Direct local proof of the trace comparison

Establish a direct local proof of the equality between the twisted orbital-integral contributions of the order-3 and order-4 torsion classes for the two non-conjugate maximal parahorics of GU_2(B_p), using fixed Haar measures and explicit local representatives.

Background

The paper proves the trace comparison between the principal and non-principal genera globally by subtracting two closed trace-formula evaluations. The comparison shows that most terms agree and isolates the surviving class-number contribution, but it does not establish equality term by term at the local level.

The unresolved problem is to replace this global comparison with a local calculation of twisted orbital integrals at the two non-conjugate maximal parahorics. The paper specifies that such a proof would require fixed Haar-measure normalizations, explicit local representatives, and an optimal-embedding computation.