A precise Hermitian-dual convention correction

Let $\overline{M}$ be the conjugate vector space and $M^h=(\overline{M}{)}^{\vee }$, where the contragredient dual consists of complex-linear functionals. For $\lambda \in M^h$,

is conjugate-linear in $x$ and linear in $\lambda$.

Thus the evaluation printed as linear in $x$ and conjugate-linear in $\lambda$ in Sections 2.1 and 6.2 of the supplied preprint requires, under this standard convention,

It now has the declared linearities. Alternatively, the source would have to explicitly change its dual convention.

Equation (eq:correctpairing) is a local convention correction. It does not verify the source's transport phases, canonical fusion normalization, all-module unitarization, or sector exhaustion. A complete audit would need to propagate the correction through the relevant adjoint and contragredient identities.