Do word boundaries organize the numbers?

Result: no verified plaintext and no positive support for the specific word-organized numerical schedules or boundary statistic tested. This narrows the hypothesis; it does not rule out every word-dependent cipher.

Avoiding duplicate work

Session 2 already tested simple sequence resets at words. Session 4 tested linear shifts based on word ordinal, word length, and previous ciphertext word sums. Those searches were not repeated. The new search uses word length/ordinal to index nonlinear prime and totient sequences.

Six schedules

Let j be the zero-based rune position in its word, L the word's rune length, and w the zero-based word ordinal within the marked section. For each of three indices, L+j, w+j, or w, test:

• prime(index+offset+1) minus 1, with prime(1)=2;
• totient(index+offset+1), with totient(1)=1.

Decode d = (ac + signschedule + k) mod 29, using a and sign in {-1,+1}, offsets 0 through 32, and k 0 through 28. No F exceptions, unknown keyword, plaintext feedback, or punctuation-consuming steps. Wraps do not split words. The word counter continues through the prefix/suffix split.

This is 22,968 settings per section, 183,744 over eight substantial unsolved sections. Counts include duplicate transformations and are not counts of distinct ciphers.

Selection and controls

Candidate settings are selected only on a complete-word prefix ending at or before min(256, floor(0.6*N)) runes. Retain up to three leaders for each family/sign combination, then ten leaders overall. Apply unchanged settings to the rest. The suffix is held out from this parameter choice, but has been studied in prior sessions and is not a globally untouched corpus.

Constructed six positive controls, one per family, by encrypting the known LP2 page-57 plaintext. That plaintext is excluded from the LP1 language-model training data. Each control used a=-1, sign=+1, offset=7, k=11. The full six-family search recovered the exact complete plaintext at rank 1 in every control. These controls validate search capability within the chosen families, not their applicability to the real cipher.

Higher scores mean greater similarity to the small trained rune-language model; scores are not solution probabilities. Leading beginnings and continuations remain incoherent. No verified candidate emerged. Full retained candidates are in word_schedule_results.json.

Structural test without a guessed decoder

For every adjacent rune pair within each substantial section, calculate its signed difference modulo 29. Label whether that transition crosses a word boundary. Measure their mutual information separately within sections and combine by transition count.

Comparison: keep the full rune sequence and its transitions fixed, but cyclically rotate each section's boundary-label vector by an independently selected nonzero offset. This preserves the observed transition distribution and number of boundaries, while disrupting their alignment. Use 1,999 draws, seed 330114. This is one aggregate exploratory statistic, not eight separately selected discoveries.

• Transitions: 12,939; word-boundary transitions: 2,889.
• Observed weighted information: 0.007826 nats.
• Rotation mean: 0.008846 nats; 95th percentile: 0.010292.
• 1,760 of 1,999 rotations matched or exceeded the observed association.
• Upper-tail Monte Carlo estimate: (1760+1)/(1999+1) = 0.8805.

Thus this particular numerical-jump statistic shows no excess association with the actual boundaries. The tail value is not an 88% probability that boundaries are irrelevant. The rotation comparison assumes shifted alignments are suitable controls and can be affected by nonstationary text structure. It does not test longer memory, nonlinear state, prime-valued word sums, or encrypted delimiters.

Decision

Downgrade the tested word-length/word-ordinal arithmetic schedules as leads. The existing scarcity of identical adjacent runes remains unexplained, and earlier work found it both within and across words. Together these results give no reason yet to place a simple reset specifically at each word boundary. A future stateful cipher hypothesis should account for that repeat suppression and the known repeated phrase before adding a broad new key search.

Reproduction

Run word_schedule_pass.py and boundary_gap_probe.py with Python and NumPy. Both use existing lp_core.py and word_core.py plus the included master transcription. Outputs are word_schedule_results.json and boundary_gap_results.json. No network, Tor access, or background task is required.