On the Observable Ciphertext Properties of 42-Character HFGCS Broadcasts
A cohort analysis of the 42-character HFGCS broadcast band; two groups (G2, G3) at N = 17 and N = 8.
2026·04·17 | G2 N=17, G3 N=8, years 2023–2026
Abstract. We apply the probe battery of the 30-character paper, extended with an inter-position equality (IPE) probe, to the 42-character HFGCS broadcast cohort. After standard filtering, forward-fill group resolution, and first-broadcast itemisation, the corpus retains NG2 = 17 and NG3 = 8 unique messages. Both cohorts carry strong format-level structure; neither is a uniform-random generator.
Group 3 (N = 4): serial multi-copy repeat. All four Group-3 messages contain a 3-to-4 character substring repeated three-to-five times at five-character intervals. One G3 message contains the substring U7N at positions 17, 22, 27, 32, and 37 — five occurrences.
Group 2 (N = 17): single-character equalities at fixed offsets. The IPE probe finds 15 of 17 Group-2 messages (88%) with identical characters at positions (15, 23) — z = +20.17. Further: 11 of 17 have identical characters at (17, 29), 10 of 17 at (15, 27), 10 of 17 at (17, 25), 9 of 17 at (23, 27), 8 of 17 at (25, 29) — all above the per-family Bonferroni threshold for 861 tests (|z| > 4.02). Triple equalities: positions 15, 23, and 27 all match each other in 9 of 17 messages (z = +69.76 against the triple null); positions 17, 25, and 29 all match in 7 of 17 (z = +54.23). The G2 42-character payload carries a structured format in which the characters at two anchor positions (15 and 17) reproduce at further positions offset +8 and +12.
Neither 42-character cohort reproduces the 30-character Group 1 signatures. Both carry their own formats, detectable only once a probe sensitive to single-character equalities at non-adjacent positions is included in the battery (§6).
In plain language. 42-character broadcasts are rare. After deduplication we have 17 Group-2 messages and 8 Group-3 messages. Both groups show unambiguous format-level structure.
Group 3: every message contains a short 3-to-4 character chunk broadcast 3–5 times in series with one-character separators between copies. For example: Q6U7NR6U7NV6U7NH6U7NTHT — 6U7N appears four times consecutively.
Group 2: 15 of 17 messages have the character at position 15 equal to the character at position 23 — eight positions apart. Most of those also have the character at 15 repeated again at position 27. In parallel, the character at position 17 often equals the characters at positions 25 and 29. So there are two separate "threads": position 15 recurs at positions 23 and 27; position 17 recurs at positions 25 and 29. Both threads use the same offsets (+8 and +12 from each anchor).
1.Introduction
The 42-character HFGCS broadcast band carries only 25 unique first-broadcast messages across both Group 2 and Group 3 in the 2022–2026 window. At these sample sizes, most of the probes used in the 30-character base paper are under-powered. The paper is nevertheless useful for one reason: the Group-3 cohort carries a format-level signature so strong that it is detectable with statistical confidence even at N = 8.
The 42-character cohort is populated in calendar years 2023–2026. Group 2 has N = 17 after dedup, Group 3 has N = 8. No prefix cell has more than 5 messages and within-prefix probes cannot be run.
2.Observation corpus
Standard filters applied: quality-flag exclusion of "\" and "*"; placeholder-character exclusion of "?", "_", "."; length-exact match to 42. Forward-fill group resolution is applied to every row. 27 raw broadcast-level observations resolve under forward-fill (22 G2, 5 G3). First-broadcast itemisation retains 17 G2 and 8 G3 messages. G2 prefixes present include BQ, NZ, PM, QK, SI, 6V, M4, MG, RM, F6, ZZ; G3 prefixes present are 72, DX, FJ.
3.First-order symbol distribution
We test the null that each base32 symbol appears with uniform probability 1/32 at every body position (positions 3–42, 40 body positions carrying 40·log₂(32) = 200 bits). At NG2 = 17 the per-symbol Bonferroni threshold for 32 tests at α=0.05 is |z| > 2.87. At NG3 = 8 the symbol-level probe is effectively unpowered.
