Geometric Containment in a 12-Point Doubling System: An Observational Correlation with the Golden Angle (137.5°)

Abstract

This study presents a closed geometric construction on a 12-point circular system. A binary doubling sequence f(n)=2n mod 9 generating the cycle 2→4→8→7→5→1→2 is mapped as six directed segments. Analytical intersection test demonstrates exactly three interior points forming a single unique control triangle. Among C(12,3)=220 possible triangles, only this triangle is generated by the defined path. Under golden-ratio normalization, central angle is ~137.5°, identical to golden angle (360/φ²) and with 0.34% proximity to inverse fine-structure constant (137.036). Reported as observational correlation, not physical derivation.