Z13 and Z32: what an exhaustive computational attack can and cannot say

Final project report, 2026-10-07. Machine-readable summaries: results/summary.json (the eight attack tasks) and results/lead/decision/numbers.json (the Z340-key lead). results/summary.json was written before the lead workflow finished; where the two disagree, this report and results/lead/DECISION.md take precedence (Appendix C).

This report covers the two unsolved Zodiac ciphers: Z13, the 13-symbol “My name is” cipher (letter of April 20, 1970), and Z32, the 32-symbol Mt. Diablo cipher (letter of June 26, 1970). The two solved Zodiac ciphers, Z408 and Z340, served only as calibration data. Eight attack tasks ran, and each was checked by an independent adversarial reviewer who reran its key computations. A follow-up workflow (results/lead/) then tested the project’s one candidate signal with a pre-registered replication, three independent skeptic reviews, a look-elsewhere test of the TORPEDO completions and a prior-art search; its verdict is in results/lead/DECISION.md. Where a reviewer corrected a number, this report uses the corrected number, and no claim is rated higher than its reviewer rated it.

Labels used throughout:

What this project is and is not

It is an exhaustive, reproducible computational analysis of Z13 and Z32, and its results are negative:

It is not a solution of either cipher. No string in this report is offered as what Z13 or Z32 says, and every candidate listed is unsupported or refuted.

Nothing here identifies the Zodiac or a bomb location. Names were tested only to measure how often names fit; a name that fits the pattern says nothing about that person. The map work tests published instructions geometrically; no point on or off the map is supported as a bomb site.

It is not a set of new discoveries either. The prior-art search found that the ideas behind most results had been published before. The project’s own decision is that nothing here clears the bar of a genuinely new finding; the few things that may be called new are listed, in fixed wording, in §7.1.

1. Bottom line

Neither cipher is solved, and this project found no candidate text for either that beats a fair null model. Every published proposal we could test is either incompatible with the cipher or indistinguishable from chance. This is a negative result, and the numbers below explain why it is the expected one.

What we can claim:

  1. The ciphers are too short to pick out an answer from the symbols alone (computed).
    • About 1 English 13-letter window in 2.1 million fits Z13’s repeat pattern. A 13-letter English text carries roughly 34 bits by our language model, and the pattern removes only about 21. That leaves thousands of fitting English strings, and tens of thousands to millions of fitting personal names.
    • About 1 English 32-letter window in 3,800 to 5,400 fits Z32. Between 10^6 and 10^19 English texts fit it, depending on how predictable the underlying text is assumed to be.
    • No amount of extra computing changes this. The limit is information, not search.
  2. Z13 is probably not an ordinary English phrase under plain substitution with no errors (computed, plus a judgement).
    • If it were, calibration says its true text would very likely be among the few dozen most fluent fits. Those fits are fragments and word salad (A DEFINITIVE AT, ON THE DEFEAT OF, IN THE DESERT IS).
    • This disfavours that one hypothesis. It leaves open a name, an enciphering slip, null symbols, a transposition, or a non-English text.
  3. Z13’s repeat pattern is not what Zodiac’s usual keys and habits produce (computed; the strength depends on the model).
    • One symbol appears three times in five positions, and only 8 different symbols appear in 13 positions. No 5-symbol stretch of the 748 solved symbols repeats a symbol three times. (Oranchak showed in 2012 that no window of Z408 shorter than 22 symbols, or of Z340 shorter than 15 in written order, is as repetitive as Z13.)
    • Real phrases enciphered with Zodiac-style 54- or 63-symbol cycling keys never reproduced either feature (0 of 20,000).
    • Depending on the model, the pattern favours a key with mostly one symbol per letter by roughly 100:1 to 6,000:1. An independent check with the real Z340 homophones points the same way (§4.5).
    • Either Z13 used a different kind of key, or the circled letter was one Zodiac gave a single symbol, or the three circles are three different symbols.
  4. One statistical curiosity, which does not hold up (computed; results/lead/; §4.4).
    • With the Z340 key’s letters on Z13’s six shared symbols, the best completions are slightly more English-like than with random key letters. A pre-registered replication with fresh code gives p about 0.01-0.015 per test (0.0147 for the primary 6-gram test, 0.0096 for the word statistic) and 0.039 family-wise over its 12 tests.
    • It fails the replication’s own negative control: Zodiac’s unrelated Z408 key does about as well on the n-gram statistics (p = 0.026 and 0.022). A frequency-free test, the real six letters against all 360 rearrangements of themselves, gives 0.144 family-wise.
    • It is not significant at project level under any accounting (Šidák over the project’s 51 analyses: 0.23 for the original 0.0051, 0.87 for the replicated 0.039). All three skeptic reviews independently reached “refuted” for key reuse.
    • The TORPEDO completions need the circles to be different symbols, which no published transcription asserts. They are not the top completion, and random keys produce comparable text; after look-elsewhere they are worth a likelihood ratio of only 1.9-3.9. They carry no weight.
    • It is a statistical curiosity, not evidence of key reuse, and no completion means anything. Reading Z13 with the Z340 key is not ours: Garlick, Ziraoui, Marclean and T.C. did it first.
  5. Nothing on the Mt. Diablo map singles out a location (computed).
    • The mailed map piece has two properties that matter for every radians-and-inches interpretation. Both were published before, most precisely by shaqmeister (forum, 2026-05-12); we confirm them independently:
      • true north is about 4.6 degrees clockwise of the map’s up direction;
      • its printed scale bar is about 9% too long for the geography (7.0-7.2 ground miles per paper inch; shaqmeister: 7.02).
    • Several published instructions point off the piece Zodiac mailed.
    • Gareth Penn’s “one radian” is 60.3 degrees.
    • The only tight coincidence, Lake Herman Road at one radian from magnetic north, was noted before (zodiackillerfacts.com illustration, about 2011; Hodel 2010; Grinell; DMW 2019). It is post hoc. Its chance probability is 0.01 to 0.33, depending on how many alternatives one admits.

What we cannot claim: an identity, a bomb location, evidence of key reuse, or evidence about whether Z32 shares a key with Z13 or with the solved ciphers. With 13 + 32 symbols, the joint-key question cannot be tested by the methods available (0 of 5 synthetic shared-key pairs were detected).

What would settle it (§8): more ciphertext under the same key, Zodiac’s worksheets or key sheets, an outside source text, or higher-resolution images of the originals. Higher-resolution images bear directly on whether Z13’s three circles are one symbol.

2. The ciphers

2.1 Verified transcriptions

All four files use David Oranchak’s ASCII convention (the one in his webtoy, Cipher Explorer and AZdecrypt). In it, z is the crosshair, 0 the circled glyph of Z13, [ an upside-down T whose base hooks up at the right, ? an omega, | a plain vertical bar, 8 the filled triangle, 9 the open triangle, and lower-case letters are mirror-reversed letters.