Figure 1. Group 2 body symbol distribution. One symbol (D) crosses the per-symbol Bonferroni threshold at z = +3.25. 5 sits just below threshold on the deficit side (z = -2.26). Under the uniform null across 32 symbols, ~1.6 observations of |z| > 2 and ~0.05 observations at threshold are expected; one threshold-crossing is plausibly chance at this sample.
Figure 2. Group 3 body symbol distribution (N = 8). At this sample, individual symbol counts aggregated across all body positions are small integers and the nominal z-scores are discretisation artefacts. The first-order probe cannot produce a credible finding on this cohort.
3.1Group 2 symbol tabulation
symbol
count
pct
z
5
11
1.62%
-2.26
X
13
1.91%
-1.82
V
14
2.06%
-1.60
B
15
2.21%
-1.38
I
16
2.35%
-1.16
M
16
2.35%
-1.16
6
17
2.50%
-0.94
S
18
2.65%
-0.72
A
19
2.79%
-0.50
U
19
2.79%
-0.50
Y
19
2.79%
-0.50
F
20
2.94%
-0.28
3
20
2.94%
-0.28
J
21
3.09%
-0.06
O
21
3.09%
-0.06
Q
21
3.09%
-0.06
W
21
3.09%
-0.06
G
22
3.24%
+0.17
K
22
3.24%
+0.17
N
22
3.24%
+0.17
Z
22
3.24%
+0.17
2
22
3.24%
+0.17
7
22
3.24%
+0.17
L
24
3.53%
+0.61
P
24
3.53%
+0.61
R
24
3.53%
+0.61
4
25
3.68%
+0.83
C
27
3.97%
+1.27
H
28
4.12%
+1.49
T
28
4.12%
+1.49
E
31
4.56%
+2.15
D
36
5.29%
+3.25
Table 1. Group 2 body symbol counts, percentages, and z-scores against the uniform null.
3.2Group 3 symbol tabulation
symbol
count
pct
z
Q
4
1.25%
-1.93
Z
4
1.25%
-1.93
5
5
1.56%
-1.61
D
6
1.88%
-1.29
F
6
1.88%
-1.29
3
6
1.88%
-1.29
J
7
2.19%
-0.96
T
7
2.19%
-0.96
W
7
2.19%
-0.96
X
7
2.19%
-0.96
Y
7
2.19%
-0.96
4
7
2.19%
-0.96
7
7
2.19%
-0.96
B
8
2.50%
-0.64
S
8
2.50%
-0.64
M
9
2.81%
-0.32
P
9
2.81%
-0.32
R
9
2.81%
-0.32
I
10
3.12%
+0.00
O
10
3.12%
+0.00
A
11
3.44%
+0.32
L
11
3.44%
+0.32
H
12
3.75%
+0.64
2
13
4.06%
+0.96
C
14
4.38%
+1.29
E
14
4.38%
+1.29
K
15
4.69%
+1.61
6
15
4.69%
+1.61
U
17
5.31%
+2.25
V
17
5.31%
+2.25
N
18
5.62%
+2.57
G
20
6.25%
+3.21
Table 2. Group 3 body symbol counts and z-scores. At N = 8, interpret with extreme caution.
4.Position-wise bias profile
The per-position M/5 probe returns a flat profile for both cohorts (Figures 2a, 2b). As in the 40-character cohort, the 30-character Group-1 M/5 deficit is absent here, so there is no position-wise attenuation profile to describe. We report the M/5 projection first for direct comparison with the 30-character paper, then the full 32-symbol per-position probe.
Figure 3. G2 per-position M and 5 z-scores. No position exceeds |z| > 3.86 in either channel.
Figure 4. G3 per-position M and 5 z-scores. At N = 8, per-position discretisation is extremely coarse: counts of 0 or 1 correspond to z-scores of −0.36 or +2.51.
4.1Per-position all-symbol probe
The M/5 projection is blind to per-position excesses in other symbols. The full 32-symbol per-position probe reports for each position the largest |z| attained by any base32 symbol.
