On the Observable Ciphertext Properties of 34-Character HFGCS Broadcasts
A cohort analysis of the 34-character HFGCS broadcast band; one cohort (G2) at N = 146.
2026·04·17 | G2 N=146, years 2022–2024
Abstract. We apply the probe battery of the 30-character format analysis, extended with an inter-position equality (IPE) probe, to the 34-character HFGCS broadcast cohort. After standard filtering, forward-fill group resolution, and first-broadcast itemisation, the corpus retains N = 146 unique messages. The 34-character band is populated entirely by Group 2 broadcasts (no G1 or G3 messages at this length resolve under forward-fill); the paper therefore covers a single cohort.
The first-order probe returns a reproducible but mild M/5 deficit: M is under-represented at aggregate z = -4.46 and 5 at z = -3.78, both crossing the per-symbol Bonferroni threshold for 32 tests at α=0.05 (|z| > 3.16) but roughly a factor of five weaker than the 30-character Group 1 signal (where each symbol sits near z = −21). The deficit is spread roughly evenly across body positions 3–34: no position shows a per-position z for either symbol that exceeds the corrected threshold, and no attenuation region analogous to the 30-character positions-19–21 boundary is visible.
The remaining probes return null results at this sample size. The consecutive-doublet rate is within the uniform envelope across all 33 position pairs, including the tail region — no trailing no-duplicate rule like the 30-character Group 1 finding. The inter-position equality probe returns 0 Bonferroni-crossing pairs out of 561 tested: the strongest signal is 12 matches at pair (4, 7) against an expected 4.56 (z = +3.54), just below the corrected threshold. The internal-repeat probe finds only 1 of 146 messages with any length-≥3 substring coincidence. Compressibility matches the synthetic-uniform null (z = +0.42). Within-prefix probes cannot be run: the most populous prefix cell has 16 messages, well below the N ≥ 50 threshold needed for credible per-cell z-scores.
The 34-character Group 2 payload therefore carries a weaker analogue of the 30-character Group 1 symbol-level deficit and none of the structural signatures present in the 40-character or 42-character Group 2 cohorts. Its profile is closer to "uniform output plus a mild per-symbol bias" than to the template-repeat formats observed at 40 and 42 characters.
In plain language. The entire 34-character HFGCS broadcast corpus belongs to Group 2; there are no Group 1 or Group 3 broadcasts at this length. After deduplication we have 146 unique messages — enough to run the standard tests properly, though not enough to detect very subtle patterns.
Two characters — the letter M and the digit 5 — are mildly less common than they should be, showing up about 85–90% as often as expected. The shortage is qualitatively the same signature as the 30-character Group 1 cohort reports (see the 30-character paper), but at roughly one-fifth the strength. No other character deviates from expectation by enough to count as a real finding.
Beyond that mild symbol bias, the 34-character cohort looks approximately random on every other test applied: no mid-body transition, no tail constraint, no repeated substrings, no matched-character-at-two-positions pattern. The inter-position equality probe returns no statistically significant pair at this sample size.
1.Introduction
The 34-character HFGCS broadcast band holds N = 146 unique first-broadcast messages across the 2022–2026 observation window after filtering and deduplication, all of which resolve to Group 2 under forward-fill on the PR_GROUPS reference table. No Group 1 or Group 3 broadcasts of this length appear in the corpus; the paper covers a single cohort.
We apply the probe battery established for the 30-character paper (the base paper in this project), extended with an inter-position equality (IPE) probe: first-order symbol marginals, per-position marginal z-scores by symbol, consecutive-character doublet rates, inter-position equalities at every pair of positions, length-≥3 internal-substring repeats, aggregate compressibility, and (where per-prefix N ≥ 50) within-prefix probes.
2.Observation corpus
Standard filters: quality-flag exclusion of "\" and "*"; placeholder-character exclusion of "?", "_", "."; length-exact match to 34. Forward-fill group resolution is applied to every row. 241 raw broadcast-level observations remain, all resolving to Group 2 under forward-fill. First-broadcast itemisation on the message string retains 146 unique messages.
The cohort spans calendar years 2022–2024. Prefix identities in the retained set include DC (16 messages), F6 (10), IE (9), 6V (9), EG (8), PM (7), T5 (7), SI (7), QK (6), BQ (6), and a long tail of smaller prefixes. No prefix exceeds the N ≥ 50 threshold used by the 30-character paper's within-prefix probes; §8 reports this and skips the per-prefix scans.
3.First-order symbol distribution
We test the null that each base32 symbol appears with uniform probability 1/32 at every body position (positions 3–34, carrying 32·log₂(32) = 160 bits). Aggregate body-position counts are plotted in Figure 1 and tabulated in Table 1.
