24 (0252's 37 of 48 against 6 copies, lower against 12). Zero candidates returned (see notes).
8
Method
Settings: 0252's f14_settings() (every 0128 schedule at every slot count 2-31, as a slot map over the 97 places, deduplicated), both forms, each decided exactly on K4 by 0128's decide(); the fitting ones are the cell.
Per setting (one job, seeded by its index): climb K4 once with 0252's climb(); then draw shuffles of K4 until one fits the setting exactly, climb it, and stop at the first copy whose best is at or above K4's; at most 12 copies, and where K4 is above all 12, go on to at most 100. Record K4's score, reading, and the number of copies it stayed above.
Plants: 12 clean (Carter windows, 0120's rule) and 12 Sanborn-style (0226's classes), each on a setting drawn from the cell, random alphabet and key, decided by the same job without the escalation; found if above all 12.
Verdict: the count of settings where K4 beats all 12 against Binomial(n, 1/13); settings above 100 copies listed with their readings and known letters, to be chased in a row of their own if the count is in excess.
9
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
F1.4 one-alphabet residue: 2093 settings; K4 above all 12 copies in 299 (chance 161, p 1.12e-24), above all 100 in 66 (chance 20.7, p 1.25e-15); plants found clean [8, 12], Sanborn-style [9, 12]. No candidate returned: a per-setting reading above its own copies is expected about 161 times by chance, so gate 4 on one setting's copies would not account for the 2093 settings searched; the verdict is the count, and the top readings are in bounds.
What was searched, as the harness recorded it.
item
F1.4 (one free alphabet residue, reopened by D2/0252)
decider
D1's one-run decider: 0140's tempering (16 x 625 x 1000) generalised to any slot map (0252); copies = shuffles the exact decider fits at the same setting, climbed one at a time, stop at the first at or above K4, at most 12, escalated to 100 where K4 beats all 12