IMSc Report116, Madras. Author-hosted notes. Chapter1, Theorem1.7, gives the six-exponentials theorem for independent input families with d times ell greater than d plus ell; Conjecture1.8 states the four-exponentials conjecture.
By Patrice Philippon, Michel Waldschmidt. Chapter 18 of New Advances in Transcendence Theory, pages 280–312, Cambridge University Press.
Theorem 1.1, printed pages 280–281, treats algebraic coefficients including the constant term. Theorems 2.1–2.2, printed pages 282–283, distinguish general algebraic coefficients from the homogeneous rational-integer case and give the refined coefficient parameter.