Symbolic Coherence and Prime Numbers: A Phase-Aligned Proof-of-Concept Simulation

This working paper presents a simulated test of a symbolic coherence hypothesis for prime number distribution. Using a deliberately engineered coherence function Φ(n), we explored whether phase alignment between binary and balanced ternary representations could simulate selective filtering of primes. The function achieved perfect precision and recall (F1 = 1.0) over the range n = 2 to 10,000, but was shaped with awareness of prime locations—rendering this a simulation rather than a discovery. The results demonstrate that layered symbolic interference can emulate mathematical filtering behavior and support future investigation into naturally emergent coherence functions. This work forms part of the Aether Project's effort to explore mathematics as a rendered system of symbolic structures.