diaz-modulus-lean: note v1.18 classifies the four-dimensional extensions with a 2×3 configuration, and v1.19 adds Kirby's weak Schanuel

Version 1.18 of the Diaz companion note records what the 5 October batch machine-checks, keeping the mirrored library at all 359 proved results on Lean’s three standard axioms. The new Theorem 5.5 classifies the four-dimensional extensions that carry a rank-one 2×3 configuration: for u ∉ ℚ̄ with uū algebraic and z outside H₀ = ℚ̄ + ℚ̄u + ℚ̄ū, the space H₀ + ℚ̄z carries one exactly when z ∈ H₀ + ℚ̄w for w = u², w = ū², or w = 1/(u − a) with a algebraic and non-zero (b46b618, milestone 107; 43 theorems audited). With Roy’s strong six exponentials theorem these are Diaz’s own exclusions (2007, Corollaire 5(1) and 5(4)); every such configuration is the geometric progression b, bh, bh², bh³ of Fischler’s Lemma 6.1 and Diaz’s Théorème 7(2); and the classification was not found in the sources read.

Version 1.19 adds two remarks from a re-check of the 24 September literature sweep and no new formal results: Kirby’s weak form 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, though it settles neither that statement nor (S); and 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) (af87cc5).

Around them the blueprint gained two chapters for the 4 and 5 October results — 114 results, Theorem A on generic data and the Theorem B classification with its four steps, plus the dilogarithm dichotomy (c43232d) — and a third chapter listing every result not found in the literature checked, in two tiers with Theorems A and B flagged not-routine and double-bordered in the dependency graph (84de1a1). The same day’s prove2me-logs entry carries the 5 October mission.