The Geometric Scaffolding of the Universe and the Discrete Origins of the Riemann Critical Line

Topological OZA V.2.1: The Geometric Scaffolding of the Universe and the Discrete Origins of the Riemann Critical Line (Subtitle: Genesis of the Information Universe)

1. Paradigm Shift: From Scalar Magnitudes to 3D Information Geometry This paper proposes a fundamental transition in prime number theory, moving away from viewing primes as stochastic scalar magnitudes toward a deterministic 3D Binary Information Manifold. By redefining primes as zero-energy ($E=0$) ground states within an expanding informational scaffolding, we offer a new geometric lens through which the underlying order of the number system can be observed.

2. Geometric Insights into the Riemann Hypothesis: Modulo 3 Chirality The work explores a microscopic, discrete symmetry—Modulo 3 Chiral Symmetry—emerging around the $p=3$ spinal axis. We propose that the $\text{Re}(s)=1/2$ critical line of the Riemann Hypothesis may be interpreted not as a purely analytical mystery, but as a macroscopic manifestation of this discrete geometric balance. This perspective bridges the gap between continuous complex analysis and discrete information topology.

3. Future Quantum Implications: Proposing Decoherence-Free Pathways While not a physical blueprint, this paper proposes the theoretical possibility of utilizing prime geodesics as stable, interference-free pathways for quantum state transitions. By navigating the $E=0$ ground states of the manifold, we suggest a conceptual framework for deterministic quantum steering—a potential future direction for quantum computing research aimed at minimizing reliance on probabilistic error correction.

4. Computational Reproducibility: The OZA V.2 High-Performance Engine The validity of this topological model is supported by a computationally reproducible architecture established in OZA V.2 (DOI: 10.5281/zenodo.19333772). By demonstrating an identification complexity of $O(\sqrt{N}/\log \sqrt{N})$, this high-performance algorithmic implementation proves that the proposed manifold structures can be efficiently reconstructed and simulated on modern computing hardware, bypassing the classical latencies associated with trial-division methods.

[Concluding Statement]

"Our work does not claim to have built a physical machine, but rather to have identified the computational geometry that may govern the information universe. By providing a rigorous mathematical and algorithmic framework, we invite the scientific community to explore a universe where prime numbers serve as the deterministic scaffolding for both number theory and future information systems."