Dark Modes as Unobserved Directions in a Reduced Phase-Topological Framework

A Structural Completion of Observable Degrees of Freedom via Orthogonal Projection

抄録

We propose a structural interpretation of dark degrees of freedom as unobserved components orthogonal to the observable projection space in a reduced phase-topological framework.
Building on previous formulations in which fermions correspond to effective directions, gauge bosons to transition operators, and scalar modes to amplitude fluctuations, we identify dark modes as degrees of freedom that do not project onto the observable subspace.
In this picture, the dark sector does not require the introduction of new independent particles, but emerges naturally as the complement of the observable structural space.
We show that such orthogonal modes remain dynamically consistent with the underlying framework while remaining unobserved under projection-based measurement. This provides a unified structural interpretation of visible and dark sectors within a common operator-based formulation.
The dark sector arises as the unique orthogonal completion required by the projection-based structure.