{"knowledge_schema": {"broad_category": "Physics \u2192 Relativity \u2192 Particle Physics", "refinement": "This problem involves understanding the behavior of particles traveling at relativistic speeds and how their velocities affect their ability to reach a certain distance within a detector.", "specific_scope": "The focus is on calculating the required Lorentz factor for a specific proportion of particles to reach the inner walls of a spherical detector based on their velocities and the geometry of the detector.", "goal": "Determine the Lorentz factor needed for three-quarters of the particles to reach the detector's inner walls."}, "summary": "This problem is rooted in the principles of relativistic physics, specifically concerning how particles behave at high velocities. It requires calculating the Lorentz factor necessary for a certain percentage of particles to reach a defined distance within a spherical detector. The task involves understanding the relationship between the Lorentz factor, particle velocity, and the geometry of the detector to find the required value for three-quarters of the particles to reach the inner walls."}