Generative Structural Theory v1.73 — Unit-Budget Reachability of Trees with Finite Branches at Zero from Non-Bidirected-Tree Starts on the Cofinally Complete Growth Sequence E

v1.72 showed that on the sequence E of v1.63 Example Φ2, from the directed triangle y = {(0, 1), (1, 2), (2, 0)} at the stage 0, budget 1 reaches every tree T with node set N_0 all of whose branches at zero are finite, and left the other starts open. This text shows that on E budget 1 reaches every such tree from every start y' in M_{s_0}, at every stage s_0, that is not a bidirected tree, with L = U = P_T and no bidirected tree term. A cycle state is a directed cycle of at least three nodes with a bidirected forest hung at its nodes, one component at each. The ear reduction of v1.66 Proposition B_Δ, begun at a pair of the start whose reverse is not in it and stopped before its last step, leads to a cycle state (Lemma Y_Ϛ); shortenings, each removing a node of the cycle, and slides, each bringing into the cycle a node joined to it in the forest, lead to a triangle state X(H; p, q) of v1.71 (Lemma Z_Ϛ, Lemma T_Ϛ). Each shortening deletes exactly one pair. Each slide consists of a pull and a retire, each deleting exactly one pair. The pull and the retire of v1.71 Lemma M_Ϟ (b) and (c) exchange one pair for one pair, so the rounds of v1.72 Lemma G_Ϝ run backwards take a branch at zero apart (Lemma R_Ϛ), and after a switch of the core nodes to two leaves at 0 every other node is brought to 0, a star triangle state (Lemma W_Ϛ). On E, with the new nodes hung at 0, this is a finite prelude (Proposition A_Ϛ), after which the phases of v1.72 run unchanged (Proposition S_Ϛ, Theorem B_Ϛ). With v1.65, v1.66 and v1.68 this gives the least deletion budget on E for every start and every tree: 0 from a bidirected tree P_S to S*, the tree S with every later node hung at 0; 1 from a start that is not a bidirected tree to a tree all of whose branches at zero are finite; and 2 otherwise; each attained with L = U = P_T (Corollary Ϛ1). From a start that is not a bidirected tree, a tree is reached with budget 1 through a bidirected tree term exactly when it has finitely many edges not incident with 0 (Corollary Ϛ2). The statements concern the sequence E only.