Experiment 33

“Trifid: the 27-cell cube that fractionates letters, with keyword cubes tested exactly and free cubes annealed”

New root in family 4. Trifid is the one classical fractionating cipher that fits 26 letters plus the question mark; the 25-letter-square systems are dead because all 26 letters occur in K4. Keyword-built cubes are tested exactly; free cubes are searched by simulated annealing on crib hits.

revertedstatus
a new rootparents
5 mintime, all phases
0candidates
0/24known letters
1

The experiment method

What the method does with the 24 known letters.

Trifidtrifid A cipher that turns each letter into three small digits, like floor, row and seat in a 27-seat cube, writes several letters' digits in rows, and regroups them, so each new letter is made from pieces of three old ones. turns each letter into three small digits, like an address with floor, row and seat in a 27-seat cube, writes the addresses of a few letters in rows, and then reads the digits off in a different grouping, so each new letter is made from pieces of three old ones. It is one of the few old ciphers that can handle all 26 letters plus the question mark the sculpture already uses. We first try cubes built from the puzzle's wordsthe puzzle's words A list of 62 words tied to the sculpture: the earlier secret words, place names, the names of the people involved, the words in the Morse code, and the themes Sanborn has named., then let a computer rearrange the cube by trial and errortrial and error Letting a program change a key one small step at a time, keeping steps that improve a score and sometimes accepting worse ones to escape a rut., rewarding every known letter it gets right.

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.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENTthe best keyword cube, CARNARVON/alt_vertical/?first, period 14layer 1?CBIQYZSJlayer 2DAREKTULFlayer 3NVGMWXPHOeach letter becomes three digits: layer, row, column (EAST shown)E2 2 1A2 1 2S1 3 2T2 2 3known letters the reading gets right7 of 24keyword cubes, exact17 of 24annealed cube, copper14 of 24annealed, shuffled copper11 of 24annealed, second shuffleannealing on a shuffled copper gets nearly as far: chanceOUT: NO READING REACHES 24 OF 24EASTNORTHEASTBERLINCLOCK
trifid

Trifid puts 27 symbols in a 3 by 3 by 3 cube. Each letter becomes three digits; the digits of a block of letters are written out in rows, read across, and turned back into letters.

keyword cubes

Cubes filled from 498 puzzle words, every period 2 to 20 and every alignment: 104,082 decryptions, the best getting 7 of 24 known letters.

annealing

Letting a search rearrange the cube freely reached 17 of 24 on the copper and 14 on a shuffled copper. Experiment 40 then solved the cube exactly from the known letters.

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.

  1. Fill a cube with KRYPTOSABCDEFGHIJLMNQUVWXZ? in order: K is at (0,0,0), R at (0,0,1), ... the 27th symbol ? at (2,2,2).
  2. Take period 5 and the first carved block OBKRU.
  3. Write each letter's three digits in a column: O gives (0,1,2) in this cube, and so on for five letters.
  4. Read the 15 digits row by row into one line and cut it into five triples: those are the five message letters' addresses.
  5. Look them up in the cube.
  6. Do this for every block, then check positions 22 to 34 and 64 to 74 against EASTNORTHEAST and BERLINCLOCK.
  7. Count the hits; 24 means the cube and period are right.
the worksheet: the first steps by hand, on squared paper
A KEYWORD CUBE BY HAND: THE DIGITS OF EASTNORT?CBIQYZSJlayer 1DAREKTULFlayer 2NVGMWXPHOlayer 3E221A212S132T223N311O333R213T223layerrowcolumnWrite the three digits of each letter in acolumn under it, as here. For a block ofletters, read the digits across row by row,regroup them in threes and look each three upin the cube.Working backwards from the carved letters,every known letter fixes which cube cell itsdigits point to; a cube must agree with all ofthem at once.
4

Worked example, generated

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

cube in KRYPTOS order with ? last; period 5, first block OBKRU

O -> (0, 1, 2)
B -> (0, 2, 2)
K -> (0, 0, 0)
R -> (0, 0, 1)
U -> (2, 1, 0)
digits in a line: 012022000001210; cut into rows of 5: [[0, 1, 2, 0, 2], [2, 0, 0, 0, 0], [0, 1, 2, 1, 0]]
message letters: SDQRM

full decryption at period 5: SDQRMRDVZW?CSJQEWUEQMG?JDXRWMRECIRYSEFWILMJMYTBSWZOEEDUDYJHXMRIILTDOUCMMHDEHDEESPGDEUDLHRPKUDXCPN; crib hits 2 of 24
5

