Full symbolic Ising multi-boundary comparisons

Complete the full four-variable comparison for the Ising planar four-boundary amplitude and the full two-variable matrix/Eynard–Orantin comparison for the Ising genus-two two-boundary amplitude.

Background

For the Ising model, the planar four-boundary expression agrees with the matrix-cycle construction at eight exact rational four-tuples, but this does not establish equality as a symbolic function of all four boundary coordinates.

For the genus-two two-boundary amplitude, the paper verifies a one-variable specialization through projector extraction and checks six most singular local Laurent coefficients. These checks do not constitute a complete independent comparison with Eynard–Orantin recursion in two variables.

References

The complete residue formula was checked against the matrix cycles at eight exact rational four-tuples. These evaluations establish agreement at the stated points; a full four-variable symbolic comparison remains open.

— Resolvent reconstruction of minimal strings beyond KdV  (2609.28964 - Ahmed et al., 24 Sep 2026) in Appendix, Section Further Ising and unitary data, subsection Two further multi-boundary outputs