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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.