Hexagonal Observer Projection: Resolving the Displacement Angle in Dimensional Oscillation Theory

This paper resolves the central open problem in Dimensional Oscillation Theory (DOT): the origin of the observer displacement angle δ = 1.815°. We show that the Möbius surface tiles exclusively in hexagons (Hales 1999), generating a discrete angular lattice with values 120°, 30°, and 5°. All observed tilt angles emerge as bare integer degrees from this lattice, shifted by a universal projection formula: measured = bare × (1 + d/N × δ/φ), where δ/φ = 248.65/137.036 produces a 2.02% correction per EM dimension. The Moon's tilt oscillation (5.00°–5.30°, amplitude 6.05%) provides direct observational confirmation of this projection mechanism, and a companion Gaia DR3 analysis detects the predicted cos²(ecliptic longitude) distortion at 20σ. The framework derives the synodic month to 6-second accuracy (T_syn = 30 − sin 28° = 29.5305 days) and connects planetary geometry to DOT's Dimensional Scaling Theorem through the universal ratio 2/3.