Experiment 265

“F6.22b, rerun: the keys K4's AMSCO settings force at period 23, scored by their English likelihood with gaps allowed, against the best forced key of each of 200 shuffles; 20 planted running-key messages”

F6.22b, rerun of 0264 with its statistic fixed. 0264 scored a forced key by the mean quadgram over 4-grams with all four letters forced and skipped keys with fewer than 8 such 4-grams. On many AMSCO routes the 24 known letters land on only 12-18 of the 23 slots, so the plants' own keys (for instance W?RA?DH?WDIFFICUL?IT?OU) were skipped and only 6 of 20 plants were found, while K4's keys are mostly fully forced. Here every forced letter counts: the key's log-likelihood under English against random letters, chained through each run of forced letters (P(d | the up to three forced letters before it), from the quadgram table's marginals), summed in bits. Everything else as 0264.

revertedstatus
experiment 264parents
64 stime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. fits a two-step cipher (a grida grid Writing the message into rows of some width and reading it out in another order, column by column for instance, which shuffles the letters without changing them. shuffle, then the tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS. with a 23-letter key) in more ways than most scrambled copiesa shuffled control The same experiment run on the carved letters shuffled into a random order. do. For each way it fits, 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. spell out almost the whole 23-letter key. If Sanborn took his key from a book or a sentence, that key should read like English; here we check whether K4's keys read more like English than the keys scrambled copies are forced to.

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.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARK4's 21 agreeing AMSCO settings at key length 23: the key each forces, written in slot order; the best key per text, scored for English (bits by which the forced letters are likelier as English than as random)K4's best key: SEV?HHEMTPMPXRMGRONEXHIbest key of each of 200 shuffles: -63.9 to -6.8, median -35.1K4 -11.8: 5 of 200 at or aboveplanted English keys (ochre dots, one per plant): 20 of 20 above every shuffleEASTNORTHEASTBERLINCLOCKIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENTOUT: NO READING; K4'S BEST KEY IS LESS ENGLISH THAN RANDOM LETTERS, EVERY PLANTED KEY FAR ABOVE
the idea

F6.22b, rerun: a key taken from any English text should read as English wherever the known letters force it, gaps and all.

the check

Every forced letter scored, given the forced letters before it in its run, English against random letters, in bits; K4's best key against the best of each of 200 shuffles; 20 planted English keys.

the bound

Planted keys +9.3 to +36.7 bits, all 20 above every shuffle; K4's best -11.8, below zero, though above 195 of 200 shuffles' bests. K4 has more settings to take a best from (21, median 8): F6.22c matches the count.

2

Experiment lineage

What this experiment was built on, from the lineage page: 9 experiments before it, back to the root of its line. Its number is in bold.

kept reverted, in its family's colour ×error or timeout reverted under today's rules built on a parent in the same family built 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.

  1. Take one of K4's agreeing settings: an AMSCO grid keyed by a word, then the table with a 23-letter key.
  2. Undo the grid for the 24 known places: each lands on a carved place, whose number mod 23 is its key slot.
  3. The key letter at that slot is the carved letter minus the known letter on the table (plus, for Beaufort).
  4. Write the 23 slots in order, '?' where nothing lands, and score each run of letters for how much more likely it is as English than as random letters.
  5. Do the same for every agreeing setting of each scrambled copy, and compare the best scores.
the worksheet: the first steps by hand, on squared paper
forced key (slot order)numberingbitsSEV?HHEMTPMPXRMGRONEXHIstd-11.8BSQNNRRODDEFPFIONECKOBZkry-33.1KDDAIRNWDHCKITEOCCWDOKWkry-38.7HERARWSWKHQTTMZBPIEDQDFkry-43.7GESNGVEHUOLIOXCJNAQQF?Astd-47.2GESNGVEHUOLIOXCJNAQQF?Astd-47.2W?RA?DH?WDIFFICUL?IT?OUstd+21.6 (planted WARANDHOWDIFFICULTITWOU)ATU???LYON?HE???DIT???Sstd+15.4 (planted ATURALLYONTHECONDITIONS)LYD????ATEDT???ACID???Dstd+13.6 (planted LYDEDICATEDTOPLACIDREAD)The first six rows are K4's best keys: all below zero bits, so less likely as English than as random letters. The lastthree are planted keys as the known letters force them, gaps and all: English shows through at +13 to +22 bits.K4'S BEST FORCED KEYS AT KEY LENGTH 23, AND THREE PLANTED KEYS AS READ, IN BITS AGAINST RANDOM LETTERS
5

Worked example, generated

The same steps run by the code on the real letters.

F6.22b: the keys K4's AMSCO settings force at period 23, read for English.

