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

We introduce local divisor graphs as a C2/C3 middle layer in the mod 6 ±1 composite programme. For each prime segment Ii = (pi,pi+1), the composite interior Ci = U6 ∩Ii, U6 = {n∈N : n≡±1 (mod 6)}, carries two related structures. The orbital shell graph records only the smallest-prime-factor shell of each composite node. The local divisor graph records all prime channels dividing the same nodes. The main exact statement is that the orbital shell graph is the smallest- prime-factor quotient of the local divisor graph: Ti = Πspf (Di).