Z13  AENz0K0M0[NAM        13 symbols, 8 distinct, pattern abcdefegehcag
Z32  C9J|#Ok[AMf8?ORTG    row 1, 17 symbols
     X6FDVj%HCELzPW9      row 2, 15 symbols; 29 distinct

The certification step checked every glyph by eye against magnified scans (data/ciphers/README.md, “Certification”):

cipher images checked (in data/images/) result
Z13 z13_letter_1970-04-20_p1_commons.gif (binarized 640x829, the best scan found); z13_glyphs_magnified_from_commons.png; z13_letter_1970-04-20_p1_zkf.jpg (colour, 407x576); z13_letter_top_zodiackillerciphers.jpg (colour, 657x262) same 13 glyphs in every image; no published source disagrees on symbol identity or order
Z32 z32_letter_1970-06-26_color_commons.jpg; z32_letter_1970-06-26_zodiackiller.png; z32_letter_1970-06-26_police_photo_zkc.jpg (SFPD photo, 5100x7014); also z32_letter_1970-06-26_color_hires_zkc.jpg same 17 + 15 symbols in all three independent images
shared glyphs Commons colour photo of Z340; Oranchak’s combined Z408/Z340 key image Z32 position 23 is % (open triangle at upper left); position 22 is the backward J j; Z13 position 9 and Z32 position 7 are the same hooked glyph [, which differs from the plain Z340 t; Z32 position 3 is the plain bar |, not the serifed Z408 I
map and later letter z32_map_1970-06-26_large_zkf.jpg, z32_map_1970-06-26_zodiackiller.png, z32_letter_and_map_1970-06-26_commons.jpg, unmarked exemplar z32_map_phillips66_*_zkf.jpg, July 26 letter z32_little_list_letter_1970-07-26_p2/_p5_zodiackiller.png used for the map geometry (§5.6)

2.2 Open transcription questions and the variants we ran

Every alternative transcription was run as its own cipher. Most have a file data/ciphers/variants/<id>.txt; z13.letters_literal is the canonical file run with pinned letters (--pin), and z32.reversed is generated by the scripts that use it (tools/keyprior_lib.js, tools/audit_make_ciphers.js). Plausibility is our judgement from the images.

id string what changes plausibility effect on our conclusions
z13.canonical AENz0K0M0[NAM default default  
z13.circles_distinct AENz0K{M}[NAM the three circles are three different symbols low about 500 times easier to fit (1 in 4,000 English windows); 1 name in 15 to 40 fits with 2 filler letters; makes every Z13 test less informative
z13.crosshair_null AEN0K0M0[NAM crosshair is a signature or null (12 symbols); also tried as a word break low similar to canonical; as a word break it removes most name fits but not all
z13.bracket_is_perp AENz0K0M0tNAM [ is the plain upside-down T medium same pattern as canonical; matters only for key carry-over (Z408 R, Z340 L)
z13.reversed MAN[0M0K0zNEA read right to left low fit counts similar to canonical
z13.letters_literal canonical, with A, E, N, K, M pinned to themselves the letter glyphs stand for themselves low no English word sequence fits by simple substitution; no real name fits without forced filler letters
z32.canonical C9J\|#Ok[AMf8?ORTGX6FDVj%HCELzPW9 default default  
z32.triangles_merged open and filled triangles one symbol adds a fourth repeat low about 3.6 more bits of constraint; no change in conclusions
z32.bar_is_serif_I, z32.t2_is_perp, z32.bar_I_and_t2_perp, z32.tau_distinct glyph identities at positions 3, 7, 22 same repeat pattern as canonical low to medium matter only for key carry-over; every carry-over test has p >= 0.28 (§5.5)
z32.reversed read right to left   low no change

The README in data/ciphers/ agrees with the task brief on every foundation fact. Two foundation statements needed qualification after review:

3. Why short ciphers resist

3.1 The information budget (computed; results/nullmodel/)

A substitution cipher hides the letters but keeps the pattern of repeats. If a symbol occurs twice, the same letter occurs twice. That pattern is all the information a short cipher offers, and it can be measured. We slid a window over 114 million letters of American fiction (1850-1945) and counted how many real English windows have the pattern. We then compared that count with how much information an English text of the same length carries.

quantity Z13 (canonical) Z32 (canonical)
length, distinct symbols 13, 8 32, 29
English windows that fit, homophonic (repeated symbols = same letter) 53 of 112,021,522 = 1 in 2.1 million 29,475 of 112,005,315 = 1 in 3,800 (other corpora: 1 in 4,465 to 1 in 5,361)
English windows that fit, strict (also different symbols = different letters) 12 = 1 in 9.3 million impossible: 29 symbols, 26 letters
constraint removed by the pattern 21.0 bits homophonic (95% CI 20.6-21.4), 23.2 strict 11.9 bits
information in an English window of that length (6-gram model, held-out text) 34.0 bits (31.1 word-aligned) 76.2 bits (73.4 word-aligned)
key entropy 37.6 bits 136.3 bits
Shannon unicity distance (from research/keys_methods.md) 10-22 symbols 37-80 symbols

Expected number of English strings that fit, 2^(information - constraint), for several assumptions about how predictable the underlying text is (homophonic):

assumption about the underlying text Z13 Z32
6-gram model, any window about 7,900 about 2.3 x 10^19
6-gram model, word-aligned (reviewer-corrected) about 1,500 (range 420-4,000) about 2.6 x 10^18
2.2 bits per letter about 190 about 4 x 10^17
1.3 bits per letter (redundancy of long running text) about 0.06 about 9 x 10^8
1.0 bits per letter about 0.004 about 1 x 10^6

What this means:

3.2 The empirical unicity curve (computed; results/nullmodel/lengthscan*, reviewer reruns in results/nullmodel/review/)

We encrypted held-out English of various lengths and asked our annealing solver to recover it.

length simple key, exact recovery, default objective simple key, 6-gram likelihood objective (reviewer) Zodiac-style 63-symbol cycling key
13 1/12 4/12 (Wilson 95% CI 14-61%) 0/12 (degenerate: no repeated symbols)
20 0/12 1/12 0/12 (degenerate)
32 8/12 9/12 0/12 (9 of 12 had no repeats)
50 10/12   0/12
75 / 100 8/10, 8/10   0/10, 0/10
150 / 200 10/10, 10/10   0/10, 0/10 (2/10 at least 90% letters right at 200)
340 10/10   5/10 exact, 10/10 at least 90% right

3.3 A solver only sees the pattern (computed)

A homophonic solver’s output depends only on the cipher’s repeat pattern, not on what the symbols look like. Relabelling Z32’s symbols gives an identical result with the same seed. So for every text that fits Z13’s pattern, the solver returns the same answer:

The reviewers showed that this “the solver always beats the truth” behaviour belongs to the default objective (joint 5-gram score plus a word term), which is not a likelihood. With the 6-gram likelihood as objective:

Consequence. Under the narrow hypothesis “Z13 is a fluent English phrase in strict substitution”, Z13 sits at the edge of solvability rather than far below it. That is why the calibration in §4.3 has teeth.