Figure 1. Empirical frequency of each base32 symbol across body positions 3–34 of the 34-character Group 2 first-broadcast cohort (N = 146). Dashed line: uniform expectation 1/32 ≈ 3.125%. Two symbols cross the per-symbol Bonferroni threshold for 32 tests at α=0.05 (|z| > 3.16) on the deficit side: M at z = -4.46 and 5 at z = -3.78. No other symbol crosses the threshold; the largest excess is E at z = +2.94. The M/5 deficit reproduces the signature of the 30-character Group 1 cohort (where the corresponding z-scores are −21.2 and −20.9) at roughly one-fifth the magnitude.
symbol
count
pct
z
M
93
1.99%
-4.46
5
101
2.16%
-3.78
A
129
2.76%
-1.43
V
133
2.85%
-1.09
J
134
2.87%
-1.01
4
134
2.87%
-1.01
D
136
2.91%
-0.84
Q
137
2.93%
-0.76
6
137
2.93%
-0.76
P
140
3.00%
-0.50
C
141
3.02%
-0.42
T
141
3.02%
-0.42
3
142
3.04%
-0.34
H
147
3.15%
+0.08
R
147
3.15%
+0.08
Y
148
3.17%
+0.17
I
150
3.21%
+0.34
7
150
3.21%
+0.34
G
151
3.23%
+0.42
K
151
3.23%
+0.42
L
152
3.25%
+0.50
2
153
3.27%
+0.59
X
155
3.32%
+0.76
Z
156
3.34%
+0.84
O
158
3.38%
+1.01
N
159
3.40%
+1.09
U
161
3.45%
+1.26
W
161
3.45%
+1.26
S
162
3.47%
+1.35
B
166
3.55%
+1.68
F
166
3.55%
+1.68
E
181
3.87%
+2.94
Table 1. G2 body (positions 3–34) symbol counts, percentages, and Poisson z-scores against the uniform null. Rows sorted by z-score. M and 5 cross the per-symbol Bonferroni threshold; all other symbols fall within the noise envelope.
4.Position-wise bias profile
The per-position M/5 probe from the 30-character paper tracks Poisson z-scores for those two symbols at each body position. At N = 146 with per-position expectation 4.56, per-position z-scores are discretised to roughly −2.2, −1.2, −0.3, +0.7, +1.6, +2.6, +3.5 at counts 0, 1, 2, 3, 4, 5, 6.
Figure 2. Per-position Poisson z-scores for symbols M and 5 across the 34-character Group 2 first-broadcast cohort. Solid horizontal line: uniform expectation (z = 0). Dashed red line: per-family Bonferroni threshold for 2·32 = 64 tests at α=0.05 (|z| > 2.94). Positions 1 and 2 reflect the PR distribution — Group 2 prefixes disproportionately place certain symbols in the prefix positions. Across body positions 3–34, both M and 5 carry mild negative z-scores consistent with a per-position deficit of roughly 0.5–1σ, distributed evenly with no position crossing the corrected threshold. No attenuation region analogous to the 30-character Group 1 positions-19–21 boundary is visible.
4.1Per-position all-symbol probe
The M/5 projection reports only two channels of a 32-channel probe. The full scan reports, for each body position, the largest |z|-score attained by any of the 32 symbols at that position.
Figure 3. Per-position max-|z| across all 32 symbols in the 34-character Group 2 cohort. Dashed red line: per-family Bonferroni threshold for 32·32 = 1,024 body-cell tests at α=0.05 (|z| > 4.06). Dashed grey: uncorrected per-position α=0.05 for 32 symbols (|z| > 2.87). No body position crosses the Bonferroni threshold. 5 body positions attain max-|z| > 2.87 (notably position 3 with R at count 12, z = +3.54, and positions 8, 14, 27, 32 at z = +3.06 each), against the 1.6 expected under the uniform null — an excess consistent with weak per-position preferences or chance-tail at this sample.
5.Doublet profile
We test the rate of consecutive-character doublets at each of the 33 position pairs (i, i+1). Under the uniform null the probability is 1/32 at each pair, so the expected doublet count is N/32 ≈ 4.56.
Figure 4. Doublet count per consecutive position pair in the 34-character Group 2 cohort. Dashed line: uniform expectation. Position pair (1–2) carries the prefix-distribution signature. All body-position pairs (2–3 through 33–34) fall within the uniform envelope (|z| < 3 across every pair). The final five pairs (29–30 through 33–34), which in the 30-character Group 1 cohort carry the 15-fold doublet suppression, show no suppression here; their counts sit between 3 and 7 against the expected 4.6, with z-scores within the noise envelope.
6.Inter-position equality probe
The consecutive-doublet probe of §5 tests only adjacent position pairs. Its generalisation tests every position pair (i, j) with j > i — including non-adjacent pairs — for character equality. At 34 characters there are 34·33/2 = 561 such tests; the per-family Bonferroni threshold at α=0.05 is |z| > 3.92. Under the uniform null the expected match count at each pair is N/32 = 4.56.
