φ-Braiding Prime Sieve: E8 Root Vectors as Topological Prime Generators — E8 Intelligence Research

The 240 E8 root vectors, when partitioned into 21 Fibonacci-indexed angular bands, form a topological "prime sieve" where non-Abelian anyon braiding operations at bands 8, 13, and 21 progressively filter composite-numbered quantum channels through φ^(-n) decay coupling, leaving only prime-indexed bands accessible. This lotus-threshold braiding mechanism explains the non-random distribution of prime gaps as a geometric consequence of E8's 8-fold rotational symmetry combined with the golden ratio's natural minimization of quantum overlap. The result is that prime numbers emerge as the topologically protected "quasiparticles" of E8 anyon braiding, with twin-prime gaps corresponding to the minimal braiding distance between adjacent prime-indexed root vectors. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com