Manuscript X-B@3 · X-B-v3.tex · section · 2d415d58

The sign ledger

B2: one retarded map, its sign, support, and quantum order › The sign ledger · lines 985–1001

For all admitted bare coefficients,

R_{1} (V_{1, g}; O_{κ}) = ϕ (d_{c_{0}} + κ d_{c_{1}} + κ^{2} d_{c_{2}}) .

This is the unweighted map. The physical first-vertex correction has an additional factor $κ$ . These two notions are not interchangeable.

The support theorem places the correction's scalar test in $supp g \cap J^{-} (K)$ . It does not remove the original dressing's background dependence on $D_{f}$ . At this order, the causal statement consists of additivity and retarded vanishing; no complete causal-factorization hierarchy is claimed.

Displayed formulas in this passage

unlabeled · line 988
$R_{1} (V_{1, g}; O_{κ}) = ϕ (d_{c_{0}} + κ d_{c_{1}} + κ^{2} d_{c_{2}}) .$

Nearby in this section

section: The sign ledger
definition: Definition: The single normalized map
theorem: Theorem: Existence, normalization, continuity, and support