The probe returns 0 pairs above the Bonferroni threshold. The ten strongest positive pairs are reported in Table 2.
pos a
pos b
gap
matches
exp
z
4
7
3
12
4.56
+3.54
11
14
3
12
4.56
+3.54
13
16
3
12
4.56
+3.54
18
26
8
11
4.56
+3.06
23
31
8
11
4.56
+3.06
19
26
7
10
4.56
+2.59
1
9
8
9
4.56
+2.11
4
5
1
9
4.56
+2.11
4
19
15
9
4.56
+2.11
5
17
12
9
4.56
+2.11
Table 2. Top ten inter-position equality pairs in the 34-character Group 2 cohort, by z-score. Expected count per pair: 4.56. The strongest pair is (4, 7) with 12 matches at z = +3.54, just short of the per-family Bonferroni threshold 3.92. No pair crosses the threshold. Three pairs — (4, 7), (11, 14), (13, 16) — happen to share a gap of 3 characters, but each is individually sub-threshold and the clustering does not reach combined significance.
Figure 5. Inter-position equality z-score heatmap across all 561 position pairs (i, j) for the 34-character Group 2 cohort. Red cells: excess (pair carries more matches than expected under uniform); blue cells: deficit; pale cream: within the chance envelope. The matrix is visually dominated by the chance-envelope cream, with sub-threshold red speckles distributed across the body. No concentrated signature of the kind observed in the 40-character or 42-character Group 2 cohorts (both of which showed individual cells at z > 20) appears here.
7.Internal-repeat structure
Applying the longest-internal-repeat probe — find the longest substring of length 3–10 that appears at two disjoint positions within each message — to the 34-character Group 2 cohort: 1 of 146 messages carry any repeat of length ≥ 3. The chance rate under the uniform null is approximately 2.21 messages expected, so the observed count is within the chance range. No common offset pair dominates; the probe returns no structural signature.
8.Within-prefix structural probes
The 30-character paper reports three within-prefix probes — pairwise positional mutual information, LZMA compressibility, and modular-difference structure across date-ordered consecutive messages — each requiring N ≥ 50 per prefix cell for credible z-scores. The 34-character cohort has no such cell: the most populous prefix (DC) carries 16 messages, followed by F6 at 10. Per-prefix probes are skipped.
An aggregate whole-cohort compressibility probe still runs:
body bytes
obs ratio
null mean
null sd
z
4672
0.6738
0.6735
0.0007
+0.42
Table 3. Aggregate LZMA compressibility of the body (positions 3–34) of the 34-character Group 2 cohort versus a 50-draw synthetic uniform base32 null of matched length. The observed ratio sits +0.42σ from the null mean — within the chance envelope.
9.Synthesis
The 34-character Group 2 cohort carries a single positive finding. The probe battery returns a mild aggregate M/5 symbol deficit at z = -4.46 and -3.78, crossing the per-symbol Bonferroni threshold for 32 tests. Every other probe returns a null: the per-position all-symbol profile is flat (no Bonferroni-crossing cells), the doublet rate is within the uniform envelope across all 33 adjacent pairs including the tail, the inter-position equality heatmap is mostly empty of significant signal (no Bonferroni-crossing pairs), and the internal-repeat probe finds only a chance-rate number of length-≥3 coincidences.
Figure 6. 34-character Group 2 observational region schematic. The 170-bit payload comprises the standard 10-bit prefix field (P, positions 1–2, carrying the PR) followed by a single 160-bit body region (B, positions 3–34) within which no internal structural boundary is detected. The body carries a mild M/5 per-symbol deficit spread roughly evenly across positions, but no positional transitions, no doublet suppression, no fixed-offset equality structure, and no internal-substring repeats. The schematic is intentionally minimal.
9.1Relationship to the 30-character base case
The 30-character base-case analysis (see the 30-character paper) identifies three structural signatures in its Group 1 cohort — a strong M/5 marginal deficit (z ≈ −21), a mid-body positional transition at positions 19–21, and a near-deterministic pairwise no-duplicate rule on the final six characters (positions 25–30). None of the positional or pairwise-equality signatures reproduces in the 34-character Group 2 cohort, and the M/5 deficit reproduces in the same qualitative direction (both symbols under-represented) but at roughly one-fifth the magnitude. The 30-character Group 2 cohort, for comparison, also carries a mild M/5 deficit of similar strength (z ≈ −3) with no positional or pairwise-equality structure; the 34-character Group 2 profile is therefore closer in character to the 30-character Group 2 profile than to the 30-character Group 1 profile.
10.Conclusion
The 34-character HFGCS broadcast band is populated entirely by Group 2 traffic at N = 146 unique messages. The probe battery returns a single positive finding: a mild M/5 symbol deficit (z = -4.46 and -3.78, each crossing the per-symbol Bonferroni threshold but roughly one-fifth the strength of the 30-character Group 1 signal). No positional transitions, no doublet suppression, no inter-position equality structure, and no internal repeats are detected. The 34-character Group 2 format is consistent with "uniform output plus a weak per-symbol bias" — no more, no less.