Generative Structural Theory v1.97 — Residual Infeasibility with No Additional Core Deletion

(Q30) of v1.96 asks whether, for the one-sided re-hangings of a transit leaf studied since v1.91, at an input with D = ∅ (no pair of the core h0 deleted in addition to the re-hanging, which itself deletes one pair of h), every undecided stop of the forcing procedure of v1.92 has a feasible set, that is, by v1.96 Lemma ϧ1 (d), a route from a to b whose pairs in R hold no relative obstruction. This text answers it "no". The input J10 on ten nodes (a minimal relation h of eleven pairs, a tree S, the leaf l = 3, side 1, D = ∅) meets every condition of an input; the procedure stops undecided at (U, ∅), and no set B ⊆ U is feasible, by a symbolic argument from three nested terminal cuts and four relative obstructions, each a route written out (Proposition ϩ4). The probing rule of v1.94 decides this stop "impossible", so J10 is not an input with a missed impossible stop, and (Q27) of v1.93 is not answered by it. Proved for every input with D = ∅: a pair of R joining the nodes reached from a to the nodes from which b is reached gives a feasible set, so that a feasible set exists whenever the least number k of pairs of R on a route from a to b is 1 (Lemmas ϩ1-ϩ3). J10 has k = 3, and it decides feasibility for its leaf, side 1 and D = ∅ only. Findings of finite cases and of draws (no ground for a general statement): in a search whose parts were fixed before they were run (finite check 27), every undecided stop with D = ∅ has a feasible set among every minimal relation on five labelled nodes and every class representative on six nodes, each with every labelled tree (6000 and 4384 stops), and in samples of random draws on eight and nine nodes (65518 and 59731 stops; draws not made distinct); in a sample on ten nodes all but one of 50489 do, the one being J10. With the population of v1.93 on seven nodes or fewer, no such stop is known on seven nodes or fewer; whether one exists on eight or nine nodes is not settled, and J10 is not claimed to be one with the least number of nodes. The new question (Q31) asks whether the probing rule decides "impossible" at every undecided stop with D = ∅ and no feasible set; a "yes" would answer (Q27), restricted to D = ∅, "no". (Q27) and (Q28) of v1.93, (Q29) of v1.95, (Q31), (Q22) of v1.88 and (Q1) of v1.76 are open.