PCF Framework
The Precedent-Current-Forthcoming (PCF) Framework identifies the primitive structure of the complex plane, bridging absolute geometry and string theory with the distribution of prime numbers.
This portal provides technical summaries and the Lean 4 formal verification suite for the framework's core constructions.
Research
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Simultaneous identities of the golden ratio and Euler's identity, formally verified in Lean 4 over the known Mersenne prime exponents
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.
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The Crystalline Worldsheet: A String Theoretical Framework based on 𝔽₁ for the de Sitter observer problem
A string theoretical framework based on 𝔽₁ for the de Sitter observer problem, carried on the golden torus.
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Odd Zeta Values from the PCF Torus: φ and π as Arithmetic-Geometric Sources
Demonstrating that the odd values ζ(2k+1) are structurally determined by the golden ratio φ and π.
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The Hilbert-Pólya Operator and the Primitive Structure of the Complex Plane: Between 𝔽₁, String Theory, and Ancient Geometry
Construction of a Hermitian operator H_PCF whose spectrum approximates the non-trivial zeros of the Riemann ζ function.