Spectral Selection Rule L; A Cosmic Physical Generation Mechanism Based on Categorical Duality and Topological Quantum Field Theory

This paper proposes a cosmic physical generation framework based on categor
ical duality and topological quantum field theory, aiming to address the immensity
of the model space in the string landscape and the resulting crisis of predictability.
The core claim of the framework is that the gauge structure, matter content, and
low-energy effective theory of the observable universe do not arise from the post
hoc selection of continuous parameters, but are necessarily determined by a discrete
mathematical structure that serves as a dynamical generative source—namely, a
symmetric fusion category—through a generalized duality principle. In the specific
context of string theory, this category is realized as the modular tensor category of
D-brane boundary conditions. Building on this, the paper successively constructs
two mutually complementary chains of derivation: a static generation chain, in
which the bulk-boundary correspondence and anomaly inflow mechanism derive
low-energy self-consistency, topological order, and quantum complexity from the
categorical invariant and the higher-dimensional topological invariant; and a dy
namical generation chain, which, through the categorical phase transition theory of
anyon condensation and the mechanism of quantum gravitational decoherence, rig
orously generates the matter structure and the macroscopic arrow of time from the
above static constraints. This theoretical framework yields a series of physically
testable predictions spanning multiple scales, including the search for topologi
cal resonances at future hadron colliders, the detection of non-Gaussianity in the
cosmic microwave background, and the verification of the time-complexity correla
tion on intermediate-scale quantum processors. Thus, “mathematical construction”
may replace “landscape selection” as a potential paradigm shift.