13th Stone: The Bullet Cluster Protocol - Axiomatic Resolution via Vacuum Hysteresis (Pre-Registered Prediction)

RESTRICTED ACCESS PROTOCOL - TIME-STAMPED PRE-REGISTRATION Access is restricted until the official release of Euclid DR1 data confirming the w0 ~ -0.794 prediction. Researchers may request access for peer review purposes by contacting the author directly. This document contains the derivation of the gravitational potential of the Bullet Cluster (1E 0657-558) within the Unified Chronofractal Field (UCF) framework under the strict zero-parameter constraint ($k=0$). The file serves as a **blind pre-registration** of the theory's "Metric Drag / Vacuum Hysteresis" mechanism. It documents the theoretical prediction of the cluster's lensing potential ($\chi \approx 2.26 \times 10^6$ (km/s)²) derived solely from baryonic inputs and established UCF constants, prior to the release of decisive cosmological data. Access Condition:The full text is currently restricted to preserve the integrity of the prediction. Access will be granted publicly upon the release of the Euclid Mission Data Release 1 (DR1), specifically conditional on the validation of the UCF Dark Energy equation of state prediction:$$w_0 \approx -0.794$$ This embargo ensures that the solution to the Bullet Cluster anomaly documented herein is historically verified as preceding the confirmation of the theory's cosmological sector.