Manuscript XVI-P@p23 · XVI-P.tex · section · 9b0037a7

Master equation through O(κ 2) by antifield number

Master equation through O(κ 2) by antifield number · lines 1556–1581

(p10 stated $E_{u} P_{d} = P_{d} E_{u}$ , which is false; the conclusion survives with the corrected intertwining. It is checked on a test polynomial in tests/test_p14.py.) The divergence test is applied to the summed component; per-bracket-pair pieces are reported only to exhibit cancellations.

order	component	terms	divergence	per-pair (individually non-divergent)
$κ^{0}$	af0 grav Noether ( $s_{0} ℓ_{2}$ )	exact	yes	—
	af0 $(X_{Ψ}, X_{Ψ})$ transformed	32	yes	$h, c ˉ$
	af1, af2 (both variable sets)	0	yes	—
$κ^{1}$	af0 grav ( $s_{0} ℓ_{3} + s_{1} ℓ_{2}$ )	2148	yes	$s_{0}$ alone: 159 per $μ$
	af0 scalar $2 (L_{0}, X_{1}) + 2 (L_{1}, X_{0})$	20	yes	each piece
	af0 $(X_{Ψ}, X_{Ψ})$ transformed	372	yes	$h, c, c ˉ$
	af1 invariant / transformed	180 / 180	yes	$h, c$
$κ^{2}$	af0 grav ( $s_{0} ℓ_{4} + s_{1} ℓ_{3}$ , $s_{2} = 0$ )	15428	yes	$s_{0}$ alone: 2088 per $μ$
	af0 scalar $2 (L_{1}, X_{1}) + 2 (L_{2}, X_{0})$	20	yes	each piece
	af0 $(X_{Ψ}, X_{Ψ})$ transformed	2392	yes	$h, c$
	af1 invariant / transformed	1356 / 1356	yes	$h, c, ϕ$
	af2 (both)	0	yes	—

Master equation through O(κ 2) by antifield number

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