  AMSCO keyed by a word, then the table with a 23-letter key: each known letter lands on a carved place p,
  and forces the key letter at slot p mod 23 (carved minus known on the table, or their sum for Beaufort).
  Written in slot order with '?' where nothing lands, a key taken from English text reads as English in runs of four.

  per text: the best such key over its agreeing settings; K4's against 200 shuffles'; 20 planted English keys for power.
6

Hypothesis, for a cryptanalyst

Family, key space, the constraint under test, and the clues it reads.

F6 (C1(a): a matrix code, then the table). AMSCO keyed by a dictionary word (0114's 891,360 routes, 3-15 columns), then a period-23 key on the sculpture's 8 table classes. With 24 known letters on 23 slots the key is almost fully forced in every agreeing setting, so a key drawn from any English text (C7(a), C5: a phrase as key; F1.3's test on this move) shows as English letters in slot order. Statistic: per text, the highest English log-likelihood ratio of a forced key (bits against random letters, each forced letter conditioned on the forced letters before it in its run, slots 1-23 in order, no wrap), over its agreeing settings and two numberings. Power: 20 plants (Carter messages, random route and class, a 23-letter window of English as key).

7

Prediction

Written before the run; the result decides it.

K4's best forced key inside the 200 shuffles' bests (p above 0.05), its letters no English; planted keys above every shuffle at least 14 of 20 (more than 0264's 6, which the skipped partial keys cost). Zero candidates.

8

Method

  1. 0263's exact count at period 23, unchanged, for K4, its 200 shuffles (seed 2620) and 20 plants, every agreeing setting kept with its forced shifts per slot.
  2. Each forced key written as letters in slot order on the standard and on the KRYPTOS alphabet, '?' where no known letter reaches; scored by its log-likelihood ratio, English against random letters, in bits: each forced letter's probability given the up to three forced letters before it in its run, from the quadgram table.
  3. Per text the best score over its settings and numberings; K4's rank among the 200 shuffles'; a plant is found when its best is above every shuffle's.
  4. K4's forced keys listed in full.
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

F6.22b rerun: K4's best forced key at 23 scores -11.9 bits (SEV?HHEMTPMPXRMGRONEXHI); 200 shuffles' bests -63.8 to -6.8, 5 at or above K4 (p 0.030); plants found 20 of 20

What was searched, as the harness recorded it.

