Title Informational Spiral Structures in Prime Distribution via π-Immersion

It has long been conjectured that every number sequence, including the prime numbers, must appear somewhere within the infinite, non-repeating decimals of π. In this study, we analyze the positions of prime numbers within the decimal expansion of π and reveal a surprising discovery: their apparent randomness dissolves when viewed through the lens of informational geometry. By mapping prime locations onto a spiral coordinate system embedded in the π-field, we uncover a coherent structure governed by measurable informational gradients (ΔC) and bifurcation attractors (Φα). We formalize this framework as the Informational Resonance Spiral Viscous Time (IRSVT), a model for representing numerical distributions as informational fields. The resulting formation—termed the Prime–π IRSVT Field Spiral—exposes latent pathways of coherence and clustering behaviors, suggesting a deterministic geometric scaffold beneath what was once considered stochastic. Our analysis demonstrates that primes, when immersed in π-space, align with attractor nodes and follow spiraling informational trajectories expressed through topological layering and angular progression. These findings open a new geometric understanding of prime distributions, connecting number theory with concepts from information physics and algorithmic complexity. The implications are profound: primes may not be random artifacts of π but precipitates of an informational lattice structuring numerical reality.