Number squares and combined keys

Result: no verified new plaintext. The page-15 number square was reproduced exactly, and 43 specified prime/Fibonacci streams were tested against the eight substantial unsolved rune sections. The square reconstruction is an established community observation, not a new discovery. Leading decryption candidates did not produce readable continuations or stand out in shuffled comparisons.

The verified clue

Visually read the 4-by-4 number square in the archived LP2 page 15 image (32.jpg in the archive's combined numbering). Starting at red 3299 and spiralling right, down, left, then outward gives:

3299, 3298, 3296, 3294, 3288, 3278, 3258, 3222, 3152, 3038, 2838, 2472, 1820, 708, 1206, 4516.

Use zero-based prime indexing: p[0]=2. Take the index sequence

0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987.

This is the Fibonacci sequence with its duplicate 1 omitted. The corresponding primes are

2, 3, 5, 7, 13, 23, 43, 79, 149, 263, 463, 829, 1481, 2593, 4507, 7817.

Applying abs(3301 - prime) reproduces every square entry. In particular, the last two entries need no special sign exception: abs(3301-4507)=1206 and abs(3301-7817)=4516. This is a numerical reconstruction; it does not establish how the surrounding runes are encrypted.

The later-message interpretation involving 3301's one-based prime index 464 remains a community hypothesis. This session did not authenticate those messages or independently validate their claimed gematria relationships. It tested precisely defined index-walk variants, with that limitation explicit.

Search definition

All transformed rune values are reduced modulo 29. The 43 streams comprise:

Modular wrapping, repeating the square and using it as a rune key are our explicit test hypotheses, not authenticated Cicada instructions.

Exact nested-prime streams were computed with an ordinary prime sieve, through zero-based prime index 3,524,578, whose prime is 59,328,163. Exact streams were never silently replaced by small modular-index approximations. A candidate was eligible only if its key covered every rune position in the target. In this search, finite exact streams were usable with word resets. They did not test an unbounded, continuous nested-prime cipher.

For each stream, tested offsets 0..16; continuous, page, paragraph, clause and word resets; ordinary or negated rune values; adding or subtracting the key; shifts 0, 1, 28, 24 and 5; and either no F skips or skipping every ciphertext F. The shifts cover common +/-1 and +/-3301 conventions modulo 29. Punctuation and non-rune content do not consume the counter. Reset markers follow the saved community transcription.

1,082,560 candidate settings across eight sections containing 12,947 runes. This includes duplicate/equivalent transformations and is not a count of distinct ciphers. The nine-rune segment and non-rune blocks were excluded from language ranking.

Candidates were selected using only the first min(256, floor(0.6 * section_length)) runes. For these eight sections that is 256 runes each. The remaining runes were decoded using the selected rule unchanged, then scored separately. The twenty leading prefix candidates per section are retained in combined_results.json; they are failed candidates, not translations.

Controls and results

The small rune-language model was trained on the same selected LP1 material as the previous session. LP2 page 57 was held out from that training and used for two constructed controls:

1. Encrypt its plaintext with exact primes at the square's Fibonacci indices, offset 3, resetting at words.
2. Encrypt it with the wrapped 464-index Fibonacci walk, offset 7, resetting at paragraphs.

The full search recovered both plaintexts exactly at rank 1. This validates these implementation paths and basic ranking behavior. It does not demonstrate sensitivity to all real Cicada ciphers.

For the real unsolved sections, best prefix scores ranged from approximately -7.49 to -7.44; their continuation scores ranged from -7.84 to -7.75. The constructed controls recovered plaintext scoring approximately -6.06 on the prefix and -4.70 on the continuation. These are heuristic model scores, not calibrated probabilities. Inspection of leading outputs showed no coherent passage.

Repeated the complete parameter selection on 32 shuffled versions of each of two targets: the opening section and the section beginning after the number square. Each shuffle preserves rune counts and punctuation layout. RNG seed: 20260918.

The empirical value is (1 + number of null scores >= observed) / 33. It is a coarse check against overinterpreting the best match after searching many settings. Neither target stands out from these shuffled comparisons. The test does not assign a probability to whether the whole prime/Fibonacci idea is correct.

Limits and next research choice

This rules out no broad cipher family. It finds no support for the particular direct additive schedules tested. Important omissions include selective per-occurrence F skips combined with these new streams, unknown word-level operations, other offset ranges or seeds, and unbounded exact nested-prime sequences across whole sections. The language model is small, so false negatives remain possible.

A useful next experiment would study structural rules at word boundaries using a stronger independently trained scoring model and a fixed validation protocol. Simply adding more arbitrary numerical combinations is unlikely to distinguish an intended key from accidental fragments.

Reproduction

Requirements: Python 3 and NumPy. The prime sieve temporarily uses roughly 100 MB or more of memory depending on the runtime.

python combined_pass.py
python combined_null.py

The second command requires the first command's output. Local input snapshots are included, so no network, Tor or external service is needed. Each script completes and exits; no background task is left running.

Sources

• Archived original LP2 page-15 image, combined numbering 32
• Cicada Solvers square page
• Community explanation of the prime-index spiral
• Community quickstart and prime/Fibonacci research suggestions
• Master transcription

The formulas and results above were checked locally against the archived image. Source agreement is not independent PGP authentication. Existing session reports and results are retained.