From Orbital Trees to Divisor Dynamics in the mod 6 ±1 Universe

We propose a structural condensation of the mod 6 ±1 program by introducing a divisor layer between the already established orbital geometry and the resonance-based spectral description. The starting point is the observation that the orbital tree of a prime segmentrecords only the smallest-prime-factor profile of its composite interior. This gives an elegant geometric image, but it suppresses the remaining factor channels that are still present inside the same segment. To recover this hidden arithmetic microstructure, we define for every prime segment a local divisor graph whose left vertices are prime channels and whose right vertices are the composite nodes inside the segment. The orbital tree is then recovered as the smallest-prime-factor projection of this divisor graph.