Pre-Registered Blind Prediction of Critical Pedestrian Density on Staircases: $\rho_{c}=0.5093\rho_{j}$ from the $ln(3)$ Coordination Scale

This work presents a pre-registered "L1 blind prediction" for pedestrian flow on staircases, extending the application of the universal $\ln(3)$ coordination scale. Using the analytical formula $\rho_{c} / \rho_{j} = (1 / (1 + \ln(3)))^{1/\ln(3)} \approx 0.5093$, we predict the critical density ($\rho_{c}$) for staircase flow based solely on published jam densities ($\rho_{j}$) from standard engineering references (Fruin, Predtechenskii, and Weidmann). Key features of this pre-registration: Zero-Parameter Prediction: The prediction $\rho_{c}=0.5093\rho_{j}$ is fixed here before any staircase trajectory data from the Forschungszentrum Jülich archive are accessed or analyzed. Cross-System Validation: This constitutes the third independent test of the $\ln(3)$ framework, following successful validations in vehicular traffic (MAPE 1.8%) and corridor pedestrian flow (MAPE 0.7%). Falsifiability: Predicted values for specific staircase conditions (up, down, mixed) are explicitly provided—for example, a predicted $\rho_{c} = 2.29$ $ped/m^{2}$ for Fruin’s down-flow—to be verified against independent experimental data. This document serves as the formal "L1 blind prediction" record to ensure scientific integrity and prevent post-hoc curve fitting.