3.4 Earlier published numbers, reproduced (computed)

4. Z13

4.1 Is it a personal name? (results/z13names/; reviewed, reproduced exactly)

Method (computed). We enumerated every way to fit Z13 with a name built from US name lists: SSA first names for births 1900-1955 and Census surnames. The search covered:

An independent dynamic program written by the reviewer matched all 416 exhaustive cells exactly.

Too many names fit. Canonical cipher, no filler letters (male / female lists):

pattern strict (simple substitution) homophonic
FIRST LAST 6 / 44 72 / 321
FIRST INITIAL LAST 208 / 234 1,494 / 2,958
FIRST MIDDLE LAST 9,723 / 51,521 72,182 / 367,670
FIRST INITIAL INITIAL LAST 4,142 / 11,454 33,725 / 76,049
LAST FIRST 12 / 3 56 / 87

No suspect fits.

The pattern gives a name no support.

4.2 Is it an English phrase? (results/z13phrases/; reviewed, reproduced exactly)

Search (computed). We enumerated every sequence of up to 5 words from a 60,006-word common vocabulary that fits Z13. This space contains every one of 2,002 above-median real 13-letter phrases in a held-out coverage test.

How many good fits (canonical):

mode consistent strings at or above the real-phrase median at or above the 75th percentile at or above the 90th percentile
simple 25,761,330 22 (24 with a deduplicated reference) 1 0
homophonic 148,816,201 64 (69) 3 (4) 0

Other transcriptions and allowances.

Z13 looks like any rearrangement of its symbols (reviewer, computed). Its fit statistics sit in the middle of the distributions for random rearrangements of its own 13 symbols:

statistic Z13 random rearrangements real phrases with the same repeat profile
fits above the median 22 median 13; 20% have 22 or more median 12; 28% have 22 or more
best fit score -8.31 median -8.59 median -8.05

So the dictionary search gives no evidence that Z13 is English at all.

4.3 What a real answer would look like (computed; judgement in the last step)

Two reviewer calibrations measure where a true text would rank among the fits:

So if Z13 were an ordinary English phrase in Zodiac’s style, enciphered without slips, its true text would very likely be among the few dozen most fluent fits. Those fits are fragments and word salad:

SOUTH THE HOUSE, OF THE DEFEAT OF, A DEFINITIVE AT, OF THE DEFECT OF, ON THE DEFEAT OF, IN THE DESERT IS, LEBANON ENABLE, OF THESE NEWTON, DO NOT IT STANDS, …

None answers “My name is”. Judgement: this disfavours the hypothesis “ordinary English phrase, plain substitution, no errors”. It leaves standing the possibilities the letter itself suggests:

Prior art: IN THE DESERT IS was already among Oranchak’s 2012 Project Gutenberg fits. The calibration argument is what this project adds (§7.1).

4.4 Did Zodiac reuse a known key? (results/keyprior/, then results/lead/; reviewed, replicated only weakly, refuted as key reuse)

Background (computed).

The question tested. With A=D, E=R, N=E, z=A, K=A, M=O pinned and the free symbols searched exhaustively, are the best completions more English-like than with random key letters? The keyprior task first found p = 0.0008. Every stricter test since then has given a weaker result:

step p-value source
first report, anneal objective 0.0008 results/keyprior/
same objective, fresh seed, pooled with the first run 0.00105 results/lead/skeptic/family.json
keyprior review, family-wise over 4 transcriptions x 2 statistics 0.0051 results/keyprior/review/family.json
over both known keys 0.0102 same
pre-registered replication, primary test (canonical, 6-gram) 0.0147 results/lead/replicate/summary.json
pre-registered replication, word statistic 0.0096 same
pre-registered replication, family-wise over its 12 tests 0.039 same
frequency-free exact test (all 360 rearrangements of the real six letters), family-wise over the same 12 0.144 results/lead/skeptic/stat/summary.json

The pre-registered replication (computed; results/lead/replicate/). The protocol was written and hashed before any statistic was computed (prereg.md, prereg.sha256), and the code was new (tools/lead_replicate_*). It ran 4 transcriptions x 3 statistics (best 6-gram score, best word-segmentation score, mean of the 10 best 6-gram scores) against 8 null models of 10,000 draws each (137 eligible windows for the window null), with real-English positive controls and Zodiac’s unrelated Z408 key as the negative control.

What the replication and the three skeptic reviews found against it (computed; results/lead/skeptic/, results/lead/skeptic/stat/, results/lead/cipherexpert/). All three skeptics independently reached “refuted” for key reuse.

Project-level correction (computed; results/lead/decision/numbers.json). The project ran 51 analyses and its result files hold 1,992 distinct p-values, 1,806 of them from keyprior itself.

accounting 0.0051 (original, most favourable) 0.039 (pre-registered replication)
Šidák over 24 key-carry-over tests 0.12 0.62
Šidák over the project’s 51 analyses 0.23 0.87
Benjamini-Hochberg q over 1,862 distinct p-values 0.12 0.23
Bonferroni / Holm over 1,992 distinct p-values 1.0 1.0

TORPEDO (computed; results/lead/torpedo/). Garlick’s DR EAT A TORPEDO (published with the letters TOTPEDO) and the related DREAM A TORPEDO get no weight:

Other carry-over results (computed).

Standing: a statistical curiosity, not key reuse. With the Z340 key’s letters on Z13’s six shared symbols, the best completions are slightly more English-like than with random key letters (pre-registered replication: p about 0.01-0.015 per test, 0.039 over its 12 tests). The effect is mostly letter frequency and the one letter both solved keys share. Zodiac’s unrelated Z408 key does about as well on n-gram statistics, and a frequency-free test gives 0.144. It is not significant at project scale (Šidák over 51 analyses: 0.23 for the original 0.0051, 0.87 for the replicated 0.039). It would require an encipherment unlike Zodiac’s own practice, and none of the 676 completions under the standard transcription means anything. All three skeptic reviews reached “refuted” for key reuse, and the TORPEDO completions deserve no weight.

Z32 and the joint key (computed).

4.5 How Zodiac chose homophones, and the triple circle (results/cyclemodel/; reviewed, reproduced, strength corrected)

Habits fitted on the solved ciphers (computed).

The triple circle (computed).

Which kind of key made Z13 (computed; strength depends on the model). Z13’s pattern favours simple substitution over a fresh Zodiac-size homophonic key by 10^2.7 to 10^3.8 (about 500:1 to 6,000:1):

The direction is robust. If such a key was used anyway, the circled letter is most likely E or O (posterior about 0.32-0.38 for E), with a single symbol.

