diaz-modulus-lean: notes 1.13 to 1.15 — Roy's strong six exponentials, and the route that stops at u³

Three more companion-note versions landed on 1 October, taking the mirrored library from 283 to 307 results. The companion note reached v1.13 (293 results) with the consequences of Roy’s strong six exponentials theorem that are now machine-checked — Diaz’s Corollaires 1, 2, 4 and 5 of the 2007 paper in general, and at a candidate the facts that u³ and axis multiples leave ℒ̃, so e^(βπu) is transcendental (f3c56f5). v1.14 (304) then takes all of Section 2 of Diaz 2007 under the same hypothesis, and pins down where that route stops: a strong six exponentials configuration fed with a candidate’s own data exists only for k = 2 and 3, so the theorem excludes u² and u³ from ℒ̃ and no higher power (2c75c4b). The day closes at v1.15 (307), where the strong four exponentials conjecture plus Baker’s theorem implies the sharp four and that implies Waldschmidt’s strong five, and Waldschmidt’s 1988 remark is corrected to compare the strong five with the sharp four rather than with Conjecture 1.2 (631d51f). No new mathematics is claimed, and prove2me-logs carries the same day from the research side, down to a note that Brownawell 1974 is “related by the exponential function” (d89c37f).