Remark: Where the boundary lies

The boundary is not at ${\Delta }_{\mathrm{F}}$ itself, which is a well-defined distribution and a fundamental solution up to the factor $-i$ (Lemma lem:DF(ii)); it is at the first pointwise product of ${\Delta }_{\mathrm{F}}$ with itself, i.e.\ at the first pair of entries both of field degree at least two. X-B's wording “it does not constitute a claimed family of time-ordered maps” is therefore exact. No statement of this section asserts that such a family does not exist; it asserts that the sheet does not define one.