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Companion note, version 1.19
Version 1.19 adds two remarks from a check of the 24 September literature sweep.
- Remark 2.3. Kirby's weak form of Schanuel's conjecture (J. Kirby, Variants of Schanuel's conjecture, arXiv:1801.08765, Conjecture 1.5) forces Im u ∈ πℚ at a candidate. So under it Diaz's conjecture is equivalent to statement (ii) of Theorem 3.5: t² + π² is transcendental for every real t ≠ 0 with e^t algebraic. The weak form says nothing about that statement itself, nor about (S). This reduction was not found in the sources read.
- Section 4. For 2×2 matrices, the extension of the Matrix Coefficient Conjecture to ℚ + ℒ that Dasgupta and Kakde expect is the sharp four exponentials conjecture with rational constants (Waldschmidt, Hopf algebras and transcendental numbers, p. 4). It would settle the candidates with |u|² ∈ ℚ, and (S) for rational γ.
No new formal results; the mirrored project still holds all 359.