Manuscript X-G-ST@1 · X-G-ST.tex · lemma · 3c97567f
Lemma: Off-shell free nilpotence
Stage 1: the normalized free auxiliary–ghost multiplet › Independent generators and off-shell nilpotence · lines 640–652 · proof included or linked
X-G-ST@1#lem:s0nil
The derivation is nilpotent on the independent fields and their graded polynomial differential algebra.
Proof. Its square is zero on each generator in (eq:s0). The square of an odd derivation is an even derivation. It therefore vanishes on every polynomial in generators and their derivatives. No equation of motion is used.