A repeated phrase as a constraint

Result: no verified new plaintext. Tested shared repeating-key hypotheses using the two copies of ᛞᛄᚢ ᛒᛖᛁ as an algebraic constraint. Unlike earlier fixed numerical-stream searches, this pass learned unknown key values from one passage, then applied them unchanged to another. All three constructed key-recovery controls succeeded. No real-text model produced a coherent validation passage.

1. State the assumption explicitly

The working hypothesis is that both identical six-rune ciphertext spans encode the same six plaintext runes under a shared additive repeating key. Ciphertext repetition alone does not establish this. No English phrase was imposed or guessed.

With rune values modulo 29, the decoder is

plaintext[i] = sign * ciphertext[i] - key[counter[i] mod period],

where sign is +1 or -1. If the six plaintext runes are equal at both occurrences, the corresponding six key values must also be equal. This equality supplies constraints on the unknown key, not its actual values.

2. Measure the two locations

All positions are zero-based. The first anchor is on LP2 page 27 in marked section 6. The second is on page 55 at the end of marked section 8.

If identical key phase explains the repetition directly, periods up to 64 dividing these differences are:

• Global: 1, 5.
• Page-reset: 1, 2, 3, 6, 7, 14, 21, 42.
• Section-reset: 1, 2, 3, 6.

These are not the only possible periods. A key can repeat the same six values at different phases. The search therefore tested every period from 1 through 64, merging any key positions that the repeated-plaintext assumption requires to be equal.

A fourth convention, phrase-aligned, allows a different starting phase in the second section. Its relative phase is set by aligning the two anchors, rather than assuming the sections start at the same phase. This is another explicit hypothesis. The alignment is imposed from the observed locations; a zero counter difference in this mode is not a newly observed numerical clue.

3. Fit without scoring the phrase

Training used the first 913 runes of section 6, ending at a word boundary. The six-rune anchor and all scored trigrams touching it were excluded. The decoder therefore had to infer the anchor's plaintext from key values learned elsewhere.

The boundary-aware language model from session 4 remained fixed and used only its established LP1 plaintext training data. Unknown keys were fitted by coordinate ascent:

• Three starts per model: one unigram-based and two randomized.
• Up to eight sweeps through the independent key positions.
• Each key position evaluated at all 29 rune values.
• Positions linked by the phrase constraint always share one value.
• Any unobserved key position would be left at zero and explicitly reported, rather than inferred from validation text.

This optimization is heuristic, not an exhaustive search of all possible keys. Random seeds and fitted keys are saved.

512 model specifications were fitted: 64 periods, four counter conventions and two signs. This count does not describe 512 distinct ciphers; some settings are equivalent after constraints collapse their key positions.

Models were ranked using training data only, with a heuristic penalty of number of independent key values * log(29) subtracted from the summed training score. This is a description-length-inspired ranking device, not a calibrated statistical likelihood or proof against overfitting.

4. Require unchanged continuation behavior

Validation used two targets:

1. The remaining 611 runes of section 6.
2. All 3,316 runes of section 8, with its six-rune anchor and scored trigrams touching that anchor excluded from the validation score.

The known anchor positions supplied the structural key constraints, but validation language scores never altered a key or selected a new relative phase. Thus the six-rune equality could not earn validation credit merely because we imposed it.

Higher scores are better on this model. These are mean trigram scores, not probabilities. The table reports raw mean scores for the models selected by penalized training score.

The improvement on training text did not extend to validation. Leading decoded passages were unreadable, and no coherent passage was identified. Across all 512 specifications, the other-section scores remained approximately -5.41 to -5.17. Favorable short fragments or a forced match at the phrase are not evidence of decryption.

5. Key-recovery controls

Constructed ciphertexts from repeated copies of the held-out LP2 page-57 plaintext, which is absent from language-model training. The control was supplied the correct period and counter convention, but not the key. It had to recover key values using the same optimization and anchor exclusions.

The third control has eight independent key classes after the equality constraints merge positions. It checks the important case where the period does not divide the anchor distance. Its original key is deliberately constructed to satisfy those constraints.

These controls establish key recovery on the specified constructed examples. They do not show that the optimizer can recover every key, that it could identify the period unaided, or that the real puzzle uses this cipher family. Repeating the same control plaintext is useful for implementation checking but is less demanding than recovering novel varied text.

What this narrows

The repeated phrase did not yield a supported shared periodic key of length 1-64 under these counter and alignment models. This gives no support to that particular explanation of the repetition. It does not rule out different plaintext meanings, a longer or nonperiodic keystream, different keys across sections, altered alphabets, selective skips, or more complex state.

A possible next step is a local shared-keystream comparison around the two anchors, without assuming periodicity. Within the two marked sections, their alignment gives only a 34-rune overlap: 28 preceding runes and the six-rune phrase. That is short and likely underconstrained, so any jointly plausible text would need careful controls and could not be treated as a translation by itself.

Reproduction

Python 3 and NumPy, with the included source snapshots:

python phrase_key_pass.py

The script uses word_core.py and lp_core.py. phrase_key_results.json retains all 512 models, keys, constraints, scores, controls and excerpts, plus complete decoded target sections for the ten best training-ranked models. All candidate texts are failed hypotheses. No background process remains running.

Source: community master transcription. The earlier transcription and authentication limitations continue to apply.