Generative Structural Theory v1.74 — Deletion-Budget Classification for Cofinally Complete Growth Sequences with Leaf Introductions at Zero

v1.73 gave, on the sequence E of v1.63 Example Φ2, the least deletion budget for every starting stage, every start in M_{s_0} and every tree with node set N_0. This text shows that the same classification holds on every sequence of the class Φ_0 of the cofinally complete growth sequences with 0 in V_0 in which every new node v comes with the pairs (0, v) and (v, 0) only, any finite number of nodes coming at once and stages with no new node allowed, with no timetable of introductions and complete stages. The members of M_{n+1} are the minimal strongly connected relations on V_n contained in R_{n+1} with the new nodes hung at 0 (Fact O_Ϸ); with it the rigidity of the bidirected tree starts, the exchanges, the budget 2 from every start and the lower bound for a tree with an infinite branch at zero carry over from v1.65, v1.66 and v1.68 (Proposition U_Ϸ, Proposition C_Ϸ, Theorem A_Ϸ, Proposition L_Ϸ). For budget 1, every group of moves among the nodes of a set V_c waits for a complete stage c, after which K(V_c) lies in every relation, and the nodes that come in the meantime are hung at 0; so the prelude of v1.73 and the phases of v1.72 run on Φ_0, the auxiliaries of a phase being the two least nodes larger than those it uses (Proposition H_Ϸ, Proposition F_Ϸ, Theorem B_Ϸ). On every sequence of Φ_0 the least budget is 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 Ϸ1); and the characterization of v1.73 of the reaching through a bidirected tree term holds there too (Corollary Ϸ2). The statements concern the class Φ_0, not every cofinally complete growth sequence.