Cascade Cosmogony: Ontological Sequence from Gaussian Integer Seed to Standard Model Content

We construct the ontological sequence from the Gaussian integer seed z = 2+i to the Standard Model particle content, with each step forced by the cascade arithmetic. The sequence is: (1) the angle arctan(1/2) exists (geometry seed); (2) the integer lattice ℤ[i] exists (number seed); (3) the norm 5 splits (Fermat); (4) the fourth power J = −7+24i crosses the real axis (polarity flip); (5) the E7 uniqueness theorem selects the Lie algebra; (6) the Kac Z4 grading produces 24 grade-1 roots; (7) the Standard Model gauge group SU(3)×SU(2)×U(1) is a subgroup of E7. No step involves a free choice.