Prior art: Pelling (2017) argued qualitatively that Z13’s many repeats point to a monoalphabetic cipher, and Oranchak (2012) showed that no 13-symbol window of the solved ciphers is as repetitive. The fitted model and the Bayes factors are what this project adds (§7.1).

Are the three circles one symbol? (computed, prior-dependent)

key model Bayes factor for three distinct symbols over one, from the pattern alone
simple 10^2.0
small homophonic 10^2.8
Zodiac-size 10^4.5

Re-ranking with the pattern likelihood (computed).

4.6 Best Z13 candidates and their standing

candidate how it arises standing (reviewer verdict) why
A DEFINITIVE AT / ON THE DEFEAT OF / IN THE DESERT IS most fluent strict fits; IN THE DESERT IS is the 6-gram MAP fit (already in Oranchak’s 2012 list) unsupported expected by chance (Z13 is typical of its own scrambles); not a message
SOUTH THE HOUSE most fluent homophonic fit unsupported word salad; homophonic share not established; drops to rank 41 once simple substitution is weighted in
IN THE RESENT IS default solver output refuted an objective artifact returned for every cipher with Z13’s pattern
OF THE DIRECTOR one assumed slip at the middle circle unsupported scramble null p about 0.08; siblings score the same
SLEEPLESSNESS circles_distinct only unsupported low-plausibility variant with hundreds of good fits
EDDIE RESENDES, CARL BOB ABARCA, MARY LULA LERMA, AMY HELENE RYAN, CHASTITY TRACY, DONALD LYLE NGO top names under various patterns and transcriptions unsupported leader changes with every assumption; prior-driven shares
DREAM A MOM WE DO, DREAD A DODGE DO Z340 key, canonical unsupported the curiosity behind it is not significant at project scale (§4.4); text meaningless
DREAM A TORPEDO; DR EAT A TORPEDO Z340 key, three distinct circles (Garlick) unsupported; no weight rank 3rd and 348th of 456,976; random keys give comparably fluent text (likelihood ratio 1.9-3.9 after look-elsewhere); needs distinct circle symbols, which no published transcription asserts
TREATY TO THE TO Z340 key, partial (E N z M) unsupported family-wise 0.026 at best; word salad
WEED AS A HAVE WH Z408 key unsupported no signal on the word statistic (p = 0.25-0.29)

5. Z32

5.1 What the pattern allows (computed)

Z32’s only constraint under homophonic substitution is three equalities: positions 0 = 25, 1 = 31 and 5 = 13. That is about 12 bits.

5.2 Free solver search (results/z32search/; reviewed, reproduced exactly)

5.3 Themes: cribs and radian/inch messages (computed)

Cribs.

Structured radian/inch messages. Three independently built grammars agree that such messages fit Z32 at the ordinary rate:

grammar derivations of 32 letters fit Z32 comparison
z32search 1,469,362,720 376,072 (1 in 3,907) null median (P = 0.60)
nullmodel reviewer 47,730,756 20,181 (1 in 2,365)  
audit about 1.46 x 10^10 about 5.1 million  

The published proposals ESTIMATE FOUR RADIANS AND FIVE INCHES (Grinell 2020) and IN THREE AND THREE EIGHTHS RADIANS TEN (DMW 2019, Stampher 2026) are among these fits, alongside trivial siblings such as ESTIMATE NINE RADIANS DIG FIVE INCHES. Stampher (2026) had already enumerated such phrases (61 of 154,572 fit, 1 in 2,534) without a null comparison.

5.4 Transpositions (computed)

5.5 Key carry-over (computed)

5.6 The Mt. Diablo map (results/mapgeometry/; reviewed, reproduced exactly, with independent geodesy)

The July 26 letter says the code “concerns Radians & # inches along the radians”. We tested that instruction geometrically, without deciphering anything.

Mt. Diablo map geometry

Left: the mailed inset with rays every radian from “map-up + 17 degrees” and rings in paper inches. Right: the same on the ground (true north up, rings every 6.4 miles), with the inset outline and Zodiac-related sites. Source: results/mapgeometry/mapgeometry_figure.png.

The map itself (computed, independently confirmed; known before, see “Prior art” below).

Prior art. These map facts were published before, and our numbers are an independent confirmation, not a discovery:

Published radian theories (computed).

theory test result verdict
Penn (1981/1987): Blue Rock Springs and the Stine site subtend one radian at the summit 60.28 degrees = 1.052 rad (5.2% over); the watch-face version also gives 60.1 degrees; chance of some pair being this close to 1 rad 0.18-0.51 refuted as “one radian”
Grinell / InStepWithTheStars: 4 rad clockwise from magnetic north, 5 in lands 2.24 mi from Ingleside station using 6.4 mi/in on the ground, 6.15 mi measured on the paper; the ray misses the San Francisco crime sites by 9-12 degrees unsupported
DMW / Stampher: ten o’clock, 3 3/8 in 1.15 mi from Blue Rock Springs at 6.4 mi/in; 0.49 mi from the Vallejo phone booth measured on paper; the point moves with the convention; 2 of 44 claim points within 1 mi of a site (one by construction), p = 0.05 unsupported
Foxon (12 in, 3 rad) and (3 in, 0 rad); Burke “7 in south”; Penn “4 in along the radian” all fall off the mailed piece, in their own conventions too (Foxon: 12 of 12 variants) refuted as instructions on this map
Lake Herman Road = 1.000 rad counter-clockwise of 1970 magnetic north, and “3 in” at 6.4 mi/in lands 0.13 mi from it the angle was noted before (zodiackillerfacts.com illustration, about 2011; Hodel 2010; Grinell, about 2024; DMW 2019); the 3-inch match is post hoc. At a realistic 0.25-mile tolerance, chance p is 0.01-0.05 in narrow integer-step families and 0.12-0.33 in wider ones. It reads counter-clockwise against the clockwise 0-3-6-9 labels. On the mailed sheet it is 0.92 rad and 2.69-2.75 in. It marks a murder site, not a bomb site unsupported (a negative result)
July 26 doodle: the bold zero sits at 241-242 degrees, the Stine site’s magnetic bearing is 241.0 p = 0.07-0.14 after look-elsewhere not significant

Grid of all radian/inch points (computed).

