Prime Tree Architecture: Self-Determination as Spiral in Factorisation-Driven Growth

We construct a tree from the natural numbers in which primes form a rigid trunk and composites branch according to their factorisation. The branching geometry is determined entirely by the Rational Algebraic Superformula (RAS) — no angular system or coordinate frame is imposed. We show three results: (1) the trunk invariably spirals whenever any non-zero coupling exists between a node's RAS shape and the growth direction, with the spiral direction structurally determined and the rate parameterised by the coupling constant; (2) the lobe depth of RAS boundaries separates primes from composites with p = 3×10⁻¹¹, and this separation is independent of the symmetry fold — it derives purely from sopfr(n) and Ω(n); (3) the mean branch spacing converges to 45° = 360°/φ(24), expressing the mod 24 prime wheel octave rather than the golden angle. We interpret the coupling constant as the degree of self-determination of the set, propose a mapping between prime factorisation patterns and plant morphological types (natural biofication), and note that the resulting framework was encoded in pre-literate mythology (Yggdrasil, the World Tree).