The diagram itself does not directly relate to melody; rather, it's a map of the formal structure of the piece. It shows the major sections, the phrases comprising those sections, their lengths in measures, and how various divisions relate via the Golden Section (GS). Presumably melody will come in later, with Neumeyer showing how Hindemith composed his melodies to adhere to the structure mapped in the diagram.
For example, the A and B sections comprise 46 measures, and the A' section is 26 measures. 46/26 ~ 1.77, which is in the GS ballpark. This is illustrated by the bottommost bracket-curve pair. (At a guess, P.GS means "the Primary [longer] segment in the ratio", and S.GS means "the Secondary [shorter] segment".)
The topmost pairs of brackets illustrate similar relationships. The left-hand pair shows that the A section (17 measures) and the first phrase of the B section (12 measures) are in a ratio of 17/12 ~ 1.42. The right-hand pair shows the first two phrases of A' (19 measures) and the third phrase of A' (10 measures) as having ratio 19/10 ~ 1.9. If we squint, we see that these again are GS-ballpark ratios.
Each bracket-curve pair shows instances where Hindemith attempted to make his phrase structures reflect the GS.