A Rational Double-Pass Matrix Model for the Voynich Manuscript Utilizing Discrete Fibonacci, \(π\), and \(Φ\) Cross-Sectional Constraints

This paper introduces a novel, multi-layered decryption framework for the 15th-century codex known as the Voynich Manuscript (Yale, Beinecke MS 408). While previous attempts at computational or linguistic decipherment have struggled with the text’s unnaturally low statistical entropy, this study presents a rigid, deterministic mathematical engine that maps the ciphertext directly to corresponding page iconography across disparate thematic sections.The proposed framework operates via a fixed, four-constraint architecture:1. An initial spatial filtration layer governed by the Golden Ratio (Φ = 0.618), which dynamically identifies and isolates positionally invariant null anchor tokens.2. A strict double-pass decryption ceiling.3. A modular, word-resetting alphabetic shift engine that maps characters sequentially using combined irrational vectors derived from the Fibonacci sequence and the first five digits of Pi (π = 3.14159).4. A standard 26-character character wheel mapping an underlying Old High German (OHG) lexical core adapted to a localized, early Renaissance Gallo-Italic phonetic syntax.When applied systematically to the opening lines of the Botanical section (Folio 2r) and the Balneological section (Folio 78r), the matrix demonstrates high internal consistency. Recurring structural words collapse into predictable geometric backbone tokens (e.g., the high-frequency term dactas consistently resolves to the matrix anchor udqjf).Crucially, without adjusting any mathematical parameters, the output text exhibits a clear semantic bridge that transitions dynamically based on adjacent illustrations. On Folio 2r, the cipher yields