Closed-form coefficients for three-row tableaux at large third row

Establish the existence of, and explicitly derive, a closed-form formula for the oscillator coefficients of all single-particle states described by SO(25) Young tableaux with three rows at a given generation, in the regime where the third row length s_3 is sufficiently large.

Background

By counting structures and particles for three-row tableaux, the authors observe saturation patterns suggesting deeper regularities. They specifically point out that for sufficiently large third-row length s_3, one may expect closed-form coefficient formulas across such families.

They signal this as an important check left for future work, inviting a concrete derivation that would extend their closed-form constructions beyond two-row families.