5.7 Best Z32 candidates and their standing

candidate how it arises standing
A TURNED THAT THE LOOKING THE WAS ABOUT; WELL THAT THEIR HAND COMPARED WITH THE; ES NOTHING FOR THERE WAS AND THE THINGS solver optima refuted (word salad at the null level; solver beats truth 12/12)
AND THERE FOR THE RADIANS WERE AND THEN best RADIANS crib completion refuted (forced completion, mid-pack against nulls, test has no power)
SURE SOMETHING OF THE FINDINGS AND YOU solver with the pattern likelihood unsupported (ungrammatical; typical solver output)
ESTIMATE FOUR RADIANS AND FIVE INCHES Grinell 2020 unsupported (fits; 1 of hundreds of thousands of on-theme fits; map step post hoc)
IN THREE AND THREE EIGHTHS RADIANS TEN DMW 2019, Stampher 2026 unsupported (fits; Stampher’s own funnel passed 61 phrases and kept 54 survivors)
Z408 / Z340 / union carry-over strings key reuse refuted (p about 0.8)

6. Published claims audit (results/audit/; reviewed, core counts reproduced exactly)

We checked 43 named proposals (18 for Z13, 25 for Z32) and all 1,153 strings on the Z13 Solutions wiki page.

claim proponent mechanical result verdict (after review)
ALFRED E NEUMAN Graysmith 2002, Bauer 2017 1 conflict (N must be both F and M), which its proponents concede; impossible in any reading order without that slip unsupported
DR EAT A TOTPEDO / TORPEDO Garlick 2020, 2025 homophonic fit with the Z340 key (TORPEDO needs a slip, or the three-distinct-circles transcription); rank 174 of the 676 completions of its own premise; 2.45 million homophonic dictionary fits read better unsupported; no weight after the look-elsewhere test (§4.4)
ANDREA J ODELL (from DREAJALORNEDO) T.C. 2024-2025 DREAJALORNEDO fits only if the circles are three different symbols; the final name is not a permutation of the 13 letters incompatible
KAYR / KAYE Ziraoui 2021 multi-step chain of free choices (Z340 key, dial numbers, A1Z26 digits, trifid, an assumed error) indistinguishable from chance
MARVIN MERRILL Baber 2025 5 conflicting positions in direct order (shown before by Hodel 2026 and 0xfab1); 0 of 92,464 columnar transpositions (92,323 distinct; blanks only at the end of the last row) and 0 of 282,352 2x7 / 7x2 grid orders fit; the prior-art rerun of the described 2x7 box (null anywhere, all 5,040 column orders, both directions) fits 0 of 423,922 distinct orders under the canonical, bracket and reversed transcriptions, and 91 homophonic orders only under three distinct circles, none with the reported LIZABETH order; 1,224,045 of 15 million FIRST+LAST names share its letter profile, and 4% (box) to 8-9% (columnar) of random profile-matching names fit some order refuted as reported (the test has low power)
EARL VAN BEST JR Stewart 2014 no letter occurs three times, so no key and no reading order fits incompatible
NAME GRANT Lafferty 2012 multi-step with free choices; the same steps yield hundreds of names indistinguishable from chance
LAWRENCE KANE; FROM TED KACZYNSKI Dragallas 2017; Oswell 5 conflicts; 16 letters for 13 symbols incompatible
AENDLSLMLCNAM (“ALLEN”) TheDecipherist 2026 strict fit, but not English; rank 254 of 676; ALLEN comes from an outside checksum unsupported
ED SHAW “Rembrandt” Z408 key plus 7 of 13 symbols treated as nulls indistinguishable from chance
THE BIG SECRETE Kelleher fits only the three-distinct-circles transcription; 418 of 649 natural fits read better unsupported
DR GEORGE HODEL / GEORGE HODEL MD Hodel (found by the reviewer) 5 conflicts in direct order; GEORGEHODELMD has Z13’s letter profile, so it is anagram-compatible like 1.2 million other names incompatible as written
SARAH THE HORSE, CHASTITY TRACY Oranchak 2013 (demonstrations) fit; offered by him as examples of how many fits exist demonstrations
IN THREE AND THREE EIGHTHS RADIANS TEN DMW 2019, Stampher 2026 fits; its fluency is within Zodiac’s own range, so fluency rank is not evidence against it unsupported
ESTIMATE FOUR RADIANS AND FIVE INCHES Grinell 2020, InStepWithTheStars fits; near the top of the grammar null and above 60% of Zodiac’s own aligned 32-letter windows unsupported
THREE RADIANS FROM MOUNT AREA TWO INCH Cragle 2022 fits; ungrammatical unsupported
OKAY I SEVEN INS SOUTH OF DIABLO MT PEAK Burke 2019 fits; less fluent than 95.6% of Zodiac’s own aligned windows unsupported
TWELVE INCHES ALONG THE THREE RADIANS Foxon 2023 on his own order (second row shifted 2, knight move from top-left) it has exactly his two declared misspellings; 15.3% of random English windows do as well on that order; he calls it unconvincing himself unsupported
RADIANS AND 5 INCHES ALONG THE RADIANS Grinell 2018 2 conflicts incompatible
LABOR DAY FIND 45.609 NORT 58.719 WEST Ziraoui 2021 the digits reproduce exactly from the Z340-key letters, but the 20-letter anagram needs a letter that string lacks, and 2 symbols are dropped unsupported
Roberts 2014; Boyouk 2022; NoName 2024   62, 38 and 33 letters for 32 symbols incompatible
Sundberg & Thelin 2014; Dickinson 2026; Praetorian 2026   multi-step proposals with free parameters (Praetorian brute-forced about 24,000 combinations) indistinguishable from chance
Penn; Cobb; Case Breakers; Garlick (Z32 video); Baber (Z32); Dominik; Lewison; Kobek; Voigt   no checkable text available untestable

Two audit arguments were corrected in review:

7. What is new, what was known, and what is negative

A prior-art search (results/lead/priorart/priorart.md) checked every candidate finding (F1-F10 below) after the draft of this report was written. It changed this section. The map facts the draft listed as new had been published five months earlier, and the Z340-key result turned out to rest on a known idea (reading Z13 with the Z340 key), while our new test of it finds no evidence of reuse (§4.4). The project’s decision (results/lead/DECISION.md, section 3) is that nothing here is a genuinely new fact about what Z13 or Z32 say, and the results should not be published as new findings. If a methods-and-negative-results repository is published anyway, the wording in §7.1 is the limit of what may be called new.

7.1 What may be called new, and in what words

To our knowledge, and subject to the gaps in §7.5:

