Spectral Selection Rule K: The Discrete Generative Elements of the Universe– A Feasible Universe Construction Principle Based on Composite Spectral Invariants and Categorical Dualities

This paper proposes a fundamental paradigm shift in quantum cosmology: vi
able universes are not selected from a vast pre-existing landscape but are directly
constructed from a set of discrete mathematical laws. We introduce a generative
framework based on categorical duality and a composite spectral invariant flow. The
core of this framework is a new spectral invariant S (the symmetric category invari
ant), which together with the higher-dimensional topological invariant Y serves as
the initial seed. Through a dynamic process of spectral invariant flow inspired by
the renormalization group, the system uniquely produces the remaining invariants
that determine low-energy physics (Z), topological order (T), quantum complexity
(C), the arrow of time (W), and matter structure (X). This constructive paradigm
introduces a meta-construction rule– the principle of maximal self-referential clo
sure– to solve the existence and uniqueness problem of the seed itself, arguing that
physical reality corresponds to the unique self-consistent fixed point structure in
logical space. The framework unifies the gauge group choice, the three generations
of fermions, the origin of the arrow of time, the cosmological constant, and the
baryon asymmetry as the necessary dynamical unfolding of the same underlying
algebraic-topological seed. Concrete predictions testable by quantum simulators,
cosmological observations, and high-energy colliders are presented.