Framework Overview & Core Architecture
The Trinary Symmetry Framework introduces an exploratory geometric and wave-mechanic coordinate system designed to analyze prime number distributions through the lens of Base-3 spatial dynamics. By leveraging a Base-3 parameterization, the framework collapses standard irrational geometric distortion metrics into a rational integer scalar ($\Omega = 2$) and maps deterministic modulo-6 arithmetic channels ($\mathcal{C}_1 = 6k + 1$ and $\mathcal{C}_5 = 6k + 5$) onto a $180^\circ$ anti-parallel phase engine.
This structural alignment achieves a 98.08% reduction in background noise while constructing an infinite-dimensional self-adjoint operator system that symmetrically aligns with the classical Riemann critical line ($\sigma = 1/2$).
Open Infrastructure & Academic Collaboration
Designed as an open conceptual infrastructure rather than a closed proof, this project explicitly invites joint academic development, stress-testing, and co-authorship across number theory, functional analysis, quantum physics, and computational mathematics. Core collaborative targets include:
- Infinite Adelic Limit: Formally proving trace-class operator convergence across global multi-prime networks.
- Spectral Matching: Establishing 1-to-1 spectral duality against non-trivial zeros of $L$-functions.
- Automorphic Representations: Mapping functional reflection symmetries onto automorphic forms and Selberg trace isomorphisms.
- HPC Scale-Out: Expanding open-source PyTorch GPU cluster architectures across distributed high-performance computing centers.
Researchers and institutions are warmly invited to engage with the framework to refine and validate these open mathematical vectors.