  1. F1 (new method, negative result). “To our knowledge, the first permutation-null test of whether Zodiac reused the Z340 key in Z13. The six shared symbols decode to letters slightly more English-friendly than random key letters (p about 0.01 per test, 0.039 over 12 pre-registered tests), but Zodiac’s unrelated Z408 key does about as well on n-gram statistics, a frequency-free test gives 0.144, and the result is not significant once the project’s other analyses are counted. We find no evidence of key reuse. Reading Z13 with the Z340 key is due to Garlick and others.” The others are Marclean (2020), Ziraoui (2021) and T.C. (2024-25).
  2. F2 (quantification). “A homophone-choice model fitted to Z408 and Z340 puts the evidence that Z13 was made with a key giving most letters a single symbol, rather than a Zodiac-style homophonic key, at roughly 10^2.7 to 10^3.8 (model-dependent). Pelling (2017) argued this qualitatively, and Oranchak (2012) showed no 13-symbol window of the solved ciphers is as repetitive.”
  3. F3b (observation). “No 5-symbol window of Z408 or Z340, in written or reading order, contains a symbol three times; Z13 does (positions 4, 6, 8).”
  4. F5 (quantification). “On Foxon’s own read order, 15.3% of random English 32-letter windows fit Z32 with at most two slips, the same standard his candidate meets.”
  5. F4 (extension of a known refutation). “Under the 2x7 box transposition as described in secondary sources, MARVIN MERRILL fits none of 423,922 orders under the standard transcription, and none using the reported keyword order under any transcription we tested. The test has low power (4-9% of random profile-matched names pass).” Credit: Hodel (2026) and 0xfab1 showed that the direct reading fails.
  6. F6, F9 and F10, one sentence each beside the prior work they extend.
    • F6, new comparison: the radians-and-inches grammar fits Z32 at the rate expected for random three-pair repeat patterns (P = 0.60; 1 in 3,907 derivations), a null comparison that Stampher’s (2026) enumeration (61 of 154,572 phrases, 1 in 2,534) did not make.
    • F9, new calibration: real phrases with Z13’s repeat profile rank near the top of their own fits (median rank 2), so the fragments at the top of Z13’s list, including IN THE DESERT IS from Oranchak’s 2012 list, count against the ordinary-English-phrase hypothesis.
    • F10, new comparison: across 36 named suspects and six transcriptions, suspects fit Z13 no more often than random names (p = 0.69, and only under three distinct circles with forced fillers), a random-name null that the checks of Quicktrader (2021, about 30,000 names) and Stampher (2026, about 31,000 Vallejo names) did not use; the test has low power.

Nothing else in this report is claimed as new. Internal calibrations, such as the solver-objective comparison in §3.3, are method checks, not findings.

7.2 Replications and confirmations, with credit

7.3 Negative results

7.4 Prior art

finding verdict what was known what this project adds
Lead: Z13 made partly with the Z340 key; DREAM A TORPEDO / DR EAT A TORPEDO known idea; refuted (3 of 3 skeptics; the replication failed its negative control) Garlick (2020, 2025; TORPEDO is his), Marclean (2020), Ziraoui (2021), T.C. (2024-25) read Z13 with the Z340 key the negative result only
F1: permutation-null test of Z340-key carry-over partly known the idea (row above); arXiv:2403.17350 names links to the solved ciphers as a possible confirmation but runs no test the test; its answer is “no evidence of reuse”
F2: homophone-choice model; near-simple key favoured by 10^2.7-10^3.8 partly known Pelling (2017), qualitative; Oranchak (2012), windows; cycling studied by Oranchak, King and Bahler (1993), Raddum and Sýs (2010), Oranchak, Blake and Van Eycke (2024) the fitted model and the numbers; strength is model-dependent
F3: windows of 22 / 15; no 5-window triple known (22/15) plus novel (5-window) Oranchak (2012) the 5-window observation, a small one
F4: MARVIN MERRILL under 2x7 box orders partly known direct reading fails (Hodel 2026, 0xfab1); the method is known only from secondary descriptions, and the Colab notebook could not be read 0 of 423,922 orders; low power
F5: Foxon’s order, 15.3% of random windows fit novel Foxon himself calls the fit weak and declares the two misspellings the measured rate
F6: radians grammar fits at the null rate partly known non-uniqueness widely known (Oranchak 2014; arXiv:2403.17350; DMW; Foxon); Stampher (2026), 1 in 2,534; Dominik (2026) the comparison with random repeat patterns
F7: map turn 4.6 degrees, scale about 7.0 mi/in, Blue Rock Springs off the sheet known shaqmeister (2026-05-12); Amicone (2020); Marclean (2023); VT_Squire (2025); zodiackillerfacts.com an independent confirmation only
F8: Lake Herman Road at one radian, 3 in partly known the angle: zodiackillerfacts.com (about 2011), Hodel (2010), Grinell, DMW (2019) nothing claimed as new: the 3-inch match was evaluated and is not significant (a negative result)
F9: IN THE DESERT IS; calibration of a true phrase’s rank partly known the phrase: Oranchak (2012) the calibration argument
F10: 36 suspects against a random-name null partly known Quicktrader (2021), Stampher (2026); single-suspect checks by Oranchak, Hodel, 0xfab1 and Bauer the random-name null; low power

8. What would actually settle it

More computation on the existing 45 symbols will not. The binding limit is information (§3), and every further search only enlarges the set of fits. What would help:

  1. More ciphertext under the same key. Another cipher, a draft or an unmailed sheet that uses Z13’s or Z32’s symbols would multiply the constraints. Even 50-100 more symbols under a small key could make Z13’s key recoverable (§3.2).
  2. Zodiac’s worksheets or key sheets. The Z340 solvers named these, a known source text, or solid links to the solved ciphers as the evidence that could confirm any proposal for Z13 or Z32.
  3. Higher-resolution images of the originals, especially the April 20, 1970 letter. The best available Z13 scan is a binarized 640x829 image.
    • The three-circles question has a Bayes factor of 10^2 to 10^4.5 riding on it, and only the images can answer it.
    • The images would also settle whether the hook on [ is deliberate, which matters for key carry-over.
    • For Z32, the illegible print code on the map inset would date the map edition.
  4. New data for the Z340-key question. The pre-registered replication (§4.4) re-tested the same 13 symbols and could only re-describe the curiosity. Only a further Zodiac cipher that shares symbols with Z340 could test it: do those symbols get English-friendly letters from the Z340 key?
  5. For the map: physical or documentary evidence. No bomb was found, and no geometric interpretation can be validated by geometry alone. A 1970 USGS quad covering Mt. Diablo would at least fix the declination Zodiac could have used (probably 17 degrees east), on which the Lake Herman Road coincidence moves by 0.1-0.4 degrees.

9. Reproducibility

Run from the repository root.

Foundation

python tools/certify_ciphers.py                 # transcriptions, derived fields, variant export
node tools/verify_calibration.js                # Z408/Z340 calibration files (25 checks)
python tools/key_analysis.py                    # key statistics, cycling, overlap, unicity table
node tools/selftest.js                          # solver self-tests (results/selftest.json)

Information and nulls (results/nullmodel/commands.log; review: results/nullmodel/review/commands.log)

node tools/run_slot.js --label nullmodel-windows -- python tools/nullmodel_windows.py --cache <scratch> --scrambled13 100 --scrambled 300
node tools/nullmodel_info.js --samples 40000 --cache <scratch> --out results/nullmodel/information.json
node tools/run_slot.js --label nullmodel-isolik -- node tools/nullmodel_isolik.js --windows 100000 --keys 2000 --out results/nullmodel/isomorph_likelihood.json
node tools/run_slot.js --label nullmodel-lengthscan -- node tools/nullmodel_lengthscan.js --n 12 --threads 4 --max-seconds 2400 --out results/nullmodel/lengthscan
node tools/run_slot.js --label nullmodel-review-objective -- node results/nullmodel/review/review_objective.js --threads 4

