IV.D346 — tau-Charge Conjugation C_tau = sigma

The tau-charge-conjugation operator C_tau is uniquely identified with the polarity involution sigma on L = S^1 v S^1. Proof: (a) any physical C reverses U(1)-holonomy charge Q = chi_plus - chi_minus; (b) sigma: j |-> -j sends chi_plus - chi_minus |-> -(chi_plus - chi_minus), reversing Q; (c) sigma is the unique involution on L swapping lobe_+ <-> lobe_- while fixing omega (from I.D18 bipolar decomposition uniqueness). Therefore C_tau = sigma.