About Omega-PCF

Omega-PCF is the research site for the PCF (Precedent-Current-Forthcoming) program: a geometric construction on the complex plane that connects number theory, spectral theory, and string theory through the golden ratio $\varphi$.

What the program does

The construction identifies a primitive ring structure $R_{\mathrm{PCF}} = \mathbb{Z}[\varphi, \varphi^{-1}, \tfrac{1}{2}]$ on the complex plane, endows it with a torus topology, and builds from it:

• A Hermitian operator whose spectrum approximates the non-trivial zeros of the Riemann $\zeta$ function.
• A resolution of the de Sitter observer problem via a single microstate (no ensemble average).
• $\mathbb{F}_1$-descent data linking the construction to Manin’s program for absolute geometry.

Formal verification

Key parts of the construction are formalized in Lean 4 (Mathlib). The proofs carry zero sorry statements.

Publications

Team

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

Contact

• hello@omega-pcf.com
• github.com/omega-pcf