Why begin with a real representation?
The phase-selection research asks how a complex structure compatible with a real Hilbert representation can be identified and, under further dynamical conditions, selected. This reverses the usual presentation in which complex phase is supplied at the outset.
Published mathematical entry points
The 2026 papers in Physics Letters A and the Open Journal of Mathematical Sciences provide the exact operator-algebraic setting. Their statements should be read with the hypotheses on symmetry, temporal orientation, and relevant invariant sectors.
Gauge symmetry as a further question
The wider programme examines how internal transformations, transport between local descriptions, and loop comparisons might acquire a physical interpretation. The existence of a mathematical symmetry is a starting point, not a derivation of a particular particle spectrum or hierarchy of force strengths.
A useful reading order
First inspect the published phase-selection problem. Then study the explanatory examples. Finally examine what extra assumptions are needed to connect these structures with gauge interactions and matter. Detailed gauge work and interactive examples are maintained on SMONAD.
ACADEMIC OVERVIEW → DETAILED RESEARCH