Date: 20 September 2026.
Result: the shortage survives exact rune-frequency conditioning in every substantial section. There are 86 identical neighboring pairs, compared with an analytic random-order expectation of 445.14. This is 80.68% fewer than that reference predicts. A separate, approximate comparison does not establish different suppression strengths between sections. No cipher or plaintext is identified.
This is a refinement, not discovery of a new anomaly. Sessions 4 and 5 already established the shortage with inventory-preserving comparisons; Session 25 described its distance and boundary behavior. Here we calculate the exact section-inventory expectation and variance, use a larger bounded shuffle comparison, and assess section variation while accounting for uncertainty in the pooled suppression rate.
Scope and comparison
The same eight substantial sections contain 12,947 runes and 12,939 eligible neighboring pairs. Section IDs are the existing transcription indices: 0, 1, 2, 4, 5, 6, 7 and 8. The nine-rune segment, index 3, and cross-section edges are excluded.
For each section, randomly reorder its runes while preserving the exact count of every rune. Repeat 9,999 times, independently by section, using seed 3301029. This destroys order while retaining composition. It does not preserve word content, per-page frequencies or bigram counts; earlier page-fragment shuffles supplied a complementary, more local comparison.
“Neighbor” means consecutive runes after ignoring non-rune material. It can cross a word boundary, page break or numerical block within a section. This is not a claim about two glyphs being physically adjacent in the image.
If a section has N runes and rune a occurs n_a times, each adjacent pair matches with probability sum[n_a(n_a−1)] / [N(N−1)]. Multiplying by its N−1 pairs gives:
Expected repeats = sum[n_a(n_a−1)] / N.
This expectation accounts for sampling without replacement and does not assume uniform rune frequencies. An exact variance calculation also accounts for overlapping neighboring pairs. Five small inventories were checked by exhaustively enumerating their distinct orders; both moments agreed in every case.
Results by section
| Section | Runes | Actual repeats | Random-order expectation | Actual / expected |
|---|---|---|---|---|
| 0 | 729 | 4 | 24.81 | 16.1% |
| 1 | 1,145 | 6 | 39.62 | 15.1% |
| 2 | 1,729 | 9 | 59.55 | 15.1% |
| 4 | 1,894 | 10 | 65.30 | 15.3% |
| 5 | 1,021 | 11 | 34.96 | 31.5% |
| 6 | 1,524 | 13 | 52.11 | 24.9% |
| 7 | 1,589 | 12 | 54.55 | 22.0% |
| 8 | 3,316 | 21 | 114.24 | 18.4% |
| Total | 12,947 | 86 | 445.14 | 19.3% |
The summed random-order distribution has an analytic standard deviation of 20.72 repeats. The simulations give a mean of 445.02 and a central 95% range of 404–487. Their smallest total is 366, still far above 86.
No simulated total, and no individual section's simulated count, was as low as its actual count. With the standard plus-one Monte Carlo calculation, the lower-tail comparison is 0.0001, the resolution of 9,999 trials. For each of the eight section comparisons, a Bonferroni adjustment gives 0.0008. These values describe the specified random-order model. They are neither a probability that a cipher theory is correct nor estimates of an impossibly small exact tail from a normal approximation.
The 19.3% ratio compares observed ciphertext to shuffled ciphertext. It does not mean that an encoder deleted or altered 80.7% of plaintext doubles. No plaintext is available to support that interpretation.
Do sections need different suppression strengths?
Section 5 retains about 31.5% of its shuffle expectation, while sections 1 and 2 retain about 15.1%. That apparent twofold difference must be judged against the small event counts.
For this separate question, use a deliberately approximate model: section repeat counts are independent Poisson counts with means equal to a common multiplier times their frequency-adjusted expectations. Conditioning on the total of 86 removes the fitted multiplier. It allocates those 86 events between sections in proportion to their shuffle expectations.
This model produces the following expected allocation:
| Section | Actual | Expected with a common multiplier |
|---|---|---|
| 0 | 4 | 4.79 |
| 1 | 6 | 7.65 |
| 2 | 9 | 11.50 |
| 4 | 10 | 12.62 |
| 5 | 11 | 6.75 |
| 6 | 13 | 10.07 |
| 7 | 12 | 10.54 |
| 8 | 21 | 22.07 |
The Pearson discrepancy is 5.354. In 99,999 conditional allocations, 62,015 are at least as discrepant, giving 0.62016 after the plus-one adjustment. Replacing the frequency-adjusted weights with section pair counts gives 0.62896. Frequency adjustment therefore makes little practical difference to this comparison.
The first-four versus last-four split from Session 25 also remains unpersuasive after allowing for count uncertainty: the first four have 29 repeats versus a conditional expectation of 36.57, with a two-sided conditional-binomial comparison of 0.10285 under the allocation model. This qualifies the earlier fixed-parameter prediction band, which treated its fitted repeat probability as known exactly.
Limit: Poisson allocation is a working approximation for rare events, not an exact fixed-inventory model of a repeat-suppressing cipher. Adjacent comparisons overlap, and actual encryption may add dependencies. These results provide no positive evidence of section heterogeneity under this coarse model; they do not prove equal rates or one shared algorithm. With only 86 events, some real differences could remain undetected.
Consequence for the investigation
Rune composition does not explain the shortage. Its presence throughout the sections is consistent with a widespread ordering constraint. That does not establish whether the cause is encryption, preprocessing, unusual plaintext or some other construction.
Together with earlier findings, a useful candidate must account for:
- A sharp shortage at immediate neighbors, without a comparable shortage at most tested longer distances.
- Suppression that continues across word boundaries and both alternating pair phases.
- Occasional identical neighbors involving 28 of 29 rune identities.
- The repeated six-rune phrase already recorded in Sessions 4–6.
The next bounded discriminator could test whether the rare exceptions cluster at recurring counter positions, extending the earlier two-phase check to a fixed range of longer periods with correction for all periods and reset choices. A concentration would still need independent validation; it would not itself identify a key. That test is not part of this session.
Reproduce
- Analysis code, Python with NumPy and the existing lp_core.py.
- Section inventories, analytic moments, simulations and controls.
Run the script beside the existing master transcription and lp_core.py. It makes no network calls and records the transcription hash. All data appeared in previous sessions: this is retrospective analysis, not a fresh validation sample. Original images were not fully retranscribed in this pass. No new key search was performed.