Z13 names (results/z13names/)

node tools/run_slot.js --label z13names-h -- node tools/z13names_run.js --threads 4 --lists male,female --modes homophonic
node tools/run_slot.js --label z13names-s -- node tools/z13names_run.js --threads 4 --lists male,female,nick_male,nick_female --modes simple
node tools/z13names_suspects.js --reps 10000 --seed 1970 --out results/z13names
node tools/z13names_stats.js ; node tools/z13names_crosscheck.js ; node tools/z13names_report.js

Z13 phrases (results/z13phrases/; reviewer script results/z13phrases/review/run_review.sh)

node tools/z13phrases_null.js --n 4000
node tools/run_slot.js --label z13phrases-H1 -- node tools/z13phrases_batch.js --plan main_homophonic --budget 2400 --threads 4
node tools/z13phrases_calib.js distinct --n 20000
node tools/z13phrases_review_calib.js ; node tools/z13phrases_review_slipnull.js

Key reuse, first pass (results/keyprior/commands.log, results/keyprior/review/commands.log)

node tools/run_slot.js --label keyprior -- node tools/keyprior_fullpin.js --ciphers z13.canonical,z13.bracket_is_perp,z13.crosshair_null,z13.reversed --keys z408,z340,union --null 10000 --null-kind permute --threads 4 --seed 1970
node results/keyprior/review/review_family.js --null 10000 --threads 4 --seed 1970 --out results/keyprior/review/family.json
node tools/run_slot.js --label keyprior -- node tools/keyprior_fullpin.js --ciphers z32.canonical,... --keys z408,z340,union --null 1000 --max-free 4 --threads 4

The Z340-key lead (results/lead/; verdict results/lead/DECISION.md)

# pre-registration: results/lead/replicate/prereg.md, hashed in prereg.sha256 before any statistic was computed
node tools/run_slot.js --label lead-replicate -- node tools/lead_replicate_validate.js --n676 200 --ncircles 20 --ncircles-word 5 --seed 4242 --out results/lead/replicate/validate.json
node tools/run_slot.js --label lead-replicate-z340 -- node tools/lead_replicate_run.js --key z340 --draws 10000 --threads 4 --out results/lead/replicate/nulls_z340.json
node tools/run_slot.js --label lead-replicate-z408 -- node tools/lead_replicate_run.js --key z408 --draws 10000 --threads 4 --out results/lead/replicate/nulls_z408.json   # negative control
node tools/lead_replicate_multiplicity.js --lead 0.0051 --lead 0.0102 --lead 0.0096 --lead 0.0147 --lead 0.0392 --out results/lead/replicate/multiplicity.json
node tools/lead_replicate_report.js                       # results/lead/replicate/summary.json and tables.md
node tools/run_slot.js --label torpedo -- node tools/lead_torpedo_null.js --n 10000 --kinds permute,stratified --threads 4 --out results/lead/torpedo/null.jsonl
node tools/lead_torpedo_headline.js > results/lead/torpedo/headline.log ; python tools/lead_torpedo_derived.py
node tools/run_slot.js --label lead-skeptic -- node tools/lead_skeptic_check.js --null 10000 --seed 777 --h1top 2000 --h1sample 2000 --fits <scratch>/keyprior/z13_homo_fits_top500k.tsv --dump --out results/lead/skeptic/check.json
node tools/run_slot.js --label lead-skeptic -- node tools/lead_skeptic_homophones.js --chars 30000000 --stride 2 --seed 99 --out results/lead/skeptic/homophones.json
python tools/lead_skeptic_family.py > results/lead/skeptic/family.json
node tools/run_slot.js --label skeptic -- node tools/lead_skeptic_stat_multiverse.js --key z340 --null perm   # other key/null pairs and the arrangement, influence, families and Bayes scripts: results/lead/skeptic/stat/commands.log
node tools/lead_skeptic_stat_summary.js                   # results/lead/skeptic/stat/summary.json
node tools/run_slot.js --label lead-cipherexpert -- node tools/lead_cipherexpert_condn.js --variant canonical --null 10000 --seed 11
python tools/lead_cipherexpert_summary.py                 # results/lead/cipherexpert/summary.json
node tools/run_slot.js --label priorart -- python tools/lead_priorart_boxperm.py --names 300 --seed 2026
python tools/lead_priorart_windows.py                     # results/lead/priorart/windows.json
node tools/lead_decision_numbers.js                       # re-reads every number in DECISION.md -> results/lead/decision/numbers.json

Homophone-choice model (results/cyclemodel/)

node tools/cyclemodel_test.js
node tools/run_slot.js --label cyclemodel-pipeA -- node tools/cyclemodel_pipeline.js --steps fit,compat,win13,win32,enum,score
node tools/cyclemodel_hyp.js ; node tools/cyclemodel_summary.js

Z32 search (results/z32search/; review in results/z32search/review/)

node tools/z32search_check_lib.js
node tools/run_slot.js --label z32search-A -- node tools/z32search_solve.js --jobs results/z32search/jobs/free_main.json,... --threads 4 --max-seconds 2400
node tools/z32search_heldout.js ; node tools/z32search_typical.js --sample 8000
node tools/z32search_grammar.js --null 20 --threads 1 --orders written,skip19,cols_bt_r2right,diag_dc2,diag_dc2_r2right --out results/z32search/grammar/grammar_quick.json

Map geometry (results/mapgeometry/; reviewer rerun results/mapgeometry/review/rerun.py, independent geodesy results/mapgeometry/review/independent.py)

python tools/mapgeometry_core.py ; python tools/mapgeometry_radian.py --trials 20000 ; python tools/mapgeometry_gridhit.py --trials 20000
python tools/mapgeometry_report.py ; python tools/mapgeometry_figure.py

Claims audit (results/audit/; reviewer slot script tools/audit_review_slot.sh)

python tools/audit_wiki_parse.py
node tools/run_slot.js --label audit-theme -- node tools/audit_z32_theme.js --samples 3000000
node tools/audit_corpus_ref.js --docs all --reservoir 3000
node tools/audit_check.js --scratch <scratch> --null-names 300 --null-phrases 1000 ; node tools/audit_tables.js > results/audit/tables.md

This synthesis (results/synthesis/)

node tools/synthesis_extract.js --journal <workflow journal.jsonl> --out results/synthesis/reports_and_reviews.json
node tools/synthesis_pvalues.js        # p-values quoted per task; also checks that no Z408/Z340 message slice is present (0 found)
node tools/synthesis_multiplicity.js   # first, rough look-elsewhere arithmetic for the Z340-key lead (superseded by tools/lead_decision_numbers.js)

Appendix A. Every nominally significant result, and what became of it

From results/synthesis/pvalues.json (p-values quoted in the reports and reviews) and the lead workflow (results/lead/decision/numbers.json), classified by hand. Calibration and positive-control p-values are listed where they bear on a claim.