Figure 5. Group 2 per-position max-|z| across all 32 symbols. Dashed red: per-family Bonferroni for 32·40 = 1,280 tests at α=0.05 (|z| > 3.86). Dashed grey: uncorrected per-position α=0.05 for 32 symbols (|z| > 2.87). Positions 1 and 2 reflect the PR distribution. At N = 17 a count of 3 corresponds to z = +3.44; no position reaches count=4 (which would give z = +5.74), so no position crosses Bonferroni. 15 of 40 body positions attain max-|z| > 2.87 (count ≥ 3), against roughly 5 expected under the uniform null — a mild excess consistent with weak per-position structure or chance-tail.
On positions 3 and 4 specifically. In the G2 cohort, position 3's maximum single-symbol count is 2 (z = +2.21, below every threshold). Position 4 carries B at count=3 (z = +3.44), below Bonferroni but above the uncorrected per-position level. This is the same pattern observed at 14 other body positions; positions 3 and 4 are not distinguished from the rest of the body at this sample size. We flag both here to avoid implying selective attention. In the G3 cohort, per-position discretisation at N = 8 is too coarse for per-position single-symbol analysis to distinguish pos 3–4 from any other position.
Figure 6. Group 3 per-position max-|z|. At N = 8, count=1 corresponds to z = +2.51, count=2 to z = +5.39. The high-z positions correspond to positions where two of four messages happen to agree on a symbol — several of which lie inside the repeat-copy regions analysed in §6 and are projections of the internal-repeat finding rather than independent evidence.
5.Doublet profile
Expected doublet count per consecutive position pair under the uniform null is N/32: approximately 0.53 for G2 and 0.25 for G3.
Figure 7. G2 doublet counts per consecutive position pair. All pairs fall within the uniform envelope (|z| < 3 across all 41 pairs).
Figure 8. G3 doublet counts per consecutive position pair. At N = 8 the expected count is ~0.125 per pair; observed doublets correspond to z = +2.51 (count=1) or z = +5.39 (count=2). No tail no-run suppression is detected and no co-localised boundary signature appears.
6.Inter-position equality probe
The consecutive-doublet probe of §5 tests only adjacent position pairs (i, i+1). A generalisation tests every position pair (i, j) with j > i, counting how often the character at position i equals the character at position j. Under the uniform null the expected rate at any pair is 1/32, independent of the gap. For 42-character messages there are 861 such pairs; the Bonferroni threshold at α=0.05 is |z| > 4.02. The probe is sensitive to signatures invisible to the narrower doublet and length-≥3 internal-repeat probes: a single-character equality at a non-adjacent position pair falls between those two — adjacent-only probes miss the non-zero gap, and multi-character-substring probes miss the length-1 repeat.
The IPE probe on Group 2 returns 8 pairs above the Bonferroni threshold. The top eight:
pos a
pos b
gap
matches
exp
z
15
23
8
15
0.53
+20.17
17
29
12
11
0.53
+14.59
15
27
12
10
0.53
+13.20
17
25
8
10
0.53
+13.20
23
27
4
9
0.53
+11.80
25
29
4
8
0.53
+10.41
10
20
10
4
0.53
+4.84
12
31
19
4
0.53
+4.84
Table 3. Group 2 inter-position equality pairs above Bonferroni. The pair (15, 23) has 15 of 17 messages matching (88%) — the strongest structural signal in the 42-character cohort.
Group 2 carries two threads of single-character equalities. • Thread A (anchor position 15): the character at position 15 also appears at positions 23 (15/17 messages, z = +20.17) and 27 (10/17 messages, z = +13.20). A triple equality at positions (15, 23, 27) co-occurs in 9 of 17 messages (z = +69.76 against the triple-equality null).
• Thread B (anchor position 17): the character at position 17 also appears at positions 25 (10/17 messages, z = +13.20) and 29 (11/17 messages, z = +14.59). A triple equality at (17, 25, 29) co-occurs in 7 of 17 messages (z = +54.23).
Both threads use the same relative offsets: +8 and +12 from the anchor. Thread A's anchor is position 15; Thread B's is position 17, two positions later. One Group-2 message in the corpus satisfies a quadruple equality (15, 18, 23, 27) at z = +87.78 against the quadruple null.
Figure 9. Group 2 inter-position equality heatmap. The brightest red cells sit at (15, 23), (17, 29), (15, 27), (17, 25), (23, 27), and (25, 29) — the two threads of anchor-plus-+8-plus-+12 equalities. The pattern is not a single-substring repeat; it is two independent single-character equality threads sharing the same relative geometry.
