Forward higher-order unitary two-boundary comparison

Complete the full genus-one two-boundary comparison between the cyclic-projector construction and Eynard–Orantin recursion for the forward [6,7] and [7,8] unitary backgrounds.

Background

The reconstruction and independent Eynard–Orantin calculations agree for the one-boundary amplitudes through genus two in the sixth- and seventh-order forward unitary backgrounds. The corresponding string commutators and trace primitives also agree through the calculated orders.

The remaining unverified case is the complete genus-one two-boundary amplitude for these two forward projections; the paper reports only the one-boundary comparisons and related checks.