Arithmetic and the first controls

Date: 18 September 2026

Result: no new page solved. This session reproduced a known solution, built a rune-preserving test harness, and completed a bounded search. It did not identify Cicada's creators or locate the hidden webpage.

Verified starting point

The transcription uses a 29-symbol alphabet. Some symbols represent several Latin letters, so all arithmetic is performed on rune indices, not on transliterated English letters.

LP2 page 56 (combined-archive page 73) decodes by subtracting successive primes minus one, modulo 29. Its ciphertext F at zero-based rune index 56 remains F and does not consume a prime. Without that exception, the first portion works but the later text becomes unreadable. The decoder reproduced the hidden-webpage instructions and their 128-character hexadecimal fingerprint. The full computational output is in results.json. This is a reproduction of an existing solution, not a discovery.

The 85 ciphertext runes match a second archive exactly. Re-encryption matches the 84 transformed positions; the skipped F matches unchanged. The script also reproduces the direct rune transliteration on LP2 page 57. The scoring model, trained only on selected solved LP1 text, ranks the correct page-56 offset and F-skip choice first among the tested control candidates.

Tests performed

Total decryption settings: 2,980,108. This count includes overlapping and duplicate transforms. It is not a count of independent methods and should not be interpreted as a measure of how close we are to a solution.

Arithmetic streams were primes, primes minus one, Fibonacci numbers, integer totients, integers, squares, cumulative primes, and prime gaps. Each used starting offsets 0 through 256, positive and negative cipher multipliers, and addition/subtraction of the stream. The broad pass tested no skipped symbols and skipping every ciphertext F. The follow-up tested no skip or one individually selected ciphertext F. It did not search arbitrary skip subsets.

The broad pass covered 12,956 runes. LP2 page 50 contains no runes in this transcription. Non-runic blocks on pages 49, 50 and 51 were excluded from cryptanalysis.

Statistical check

For the first three-page stream, the strongest standardized period peak was at period 35. After allowing for selection across all 63 periods, the empirical permutation p-value was approximately 0.927. About 93% of the shuffled texts produced an equally large or larger maximum. This gives no useful evidence for a simple repeating key in the tested setup. It is not a probability that the cipher is random, and does not rule out a repeating key with skips, resets, changing alphabets or other layers.

Structural observation

The community-noted six-rune sequence ᛞᛄᚢᛒᛖᛁ occurs on LP2 page 27 at rune offset 28 and page 55 at offset 70. This session confirmed those locations; it did not discover the repetition. Repetition alone does not establish shared plaintext or key reuse.

Interpretation and next experiment

These results provide a reproducible baseline, not a breakthrough. The top-ranked candidates were inspected and contain scattered English-like fragments without coherent passages. They are retained as failed candidates for audit, not proposed translations. A small language model can mis-rank a real solution, so a negative search result cannot eliminate a whole cipher family.

The next focused experiment should model key advancement at the book's actual paragraph and section markers and selectively unencrypted symbols. First verify those markers against source images, then test a small, explicitly specified set of reset/skip rules. Evaluate any promising output on a continuation that was not used to choose the rule. Avoid selecting arbitrary skips simply because they manufacture a few English words.

Reproduce

Requirements: Python 3 and NumPy. No network access is needed to run the saved experiments.

python first_pass.py
python period_probe.py

The programs read the adjacent community transcription and write results.json and period_results.json. The source transcription is preserved unchanged. The rune-language scoring model is intentionally small and is used only to rank outputs. The two experimental scripts were authored for this session.

Evidence and limits

• Community transcription
• Known page-56 solution and transcription
• CicadaSolvers briefing
• Previously documented six-rune repetition

Source revision and file hashes are in provenance.json. The full transcription was not manually checked page by page. Archive agreement is not independent PGP authentication; no such authentication was performed in this session. Page numbering uses LP2's original 0-57 scheme throughout this report. Combined-archive image numbers add 17.