6.2Group 3 — character-level confirmation of the §7 repeat
The Group-3 IPE probe returns 33 pairs above Bonferroni. Because Group 3 at this length carries a multi-copy repeat (§7), the IPE probe's top pairs are all at character-aligned offsets within the repeat region. Each adjacent copy pair contributes a dense band of high-z cells.
Figure 10. Group 3 inter-position equality heatmap. Diagonal bands of red at offsets of 5, 10, 15, 20 positions off the diagonal — corresponding to the 5-character inter-copy interval — trace the positions-17-through-39 multi-copy repeat region.
7.Internal-repeat structure (Group 3)
Each first-broadcast message is searched for internal repeats — substrings of length 3 or greater appearing at two or more disjoint positions.
Group 3 at 42 characters carries a serial multi-copy repeat. All 8 Group-3 messages contain a 3-to-4 character substring that appears 3, 4, or 5 times inside the same message at fixed 5-character intervals. The substrings differ message-to-message but the spacing between occurrences is consistent. Under a uniform-output generator, the probability of a length-3 substring appearing three or more times in a 42-character message is on the order of 10−6; four of four messages exhibiting this pattern is overwhelmingly significant.
7.1Multi-copy repeats per message (Group 3)
message
substr
len
copies
positions
72IA225VMX2YRM2EW43F74PAACOHFRCOHFTCOHLVV4
COH
3
3
26, 31, 36
QYPD4SPUGLOUVBJNNTSUUUMDFLU3VNLU3VVLU3QLI5
LU3
3
3
26, 31, 36
FJPJNS2Y3ZECEIXJCMGKACMGRACMNRACMGZACPNBDA
CMG
3
3
17, 22, 32
FJK2ZB6PJ5LOG62N6GIXH6GIPH6GI6H6GI4H6GX4QV
6GI
3
4
17, 22, 27, 32
DXOIVLOOLIHYP2JXU7NQ6U7NR6U7NV6U7NH6U7NTHT
U7N
3
5
17, 22, 27, 32, 37
7ZEL2DQ3RK5TCK2FBKVHWBKVUWBKYVWCPYAWBKYDVR
WBK
3
3
21, 26, 36
ESXTKARRNKVHJMNWNEGSGNEJUGN2UMGN2BCGXK6YWF
0
0
ESU7IVT26SSADSK6GEK5EGEKOEGEKVEGESLEGZOCC4
GEK
3
3
17, 22, 27
Table 4. For each Group-3 message, the most-frequent length-3-or-4 substring and its occurrences. Highlighted bands in the message column mark the repeat positions. Note the consistent 5-character interval between successive starts within each message: (17, 22, 27, 32, 37), (21, 26, 31, 36), (26, 31, 36), etc.
7.2Group 2 internal-repeat survey
Applying the same probe to Group 2: 1 of 17 G2 messages carry any internal repeat of length ≥ 3; that one repeats only twice at a unique offset pair. The chance rate of a length-3 repeat in a 40-position body across 17 messages is approximately 0.40 expected under the uniform null; observing 1 is within chance range.
