{"knowledge_schema": {"broad_category": "Physics \u2192 Relativity \u2192 Particle Physics", "refinement": "This problem involves understanding the behavior of particles traveling at relativistic speeds and their decay rates in relation to distance traveled.", "specific_scope": "The focus is on determining the Lorentz factor required for a specific fraction of particles to reach a detector's walls, given their initial conditions and decay properties.", "goal": "Calculate the Lorentz factor that allows approximately two-thirds of the particles to reach the detector's inner walls before decaying."}, "summary": "This problem is rooted in the principles of relativistic physics, specifically concerning the behavior of particles with high speeds and their decay rates. It requires calculating the Lorentz factor necessary for a certain fraction of particles to reach a detector's walls, given their ultra-relativistic speeds. The goal is to find the Lorentz factor that results in approximately two-thirds of the particles surviving long enough to reach the detector, which is a key concept in understanding particle interactions and decay in high-energy physics."}