Universidad de Norteamérica

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

We present a sustained study of a single object followed across representations, where the content lives in the equivalences between them. We prove and formally verify in Lean 4 that the golden ratio φ=(1+√5)/2 satisfies simultaneously twelve identities across five canonical stru...

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

We demonstrate that the odd values ζ(2k+1) of the Riemann zeta function are structurally determined by φ=(1+√5)/2 and π. The Euler product of ζ is built from local factors fp(s), one for each prime. We prove that the Frobenius lift φp = Fpφ + Fp-1—where Fn is the n-th Fibonacci n...

The Crystalline Worldsheet: A String Theoretical framework based on φ and π for the de Sitter observer problem

We propose that the obstruction to holography in de Sitter space is epistemological—a matter of representation—rather than ontological. We trace it to the non-paradoxical self-reference of binary language, in the precise sense of the Lawvere fixed-point theorem and the Yanofsky d...

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

We construct a Hermitian operator HPCF whose spectrum approximates the non-trivial zeros of the Riemann ζ function with mean error <1.7% across twelve orders of magnitude (n=1 to n=1012, 125 zeros). The construction proceeds without reference to ζ(s) or its zeros, drawing instead...