cat _posts/2026-10-01-diaz-modulus-lean-waldschmidt-s-1973-theorem-is-machine-checked-and-schneider-s-eighth-problem-with-it.md
diaz-modulus-lean: Waldschmidt's 1973 theorem is machine-checked, and Schneider's eighth problem with it
The Diaz companion note reached
v1.12:
Waldschmidt’s 1973 theorem in its algebraic-independence form is now
machine-checked — if x₁, x₂ and y₁, y₂ are linearly independent over ℚ and
e^(x₁y₂), e^(x₂y₂) are algebraic, then two of the eight numbers x_i, y_j,
e^(x_iy_j) are algebraically independent
(8b015b3) — formalised
as a one-column extension of the four exponentials development rather than a new
development of its own. That closes what the
previous version had
to carry as a hypothesis: the consequence added in v1.11 is unconditional,
Section 4 no longer says the theorem is not formalised, and the status “Proved,
assuming Waldschmidt 1973” is gone from Appendix A. It brings Schneider’s
eighth problem — at least one of e^e and e^(e²) is transcendental — and the
e^(π²) statement with it. No new mathematics is claimed, the mirrored library
stands at 283 results, and
prove2me-logs carries the same day
from the research side
(22c5195).