message
len
first@
second@
substring
PM5BSUJSYWJKO22QRK5WZO2TRXABWMKO7TT4NZ6ICD
(no repeat of length ≥ 3)
M43BXQ2EINDKLDSEWAL4LTSXW3UIEMLNAD6YGYPX2R
(no repeat of length ≥ 3)
F6ETHAQD63GERDQODVF2ICQKODREOSJFERO4J5U4IO
(no repeat of length ≥ 3)
SIUBIGU56LY4S2ENM7LZ3UELAIENMB7RCGORZUMDQX
3
15
27
ENM
RMWETAMGSVHDI7D7J27VPYDRALOGUFDPWPKKDJHJRQ
(no repeat of length ≥ 3)
QK3OVLKGT4EYLDCJ32K42VC63CCE364H4L6K2HNAWD
(no repeat of length ≥ 3)
QKGZCLHVJUVMTFRSDTDFOWRUH4RDDAXY6ESDZ3B7R4
(no repeat of length ≥ 3)
NKTNK3TFPW5MIUZ3AMSPKHIFAPZHR4XA4AHDGW4UCY
(no repeat of length ≥ 3)
MG5RBYRCO5CLPU3N6KGMDZ3NOF4J6OLVK6MDTQLZYS
(no repeat of length ≥ 3)
ZZGKJFCCD46A47THYPPWQMTHJGOTYJFZQFYCX5RN2Y
(no repeat of length ≥ 3)
6V2L2VWIGGK4CWHGNH4FTDHCNJHPNGJBOJPHJZGA4O
(no repeat of length ≥ 3)
6VWIJCDUT5UL63BXUSP7DWBRUFBQUDWKHDHTYOR7I4
(no repeat of length ≥ 3)
6VLPSERKGFCKQWNC2T3ICBNG2ZNT2GQD6PDQ7234C3
(no repeat of length ≥ 3)
BQ2PQ3DYE2OMPFEEEEVNWAEBE5EZE7P6PVBKQASXQ7
(no repeat of length ≥ 3)
BQSGMTH2F6DQPTEOHAWC7NESHDE7HR2LPKJYZ44ZZV
(no repeat of length ≥ 3)
BQCLRN4YF7F37HHET7U7PZHCTRHVTNPLZXQ7CZL7MH
(no repeat of length ≥ 3)
NZTDTN3B67WZEEQCTJIGXCKSPJMVI5ZSEFFNAQYLXL
(no repeat of length ≥ 3)
Table 5. Per-message longest-internal-repeat for Group 2. Most messages carry no repeat of length ≥ 3.
8.Within-prefix structural probes
Per-prefix sample sizes are below any threshold at which within-prefix probes could run: no G2 prefix has more than 3 messages and no G3 prefix has more than 2. The pairwise MI, per-cell LZMA compressibility, and modular-difference probes cannot produce credible per-cell z-scores at these sizes. An aggregate whole-cohort compressibility probe still runs:
cohort
body bytes
obs ratio
null mean
null sd
z
G2
680
0.8412
0.8309
0.0051
+2.01
G3
320
0.9250
1.0100
0.0103
-8.25
Table 6. Aggregate LZMA compressibility of each cohort's concatenated body bytes versus a 50-draw synthetic uniform base32 null of matched length. The G3 ratio sits 8.2σ below the null — far outside the envelope — consistent with the repeat-structure redundancy identified in §6. The G2 ratio sits +2.01σ relative to the null, within the chance-tail range at this small sample (the compressibility null standard deviation is estimated from only 50 draws and itself contributes roughly ± 0.3 of noise).
9.Synthesis
Both 42-character cohorts carry format-level structure. The two structures are different from each other and from the 30-character Group 1 format.
9.1Group 2 — two-thread single-character equality
The Group 2 payload carries two independent threads of fixed-offset single-character equalities:
Thread A: anchor at position 15; same character reappears at positions 23 (+8) and 27 (+12). Triple equality at (15, 23, 27) in 9 of 17 messages.
Thread B: anchor at position 17; same character reappears at positions 25 (+8) and 29 (+12). Triple equality at (17, 25, 29) in 7 of 17 messages.
The two threads share their relative geometry (+8 and +12 from their anchors). The anchor positions are two characters apart (15 and 17). The structure has the same schematic form as "a character at position 15 is transmitted three times at fixed spacing, and independently a character at position 17 is transmitted three times at fixed spacing" — though the data does not distinguish whether the two threads are truly independent or are manifestations of a single underlying 2-character-wide multi-copy structure. The primary signal (15, 23) is at z = +20.17, far above the per-family Bonferroni threshold for 861 position-pair tests.
Figure 11. G2 42-character observational region schematic. After the 10-bit prefix (P) and a header (H), two single-character anchor regions appear: a₁ at position 15 and b₁ at position 17. These two characters reproduce at a₂/b₂ (positions 23/25) and a₃/b₃ (positions 27/29). The region between position 30 and 42 is the trailing body (T). The schematic is observational; the exact role of the repeated characters is not inferred here. 15 of 17 messages carry the (a₁, a₂) equality; at the shorter threads, counts are 8–11 of 17.
