Companion note, version 1.15

Version 1.15 records what the third batch of 1 October 2026 machine-checks. Each result carries a conjecture as a hypothesis.

• The strong four exponentials conjecture (Conjecture 1.2), with Baker's theorem, implies the sharp four exponentials conjecture, and that one implies Waldschmidt's strong five exponentials conjecture. Item (2) of Section 7 is corrected: Waldschmidt's 1988 remark that the strong five is "clearly" weaker compares it with the sharp four (that paper's "strong four"), not with Conjecture 1.2. The order the list claims now has a proof.
• The second open statement on p. 399 of Waldschmidt's book follows from Conjecture 1.2 in full, without Baker's theorem: if λ ∈ ℒ ∖ {0} and |u|, e^{uλ} are algebraic, then u ∈ ℚ or uλ/λ̄ ∈ ℚ.
• Under the strong five exponentials conjecture, (log a)(log b) ≠ log c for non-zero logarithms (Waldschmidt 1988), so e^{λ²} and e^{π²} are transcendental.
• One sentence in Section 5: the homogeneous form of the conjecture on algebraic independence of logarithms holds at a generic candidate's own logarithms u, ū, iπ, so it cannot refute a generic candidate through them.

No new mathematics is claimed. The mirrored library holds 307 results.