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

Formal proof that the HAL fold operator P-hat generates smoothed BMS supertranslations on S2. Lemma 1: [P-hat, d/du] = 0 (purely angular operator). Lemma 2: d_u C0 = -kappa P-hat C0 (Bondi EOM). Theorem: P-hat = (1-alpha2 nabla_S2)^{-1} Q_BMS_GR. Observable modes l less than 10: below 1.3 percent deviation. Task 2 Step 4 closed. Strominger triangle closes with C0 factor.