About Omega-PCF

Omega-PCF is a dedicated research portal focusing on the primitive structural properties of the complex plane and their implications for number theory and physics.

The PCF Framework

The Precedent-Current-Forthcoming (PCF) Framework identifies the primitive structure of the complex plane, establishing a unified geometric foundation that bridges:

• Absolute Geometry ($F_1$): Integrating Manin’s program with modern categorical logic and descent data.
• String Theory: Realizing the complex plane as a dynamical system on a torus generated by the golden ratio $\varphi$.
• Spectral Theory: Constructing non-circular Hermitian operators for the Hilbert-Pólya conjecture.

Formal Verification

The entire deductive chain of the PCF Framework is formalized in Lean 4, ensuring that our constructions are verified with zero sorry statements and rely only on well-established geometric axioms.

Research Team

The portal serves as the primary technical companion for the collective work of:

• J.A. González García
• V.M. González García
• I.M. Dressler Pérez
• L.M. García Ordóñez
• M. Moreno

Contact

For inquiries regarding the manuscripts or the formal verification suite:

• Email: [email protected]
• GitHub: omega-pcf