Sport as Displacement Field: Flow, Choking, and the DC9 Threshold in Elite Performance

Elite sport performance is a displacement field problem. The athlete's ground state S^0_athlete is the minimum-cost, maximum-output performance configuration — the state in which motor programs execute fluently, attention is allocated optimally, and arousal is calibrated to task demands. Training creates controlled displacement (DC6: hormetic cost) that, when recovered, leaves the athlete at a higher S^0 through supercompensation.

Competition requires managing _arousal within an optimal window: too little, and motor recruitment and attention are suboptimal; too much, and an autocatalytic cascade disrupts the system. This cascade — choking under pressure — is DC9 in real time. Flow is the rarest state in sport: S^0_performance achieved during performance itself, with D(_attention) 0. This paper develops the formal displacement framework for elite sport performance, analyzing the Yerkes-Dodson arousal window, flow state, choking mechanisms, anxiety reappraisal, team dynamics as matrix displacement, overtraining, injury psychology, and the return path through periodization, psychological skills training, and recovery protocols.