Compact T-Gate Count for Multi-Controlled X Gates via Margolus Sandwich: T = 8n − 9

We derive and verify a compact formula for the T-gate count of n-controlled X gates (CnX): T = 8n − 9, requiring n − 2 clean ancilla qubits. The construction replaces every structural Toffoli gate in the standard V-chain compute/uncompute cascade with a relative-phase Toffoli (Margolus gate, 4T each), retaining only the terminal Toffoli at full 7T cost. The spurious phase introduced by each Margolus gate cancels exactly in the compute/uncompute sandwich via a commutation argument that holds structurally in any V-chain cascade. The formula saves 6n − 12 T-gates over the standard 14n − 21 decomposition and composes additively with Gidney measurement-based uncompute. Verified at n = 3, 4, 5 via classical numerical unitary comparison (errors at floating-point precision) and hardware-verified at n = 3 and n = 4 on IBM Heron r2 (ibm_fez), with all IBM job IDs published for independent audit.