Motti Intermediate Physics - HAL: The Fold Operator as a Smoothed BMS Generator - A Formal Proof via Two Lemmas

Key Points

• The aim is to prove that the HAL fold operator generates smoothed BMS supertranslations on the 2-sphere.
• Formal proof via two lemmas regarding the fold operator and its commutation relation with derivatives.
• Application of Bondi equations to establish relationships between variables.
• Analysis of the theorem demonstrating the fold operator's functional role in generalized coordinates.
• The fold operator produces observable modes with less than 1.3 percent deviation for l values below 10.
• The derived theorem reaffirms the connection between the fold operator and BMS transformations.
• Closure of the Strominger triangle is verified with respect to the C0 factor.