The substrate framework’s complete particle catalogue — chain position and mass for every Standard Model mode and every predicted dark-sector mode — reduces to a single closed-form equation parameterized by a small per-group identity vector. The Standard Model + framework dark sector partition into seven particle groups, and each group has one identity-vector schema. Per-particle data within a group is a finite tuple of integer-valued slots.
Eliot Gable (Mon,) studied this question.