Tag: Golden-Ratio

All the articles with the tag "Golden-Ratio".

• Simultaneous identities of the golden ratio and Euler's identity, formally verified in Lean 4 over the known Mersenne prime exponents

  29 Jul, 2026

  Formal verification in Lean 4 that the golden ratio φ satisfies twelve identities across five canonical structures, specialised to the 52 known Mersenne prime exponents.

• The Crystalline Worldsheet: A String Theoretical Framework based on 𝔽₁ for the de Sitter observer problem

  13 Jul, 2026

  A string theoretical framework based on 𝔽₁ for the de Sitter observer problem, carried on the golden torus.

• Odd Zeta Values from the PCF Torus: φ and π as Arithmetic-Geometric Sources

  18 Apr, 2026

  Demonstrating that the odd values ζ(2k+1) are structurally determined by the golden ratio φ and π.

• The Hilbert-Pólya Operator and the Primitive Structure of the Complex Plane: Between 𝔽₁, String Theory, and Ancient Geometry

  18 Apr, 2026

  Construction of a Hermitian operator H_PCF whose spectrum approximates the non-trivial zeros of the Riemann ζ function.