The Acosta Prime Helix: A Global Arithmetic Network Where Every Prime is Simultaneously Node, Root, and Bridge

We introduce the Acosta Prime Helix H(p)H(p), a deterministic sequence generated by hn+1=pπ(hn)+hn+1hn+1=pπ(hn)+hn+1. For seed p=23p=23, eleven verified levels (23→3.20×101223→3.20×1012) reveal that primes form a global arithmetic network G∞G∞ where every prime is simultaneously: (1) a node in the network, (2) a root generating its own trajectory H(p)H(p), and (3) a bridge connecting distinct trajectories—the arithmetic triad. This transforms primes from static objects to processes in a deterministic field. G∞G∞ is provably connected with small-world topology (diameter O(log⁡log⁡X)O(loglogX)). Within helix intervals, twin prime density stabilizes at ρn≈0.35ρn≈0.35—a 28.5×28.5× elevation over Cramér's random model—revealing that Cramér's assumption of local independence is systematically violated. These deviations arise from deterministic correlations induced by Q(−23)Q(−23) (class number h=3h=3) and dodecahedral symmetry (A5A5).