We develop a unified arithmetic framework linking consecutive Heronian triangles, real Pell-type equations, complex multiplication (CM) structures, and cyclotomic units inside the field K24 = Q(ζ24). For the family of consecutive triangles T(a) = (a−1, a, a+1), we show that the Pell backbone, the real biquadratic field K24+ = Q(√2, √3), and the Gaussian/Eisenstein CM layers combine into a system of norm identities: X^2 + Y^2 = N2 N3 A^2 − AB + B^2 = N3 N6 with N6 = N3 + 3N2. Introducing the CM-induced geometric condition r·u = z^2, relating the global inradius and the Pythagorean inradii, the full Pell–CM–cyclotomic system reduces to an explicit elliptic curve of rank 0. This forces the entire configuration to collapse to a single rational point. The unique solution corresponds to a = 14, proving that the triangle 13–14–15 is the only consecutive Heronian triangle whose Pell structure, CM structure, and cyclotomic structure embed simultaneously inside K24. This provides a complete arithmetic explanation of the "cyclotomic node" phenomenon and establishes the Node 24 Uniqueness Principle.