Generative Structural Theory v1.104 — Depth-Four Probing on a Specified Family of One-Node Extensions of J15a

v1.103 proved, at the input J15a on fifteen nodes, an undecided stop with D empty (no pair of the core deleted in addition to the re-hanging of the leaf) and no feasible set at which the probing rule of depth three does not decide "impossible", so that a common depth d as in (Q33) of v1.99, if it exists, has d ≥ 4. This text asks whether one more node added to J15a gives such a stop missed at depth four. It fixes the family F of the one-node extensions of J15a to sixteen nodes, 5,597 labelled pairs with 30,195 choices of the leaf and the side with D empty, after a preliminary check on parts of it and before the main check, and searches all of it by a finite check run in 48 parts on two machines. The forcing procedure ends undecided at 11,341 choices; at 2,832 of these no feasible set exists, decided exactly and apart from any rule of probing. Of the 2,832, depth one first decides "impossible" at 799, depth two at 808, depth three at 515 and depth four at the other 710; the rule of depth four was run at these 710, and decides "impossible" at the 2,122 others by the monotonicity of the rule in the depth (v1.99 Lemma ϭ1 (d)). So in F every undecided stop without a feasible set is detected by depth four, and no miss at depth four is found in F. At 93 of the 710 stops some pair probed lies outside I_4 while depth four still decides "impossible". These are findings of finite checks on F only. They give no bound beyond that of v1.103, do not show that depth four suffices on other inputs or on sixteen nodes in general, and do not settle (Q33). The two implementations compared are those of the drafting side, and their agreement is not an independent verification.