item
F6.22b (chase of 0263's AMSCO period-23 count)
routes
891,360
classes
8
period
23
order
A (move, then the table)
agreeing settings
k4
21
copies min median max
1, 8, 31
statistic
per text: best English log-likelihood ratio (bits, against random letters) of a forced key, slots 1-23 in order, no wrap, standard or KRYPTOS numbering, each forced letter conditioned on up to three forced letters before it in its run (quadgram table marginals), over its agreeing settings
k4 best
-11.85
k4 best key
SEV?HHEMTPMPXRMGRONEXHI
copies best min median max
-63.85, -35.14, -6.76
copies at or above
5
p
0.03
k4 forced keys
  1. route
    THIOPHOSPHATE, 13, 1, inverse
    class
    kry/kry/True
    numbering
    std
    key
    SEV?HHEMTPMPXRMGRONEXHI
    score
    -11.85
  2. route
    BLACKBIRDING, 12, 2, inverse
    class
    std/std/True
    numbering
    kry
    key
    BSQNNRRODDEFPFIONECKOBZ
    score
    -33.14
  3. route
    ADULTEROUSLY, 12, 2, inverse
    class
    std/std/False
    numbering
    kry
    key
    KDDAIRNWDHCKITEOCCWDOKW
    score
    -38.73
  4. route
    TEMPERABILITY, 13, 1, inverse
    class
    std/kry/False
    numbering
    kry
    key
    HERARWSWKHQTTMZBPIEDQDF
    score
    -43.73
  5. route
    SNECKDRAWN, 10, 2, inverse
    class
    kry/std/False
    numbering
    std
    key
    GESNGVEHUOLIOXCJNAQQF?A
    score
    -47.23
  6. route
    TENORISTER, 10, 2, inverse
    class
    kry/std/False
    numbering
    std
    key
    GESNGVEHUOLIOXCJNAQQF?A
    score
    -47.23
  7. route
    UNMINISTER, 10, 2, inverse
    class
    kry/std/False
    numbering
    std
    key
    GESNGVEHUOLIOXCJNAQQF?A
    score
    -47.23
  8. route
    UNIMAGINATIVENESS, 10, 2, inverse
    class
    kry/std/False
    numbering
    std
    key
    GESNGVEHUOLIOXCJNAQQF?A
    score
    -47.23
  9. route
    THIOPHOSPHATE, 13, 1, inverse
    class
    kry/kry/True
    numbering
    kry
    key
    MTU?AATFNIFIWLFSLHGTWAB
    score
    -47.76
  10. route
    SNECKDRAWN, 10, 2, inverse
    class
    kry/std/False
    numbering
    kry
    key
    STMGSUTAQHEBHWYCGKJJO?K
    score
    -48.07
  11. route
    TENORISTER, 10, 2, inverse
    class
    kry/std/False
    numbering
    kry
    key
    STMGSUTAQHEBHWYCGKJJO?K
    score
    -48.07
  12. route
    UNMINISTER, 10, 2, inverse
    class
    kry/std/False
    numbering
    kry
    key
    STMGSUTAQHEBHWYCGKJJO?K
    score
    -48.07
and 30 more
plants
found
20
of
20
each
  1. route
    VARIOLIZATION, 13, 1, inverse
    class
    std/kry/beau
    key
    WARANDHOWDIFFICULTITWOU
    numbering
    std
    best
    21.62
    best key
    W?RA?DH?WDIFFICUL?IT?OU
    found
    yes
    live
    8
  2. route
    UNSPONTANEOUSLY, 15, 1, inverse
    class
    std/std/vig
    key
    ATURALLYONTHECONDITIONS
    numbering
    std
    best
    15.44
    best key
    ATU???LYON?HE???DIT???S
    found
    yes
    live
    3
  3. route
    PREVALESCENT, 10, 2, inverse
    class
    std/kry/vig
    key
    LYDEDICATEDTOPLACIDREAD
    numbering
    std
    best
    13.56
    best key
    LYD????ATEDT???ACID???D
    found
    yes
    live
    36
  4. route
    NONZEALOUS, 10, 1, inverse
    class
    kry/std/vig
    key
    YIMPRESSIVEORIGINALLYTH
    numbering
    kry
    best
    22.37
    best key
    YIM???SSIVE??IGINAL?YTH
    found
    yes
    live
    11
  5. route
    ESCHATOCOL, 10, 2, forward
    class
    std/kry/beau
    key
    HEMSELVESUNDERSHELTERIN
    numbering
    kry
    best
    22.35
    best key
    HEM?E?VE??NDER??EL??RIN
    found
    yes
    live
    10
  6. route
    OVERHEADINESS, 10, 2, forward
    class
    std/kry/vig
    key
    PASSINGTHESTONESANDBASK
    numbering
    kry
    best
    30.84
    best key
    ?AS?ING?HESTONESAND??SK
    found
    yes
    live
    13
  7. route
    THERAPEUTIST, 12, 2, forward
    class
    std/std/beau
    key
    EBUTALTHOUGHHEHADRESIGN
    numbering
    kry
    best
    20.91
    best key
    E?UTAL??O??H?EH?DRESIGN
    found
    yes
    live
    11
  8. route
    PAMPRODACTYLOUS, 15, 1, inverse
    class
    kry/kry/vig
    key
    SCOVEREDWITHTHINGOLDFOI
    numbering
    kry
    best
    18.92
    best key
    ??OVEREDWI?????NGO???O?
    found
    yes
    live
    3
  9. route
    BLEMISHMENT, 11, 1, inverse
    class
    kry/kry/beau
    key
    HEGOLDFOILFROMTHESMALLP
    numbering
    std
    best
    31.3
    best key
    ?EGOL?FOILFROMTHE??ALLP
    found
    yes
    live
    21
  10. route
    NONMAGNETIC, 11, 2, forward
    class
    std/kry/beau
    key
    CAMEINTOTHEVILLAGEONEAF
    numbering
    kry
    best
    19.16
    best key
    ??MEINTO?H?VILL?GEON?AF
    found
    yes
    live
    6
  11. route
    METEMPIRICALLY, 10, 2, inverse
    class
    std/kry/vig
    key
    TTERTODEALWITHITWESHOUL
    numbering
    kry
    best
    16.09
    best key
    TT?RTODEALWI?HITW??H?UL
    found
    yes
    live
    8
  12. route
    MUNITIONER, 10, 1, forward
    class
    std/kry/beau
    key
    TTEREDFROMTHESETRIALSAN
    numbering
    std
    best
    22.97
    best key
    TTEREDF?OMT??SETR?ALSAN
    found
    yes
    live
    5
and 8 more
copies
200 fresh shuffles (seed 2620, as 0263)
exhaustive
yes
compute seconds
38
modal cost estimate
as 0263 (65 s on 32 cores, $0.03) plus key scoring: about $0.05

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 2026-11-05 17:14 UTC; updated after every experiment.
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