result nominal p fate
Z340 key letters on Z13, full pin 0.0008 (objective), 0.0105 (word); replication 0.0096-0.0152 per canonical test weaker at every stricter step: family-wise 0.0051 in keyprior, 0.039 over the replication’s 12 tests, 0.144 frequency-free; the Z408 negative control reaches 0.026; not significant at project scale (Šidák over 51 analyses 0.23-0.87); refuted as key reuse by three skeptics; no meaningful completion; a statistical curiosity
Z408 key on Z13, 6-gram statistics (negative control) 0.026, 0.022 the control the Z340 result had to beat, and did not
Z340 key, partial pin E N z M 0.00045 per subset family-wise 0.026 (best statistic), 0.05-0.12 (counts); same curiosity
Z340 key under three distinct circles (TORPEDO) 0.012 (word), 0.002 (objective); replication 0.0057 (top-10 6-gram) same curiosity on a low-plausibility transcription; the TORPEDO content is worth a likelihood ratio of 1.9-3.9 after look-elsewhere; joint chance 0.0051-0.0082, which is 0.23-0.34 over 51 analyses
Z408 key, [ read as the plain upside-down T 0.0085 (objective) Z408 family-wise 0.046; word statistic 0.18; no meaningful completion
suspect names with one allowed slip 0.001 selection artifact: driven by names that entered the list because they had been fitted to Z13; 0 fits once they are excluded
Z32 pair placements (RADIANS + INCHES) 0.02 control pairs (HOUSE + GARDEN 0.03, PEOPLE + TOWN 0.02) do the same; geometry of Z32’s repeats
Z32 held-out English fit under read order cols_tb_rl 0.037 1 of 51 orders; chance expectation
Z32 radian grammar, read order skip19 below 0.001 artifact of the grammar’s own lead words (BOMB…, SET S…)
Z32 radian grammar, one of 8 message forms 0.05 1 of 8 forms; chance
Z32 THREE crib costlier than all nulls robust over 4 seeds solver and pair-geometry artifact; the crib test has no power
Lake Herman Road one radian, 3 inches 0.003-0.09 (face-value precision) 0.01-0.05 (narrow) to 0.12-0.33 (wider, still post-hoc families) at a realistic 0.25-mile tolerance; not on the mailed sheet; the angle was noted before (zodiackillerfacts.com, Hodel, Grinell, DMW)
map claim points near Zodiac sites 0.05 2 of 44 points, one by construction
homophone-likelihood re-ranking gain (calibration) 0.004 a real but small method gain (about 1.9x in rank); singles out no candidate
cross-key vowel/consonant agreement below chance (key construction) about 0.02 not about Z13/Z32; predicts nothing

Appendix B. Main corrections made by the reviewers and the lead workflow

task original corrected
keyprior Z13/Z340 result “not significant after correction” family-wise p 0.0051 (Z340), 0.0102 (both keys); partial-pin family-wise 0.026, not 0.129
keyprior (lead workflow) family-wise 0.0051 read as “an unexplained anomaly” pre-registered replication 0.039 over 12 tests; Z408 negative control 0.026 on the same test; frequency-free 0.144; not significant at project scale; refuted as key reuse by three skeptics
keyprior Z32 partial pins “worse than random” (pMean 0.95-1.00) pseudo-replication; key-level p 0.67-0.93: unremarkable
keyprior arrangement null p 0.0055 0.0028, best of 360 on the anneal objective only; under the replication’s statistics the real arrangement ranks 28th (6-gram), 9th (word) and 29th (top-10)
keyprior (lead workflow) the Z408 key “shows nothing” true for the word statistic only (0.25-0.29); 0.026 and 0.022 on the 6-gram statistics
cyclemodel simple vs Zodiac-size key, 10^3.3-10^3.8 10^2.7-10^3.8 (allocation model)
cyclemodel circle letter “must be rare” most likely E or O with a single symbol
cyclemodel circle posteriors (distinct 0.59-0.91) prior-dependent (same 0.06-0.91); only Bayes factors robust
cyclemodel 13-letter calibration “not significant” pooled n = 28: p = 0.004 (two-sided sign test), top-1 hits 1 to 4
nullmodel 13-letter simple-key recovery 1/12, “solver always beats truth” 4/12 with a 6-gram likelihood objective; the claim holds for the default objective only
nullmodel Z13 word-aligned expected fits 1.1e3 / 253 1.5e3 / 386
nullmodel 6-gram “posteriors” as probabilities unnormalized relative scores
nullmodel short Zodiac-style length-scan points as unicity data degenerate (no repeats); uninformative
z13names 37 persons 36 persons
z13names EDDIE RESENDES within-pattern share 0.93 about 0.58 allowing for unlisted names
z13names circles_distinct top posteriors (e.g. MARILYN STORMS 0.65) 0.28 with exact denominators
z13phrases “20 to 60 equally good” candidates for generic English the truth would rank near the top (median rank 2); the bound does not cover names
z13phrases theme hits 13 16
z13phrases full-vocabulary 3-word estimate 27M +/- 6M at least 1.78M observed; the extrapolation is biased low
z32search “RADIANS became unfavourable” and “read order was seed noise” wrong reasoning; the right reason is that the tests have no power and these levels are ordinary
z32search 10^19-10^20 compatible texts 10^6-10^20 depending on the entropy rate (the nullmodel estimate used in §1 and §3.1 tops out at about 2 x 10^19)
z32search 88 of 88 cribs fit everywhere; 1,065 fluent strings 80 of 88; 1,065 all-dictionary strings, none grammatical
audit Foxon fits with 0 conflicts under some order 2 conflicts on his own order, exactly his declared misspellings; fair null 15.3%
audit fluency rank as evidence against the Z32 proposals not evidence: Zodiac’s own text ranks similarly
audit MARVIN MERRILL incompatible refuted as reported (also 0 of 282,352 grid orders, and 0 of 423,922 2x7 box orders in the prior-art rerun); the audit’s columnar family placed blanks only at the end of the last row, not anywhere; the test has low power (4-9% of random profile-matched names pass)
mapgeometry drawn 0-arm 3.02 +/- 0.07 degrees 1.9-3.2 degrees (freehand stroke)
mapgeometry Lake Herman Road face-value p 0.003-0.09 0.01-0.05 (narrow) to 0.12-0.33 (wider) at a 0.25-mile tolerance; on the mailed sheet 0.92 rad and 2.69-2.75 in
mapgeometry school rates “no excess” uninformative (null not spatially matched)
synthesis draft (prior-art search) map rotation and scale error listed as new known: shaqmeister (forum, 2026-05-12) and others; an independent confirmation only
synthesis draft (lead workflow) the Z340-key result listed as an open anomaly among the new findings a negative result: a statistical curiosity, not key reuse

Appendix C. What was not done, and limits

Runs cut short by machine contention.

Hypotheses not tested.

Model limits.

Prior art.

Process.