Closed-form expressions for all states at fixed generation (conjecture)

Prove or refute the conjecture that all open bosonic string states at fixed generation admit closed-form oscillator realizations via the authors’ generalized Regge-trajectory techniques, except for those bottom-of-trajectory states whose number of oscillator structures has not stabilized.

Background

The authors exhibit closed-form constructions along many trajectories and families, observing linear patterns that enable formulas spanning infinite sets of states. Based on this, they conjecture a comprehensive closed-form description at fixed generation, with the caveat that seeds at the bottom of generalized trajectories may require special handling when structural stabilization has not yet occurred.

Establishing this conjecture would provide powerful, algorithmic control over large swaths of the spectrum.