From the Division-Algebra Cascade to SO(10)

We show that the minimal discrete épure's division-algebra cascade leads to the SO(10) grand-unified structure, without postulating it. Each link is an established fact, chained from the cascade: 𝕆 (dimension 8, selected by the Hurwitz bound) generates SL(2,𝕆)=Spin(9,1), the 10D Lorentz group; its Weyl spinor is 𝕆²=16, exactly the SO(10) spinor and the content of one fermion generation. Three features are derived rather than chosen: the real form (9,1) is fixed by the programme's one-time signature rule (q=1); the ten dimensions are internal (a charge space, not propagation, which remains (3+1)), so nothing compactifies — a structural advantage over string constructions; the Higgs sits in the octonionic 10 representation, identified with the programme's dilaton. A decisive consistency test is passed: the 16 decomposes exactly into one Standard Model generation with correct charges, and the residual gauge group coincides with the automorphism group derived independently. The bridge enlarges the derivable territory: the GUT-scale Weinberg angle sin²θ_W=3/8 (a pure ratio), electric-charge quantisation, and quark-lepton mass relations (m_b=m_τ at unification) — relations derived, values posited, as the programme's 'no fixed point' principle requires. Inherited falsifiable predictions: proton decay and a right-handed neutrino with seesaw. We mark explicitly what is proper to the programme (leading to SO(10), fixing the real form, the internal status of 10D) versus inherited from grand-unified theory.