Hypothesis, for a cryptanalyst

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

Delastelle's trifid (1901; in the ACA list and the manuals Scheidt taught from, C5) maps each of 27 symbols to a point in a 3x3x3 cube, writes a block of p letters as three coordinate rows, and reads the rows off in triples: a spatial system in Sanborn's sense (C3) and a matrix in his (C1), with the sculpture's own '?' as the 27th symbol. Playfair, bifid and the four-square family are dead because K4 uses all 26 letters (knowledge/04-structure.md); a 2x13 grid cannot fractionate; trifid can. Two tests. Exact: cubes built from every vocabulary word by the four Friedman mixings with '?' first or last, periods 2-20, every alignment, scored by crib hits after decryption. Search: for periods 2-15 and every alignment, simulated annealing over free cubes with crib hits as the objective, two restarts each, then more iterations for the best settings. A true cube gives 24 of 24; chance gives about 1 of 24 per decryption. In a dry run the annealer, with a coordinate-level objective, reached only 17 of 24 on a planted free cube at the planted cube's own period and alignment, so the search is weak and its result is not a bound. Bounds: complete for keyword cubes only; free cubes stay open.

6

Prediction

Written before the run; the result decides it.

No keyword cube at any period and alignment gets more than 5 of 24 crib letters right. Annealing on free cubes reaches at most 10 of 24 at its best setting, the same as on shuffled K4. Zero candidates pass.

7

Method

  1. Build keyword cubes: for each vocabulary word and mixing, the 26-letter mixed alphabet with '?' appended or prepended, filled into the cube in order.
  2. For each cube, period 2-20 and alignment, decrypt and count crib hits.
  3. For periods 2-15 and alignments, anneal a random cube by swapping two symbols, accepting by crib hits with a temperature schedule, two restarts of 4,000 steps.
  4. Re-anneal the five best settings with 20,000 steps.
  5. Repeat the search on two shuffles of K4 for calibration.
  6. Submit any decryption with all 24 cribs.
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

Keyword cubes: best 7 of 24 hits over 104082 decryptions. Annealing: best 17 of 24 after refinement (settings best 17); shuffled K4 reaches [14, 11].

What was searched, as the harness recorded it.

family
trifid, 27-symbol cube, periods 2-20
keyword cubes
498
exact decryptions
104,082
exact best hits
  1. hits
    7
    cube
    CARNARVON/alt_vertical/?first
    period
    14
    offset
    9
  2. hits
    6
    cube
    WONDERFULTHINGS/keyed_columnar/?last
    period
    10
    offset
    6
  3. hits
    6
    cube
    WEBSTER/keyword/?last
    period
    8
    offset
    2
  4. hits
    6
    cube
    SHADOWFORCES/keyed_columnar/?last
    period
    12
    offset
    9
  5. hits
    6
    cube
    SHADOW/keyed_columnar/?first
    period
    14
    offset
    11
  6. hits
    6
    cube
    INTERPRETATION/columnar/?last
    period
    2
    offset
    0
  7. hits
    6
    cube
    DIGETAL/columnar/?first
    period
    19
    offset
    4
  8. hits
    6
    cube
    CARTER/columnar/?first
    period
    16
    offset
    8
  9. hits
    6
    cube
    BERLIN/columnar/?last
    period
    7
    offset
    5
  10. hits
    6
    cube
    ALEXANDERPLATZ/keyword/?last
    period
    19
    offset
    17
annealing settings
119
annealing best by setting
  1. hits
    17
    period
    14
    offset
    8
  2. hits
    17
    period
    2
    offset
    0
  3. hits
    16
    period
    15
    offset
    7
  4. hits
    16
    period
    14
    offset
    7
  5. hits
    16
    period
    8
    offset
    2
  6. hits
    16
    period
    7
    offset
    5
  7. hits
    16
    period
    5
    offset
    3
  8. hits
    15
    period
    15
    offset
    4
  9. hits
    15
    period
    14
    offset
    4
  10. hits
    15
    period
    13
    offset
    7
refined best
  1. hits
    17
    period
    14
    offset
    8
    cube
    GDUSW?RNBLTPXJAKQVHYMCZFOIE
  2. hits
    17
    period
    2
    offset
    0
    cube
    UKBJSYEVGL?AZTQORMFPWCINXDH
  3. hits
    16
    period
    15
    offset
    7
    cube
    LMEFTKISZWJDNRO?HCQYBVUPAGX
shuffled control best hits
14, 11

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.
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