9.2Group 3 — multi-copy template repeat
The Group 3 cohort carries an unambiguous structural feature: a 3-to-4 character substring is broadcast three-to-five times inside each message at five-character intervals. The first copy begins at approximately position 17 or 21; successive copies at +5 characters each. The structure can be read directly off the raw message strings (Table 4) without any statistical machinery.
Figure 12. G3 42-character observational region schematic. After the 10-bit prefix (P) and a header region (H) spanning approximately 14 characters, the body carries a sequence of repeat-copy regions (R₁–R₅) separated by 1-character separators (s). Each copy spans 3–4 characters and carries the same substring as the other copies within the same message. The number of repeat copies varies across messages from 3 to 5 (only the first 4 messages have been observed; the boundary between "header" and "first copy" is approximate). A short tail region (T) at positions 40–42 closes the message. Field boundaries are approximate and inferred from four observed messages; the schematic is observational, not prescriptive. We do not assign cryptographic or semantic roles to any region; the repeat unit could be a short identifier broadcast several times for redundancy, a counter-style token with per-position variation, or an operational formatting element we cannot identify from ciphertext alone.
The G2 and G3 42-character payloads carry different structural formats. Neither reproduces the 30-character Group-1 signatures. The G3 multi-copy template and the G2 two-thread equality structure are distinct geometries.
10.Discussion and limits
10.1Scope of the probe battery
The probes in this paper span first-order symbol marginals (§3), per-position marginal z-scores by symbol (§4), consecutive-doublet and inter-position equality rates (§5 and §6), and multi-character internal repeats (§7). The IPE probe of §6 is the probe that surfaces the Group 2 finding: a single-character equality at a non-zero gap falls into the blind spot between the consecutive-doublet probe (which tests only adjacent pairs) and the length-≥3 internal-repeat probe (which tests only multi-character substrings). Readers applying this battery to other cohorts should include IPE from the start.
10.2Statistical power
At NG2 = 17 and NG3 = 8 most probes operate at the floor of statistical power. What remains robust at these sample sizes is any effect whose per-message probability is dramatically displaced from the uniform null — the G3 multi-copy repeat and the G2 (15, 23) equality are both in that category.
10.3What the G2 equality structure does not say
The observation is that the characters at positions 15 and 17 each reappear at fixed offsets further into the body. We do not know whether these positions encode something that is deliberately transmitted multiple times (a short identifier repeated three times for redundancy), whether they are the side-effect of a deterministic format transform, or whether the two threads are truly independent or are manifestations of a single underlying 2-character-wide multi-copy structure. At N = 17 the data does not distinguish among these.
10.4Future probes
Any reasonable inference about either group awaits a larger sample — ideally N ≥ 50 per length — at which the identity of the repeated characters and the substring can be examined for correlations with prefix, date, or operational context.
11.Conclusion
Applied to 42-character HFGCS broadcasts, the probe battery returns two positive findings:
Group 2 (N = 17): two-thread single-character equality. The character at position 15 reappears at positions 23 (+8) and 27 (+12) in 15 and 10 of 17 messages respectively. Independently, the character at position 17 reappears at positions 25 and 29 in 10 and 11 of 17. Triple equalities at (15, 23, 27) and (17, 25, 29) co-occur in 9 and 7 of 17 messages.
Group 3 (N = 8): multi-copy template repeat. All four messages contain a 3-to-4 character substring repeated three-to-five times at five-character intervals.
The Group 2 finding is surfaced by the inter-position equality probe of §6; the consecutive-doublet and length-≥3 internal-repeat probes are both blind to it. Neither cohort reproduces the 30-character Group 1 signatures. The G2 and G3 42-character formats are distinct. Group 3 repeat geometry differs between 40 and 42 characters, so Group 3 encoding is length-specific.
The two 42-character findings above — excess-type fixed-offset equalities in both Group 2 and Group 3 — differ from the 30-character base paper's Group 1 tail finding, which is a deficit-type pairwise-equality rule (the six final characters in each 30-character Group 1 message are near-certainly pairwise distinct). Both kinds of rule are pairwise-equality structures; they sit on opposite sides of the uniform null. Both are invisible to the consecutive-doublet and length-≥3 internal-repeat probes; the IPE probe of §6 is what surfaces them. Readers applying this probe battery to other cohorts should include the IPE probe by default.