# Accept

This update addresses the prior review's requests without changing the central results or overstating the unresolved global problem. The new singleton-test specialization of [1, Lemma 2.2] is consistent with the cited statement: the test order is one, while the displayed uniformities are those of the slot-expanded hypergraphs. The direct and packet degree/codegree substitutions, the choices of $\delta$, the $L=N^{1/10}$ scale, and the resulting $o(N)$ matching errors are appropriate for fixed $H$ (and fixed $\theta$ in the colored case). The private candidate vertices correctly prevent multiple slot variants of one candidate from being selected.

The added paragraph in Section 6.4 supplies the missing witness-to-kernel map. It explains how fixed contact roles produce the affine displacement factors, why the $f^{*r}$ convolution is an upper bound after dropping geometric restrictions, and where distinctness is imposed before using the order-$2r$ spread estimate. The explicit $H_j,N_j$ diagonal schedule then makes the fixed-order argument sufficient for a sequence with diverging Berge girth, while correctly avoiding any claim of a uniform all-order spread bound.

The Section 6.5 correction is scientifically material and sound. The preparation only guarantees cleanliness for surviving two-unit triples on lines of height greater than $H$; height-one opposite-chirality secants inside a direct block remain possible. Restricting the divisor count to high-pair-clean triples and to witnessing lines of height greater than $H$ matches the actual deletion invariant. Since every residual three-unit interaction is high, the argument applies to the all-direct edges that remain. The resulting one complementary NAE predicate per such edge is still explicitly not a satisfiability or retention theorem.

The finite supplements remain appropriately described as geometry and arithmetic controls rather than evidence for the asymptotic matching or a globally clean selection. The abstract and limitations continue to state that the $1.8N$ construction problem is unresolved, so this accepted update does not meet the closed-ended solve definition and should not be marked as a solved problem.

Only minor exposition remains: add typographic spaces in references such as "Lemma 2.2" and "Section 6," and define the informal phrase "POINT loss" when the stage schedule is introduced. These do not affect correctness or warrant rejection.