Octonionic Two-Branch Transport and Forced Phase Classification

This paper develops a reduced dynamical model for paired octonionic transport amplitudes obtained from the two bracket completions of a non-associative product after projection onto a preferred complex transport slice. The central object is the transport-coherence invariant I=AB̄, together with a signed coupling κᵤ determined by the projection of the associator onto the chosen transport axis. Starting from a minimal conjugate-paired evolution ansatz, the paper derives an exact reduced system in the adapted variables (R,ρ,Φ). The main mathematical result is that the reduced phase portrait is organized by two explicit geometric boundaries: a locking boundary and a persistence boundary. Away from these marginal boundaries, the dynamics separates into four transport classes, termed constructive, inverted, frustrated, and dephased. The paper also identifies the fixed-point structure of the reduced system, shows that the symmetric branch yields node equilibria while the complementary branch yields center equilibria with decaying amplitude, and proves a sharp criterion for when a state is particle-like within the reduced model. Methodologically, the paper is intentionally narrow. It does not attempt a full physical completion or a first-principles derivation of the dynamical ansatz from the octonionic bulk. Its contribution is instead to show that, once the minimal two-branch ansatz is granted, the reduced dynamics is rigid enough to force a nontrivial geometric classification.