Where Are the Missing Particles?

The particle spectrum is incomplete — and we know exactly where to look. Using a single geometric law validated on the full PDG 2024 catalog (508 particles, zero free parameters), we identify ~170 missing states and provide a complete experimental roadmap: mass windows, width constraints, decay channels, and laboratory assignments for each. Key results:- A photonic gap (θ < 98°) where no massive particle can exist- A prime discovery window (140°–150°) with ~47 high-priority states accessible in existing LHCb data- Ultra-stable hidden bosons detectable via displaced vertices at FASER and SHiP- 74 missing mesons, 79 baryons, 7 BSM bosons — individually cataloged Every prediction is falsifiable. Every target is assigned to a specific facility: LHCb, BESIII, PANDA, ATLAS/CMS, NA62, SHiP, or FASER. This is not a model — it is a map. The experimental investment required is modest: reanalyze existing datasets with the geometric constraints provided here. Paper VI in the Angular World Architecture (AWA) series.