The intuition of the positivity condition can be explained through the following analogy with Morse theory. Given a compact oriented manifold $M$ with a Morse-Smale function $H$, then

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  The degree zero (resp. $n$) elements in the Morse cochain complex are generated by the local maxima (resp. local minima) of $H$ whose unstable submanifolds (resp. stable submanifolds) have preferred orientations.

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  The fundamental class $1\in H^{0}(M)$ is represented by the sum of the local maxima with the preferred orientation. Similarly with the generator of $H^{n}(M)$.

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  A generic point on $M$ lies on exactly one Morse flowlines which starts with one local maximum point and ends on one local minimum point. More formally, if we construct the universal family of Morse flowlines that start with some local maximum and ends on some local minimum, the evaluation map would sweep out the fundamental cycle of $M$ as an $n$-dimensional current, without any cancellation effect.

Now for simplicity, if we start with an embedded Lagrangian brane $L$, and preform a small generic Hamiltonian deformation $\phi_{H}(L)$, then the Floer cohomology $HF^{*}(L,\phi_{H}(L))$ is computed as the Morse cohomology, so the Morse theory statements above would imply the positivity condition at least in such special cases. The intuition is that if the Lagrangian $L^{\prime}$ (together with its brane structure) is a sufficiently small deformation of $L$, then we expect the positivity condition to hold for the bordism current between $L$ and $L^{\prime}$.

In general the bordism current $\mathcal{C}$ receives contributions from many $(n-1)$-dimensional moduli spaces of holomorphic curves. We now focus on one moduli space by fixing the choice of the Lagrangian intersections $p_{1},\ldots p_{k},q$ and the homotopy type of $u:\Sigma\to X$, and consider a connected open subset of the moduli space which contains only automatically transverse curves. We observe:

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  For a fixed automatically transverse holomorphic curve $u:\Sigma\to X$, along $\partial\Sigma$ between any two successive corners, by the nowhere vanishing of $\Omega(\cdot,v_{1},\ldots v_{n})$, the Jacobian of the boundary evaluation map cannot change sign. That is, either the orientation of the universal family agrees with the orientation of $L$ (resp. $-L^{\prime}$) along $u:\partial\Sigma\to L$ at every point along the boundary portion of $\partial\Sigma$, or the two orientations disagree at every point.

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  The Lagrangians are graded by assumption, and the orientations are canonically determined by $e^{-i\theta}\Omega$. The corner behaviour (cf. Remark 3.7) implies that at the degree one self intersections, $e^{-i\theta}\Omega(\cdot,v_{1},\ldots v_{n-1})$ does not change sign. On the other hand, at the $CF^{0}(L,L^{\prime})$ and the $CF^{0}(L^{\prime},L)$ ends along $\partial\Sigma$, the 1-form $e^{-i\theta}\Omega(\cdot,v_{1},\ldots v_{n-1})$ changes orientation sign. Thus at a fixed automatically transverse curve, the orienation of the universal family and $L-L^{\prime}$ either completely agree along every point of $\partial\Sigma$, or completely disagree.

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  As we deform among automatically transverse curves, the orientation signs cannot change. Thus either all these holomorphic curves contribute positively to $\partial\mathcal{C}$, or they all contribute negatively.

The above discussion also suggests the limitation of the positivity condition: if we encounter a holomorphic curve in the moduli space, which is not automatically transverse, then it is possible to switch orientation signs. For arbitrary exact immersed Lagrangians, it seems unreasonable to expect the positivity condition, and it is conceivable that counterexamples may arise from $h$-principle constructions. Whether counterexamples occur for more restrictive Lagrangians seems less clear, and we leave the following sample questions as food for thought: