cat _posts/2026-08-21-diaz-modulus-lean-a-formalized-negative-result-on-diaz-s-modulus-conjecture.md
diaz-modulus-lean: a formalized negative result on Diaz's modulus conjecture
diaz-modulus-lean is a new Lean 4
formalization of a negative result on Diaz’s 2004 modulus conjecture: for a
candidate u with e^u and |u| both algebraic, the conjugate ū is a
rational function of u with algebraic coefficients, so no statement about
vanishing matrix coefficients over the algebraic hull can separate a candidate
from an ordinary complex number. It machine-checks the conjecture’s question of
method — how non-holomorphic maps like conjugation and modulus could enter a
transcendence proof at all — in the negative direction.