{
  "seed": 3301035,
  "formula": "p[i] = (a*c[i] + b*p[i-1] + k) mod29",
  "ranges": {
    "a": "1..28",
    "b": "1..28",
    "k": "0..28",
    "initial_plaintext_state": "0..28"
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  "counter_and_reset": "Natural GP zero-based rune values. Continuous plaintext state through each marked section; punctuation, words and pages do not reset or advance it. Initial state searched separately for every target.",
  "selection": "First 60% capped at 256 runes, cut at a complete word. Top 20 settings retained by prefix score only. Decode whole section once; carry resulting plaintext state into suffix without refitting.",
  "scoring": "Unchanged LP1-trained word-boundary trigram model FULL_MODEL. Mean natural-log score per rune plus word-end event; a heuristic, not a calibrated probability.",
  "algebra_checks": {
    "phrase_difference_coefficients_checked": 28,
    "random_roundtrips_and_repeat_identities": 29,
    "repeated_phrase_rule": "With identical a,b,k, aligned plaintext differences equal b**(j+1) times the entering-state difference mod29. For b!=0, either all six corresponding plaintext runes match or none do.",
    "double_rule": "For i>=2, c[i]==c[i-1] iff p[i]-(1+b)*p[i-1]+b*p[i-2] == 0 mod29. For b=1 this means three plaintext values in arithmetic progression, including constant triples."
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      "prefix_words": 13,
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          "prefix_text": "PARABLE LIKE THE INSTAR TUNNELING TO THE SURFAKE WE MUST SHED OUR OWN",
          "suffix_text": "KIRKUMFERENKES FIND THE DIUINITY WITHIN AND EMERGE",
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          "prefix_score": -4.649586621185585,
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  "elapsed_seconds": 8.431153359000746,
  "limits": [
    "Exhaustive only for stated affine recurrence and parameter ranges; no arbitrary symbol permutation, nonlinear update, longer memory, variable key or additional encoding layer.",
    "b=0 has no plaintext feedback and was covered by earlier affine tests; it is omitted here.",
    "A separate key may be selected for each section. Retained candidates are ranked solely by prefixes, not by suffix scores.",
    "Language model and corpus were used in prior sessions: suffix exclusion applies to this fitting procedure, not to all historical exploration.",
    "Controls reuse one held-out 95-rune solved passage with three keys; they verify recovery in those constructions, not all natural language.",
    "Only the top 20 prefix candidates per target have full continuation scores and saved texts; lower-ranked settings were all prefix-scored but not exhaustively judged as complete plaintext.",
    "One random anti-repeat baseline uses section-0 layout and p=86/12939; it is descriptive, not a null ensemble or significance test.",
    "No result is declared a solution based solely on a language score."
  ]
}