Generative Structural Theory v1.109 — Alternative Moves at Certified Local Obstructions under Deletion Budget Two

This version provides explicit complete chains for two fixed eighteen-node inputs, M1 and M12, each possessing a certified local obstruction to a one-sided leaf move. Versions v1.107 and v1.108 established that, for each of twelve fixed candidate records M1–M12, the choice of leaf 3, side 1, with D = ∅ has an undecided stop with no feasible set, first detected at probing depth six. Such an obstruction excludes a move of that particular form; it does not by itself exclude a complete chain satisfying (Q1). For M1, a chain starts with a move at leaf 3, side 0 and consists of 12 states and 11 transitions. For M12, a chain starts with a move at leaf 1, side 1 and consists of 14 states and 13 transitions. Each chain runs from the original relation h to P_S, the relation containing both directions of every tree edge. Every state lies within h ∪ P_S and is strongly connected and inclusion-minimal. Every transition deletes at most two directed edges. Both chains were checked by two implementations, including a separate implementation reading the inputs from the original candidate records. Altered-chain controls test the detection of nonminimal states, edges outside the allowed relation, excessive deletions, and an incorrect endpoint. These are computational checks within the preparation of the work, not third-party independent verification. For M12, the limited construction found no chain from the initial move at leaf 3, side 0, but found one from leaf 1, side 1. This comparison concerns the outcome of the specified construction and witness-selection rules; it does not establish that no chain exists from the former initial move. The result establishes that certified local infeasibility and the existence of a complete chain under deletion budget two are compatible for these two fixed inputs. It does not settle (Q1) in general, establish corresponding chains for the other ten candidates, prove shortest chain lengths, or show that deletion budget two is necessary. The supplement supplies the complete inputs, all chain states and transitions, verification results, and SHA-256 records. The accompanying ZIP contains the text versions and a self-contained verification appendix with input data, chain files, checking scripts, controls, and reproduction instructions. The checking scripts use only the Python 3 standard library; the documented commands assume a shell providing python3, sha256sum, and mkdir.