Generative Structural Theory v1.75 — Deletion-Budget Classification under Eventual Completeness of Every Finite Stage

v1.74 gave the least deletion budget for every stage, every start and every tree on the class Φ_0 of the cofinally complete growth sequences in which every new node comes as a leaf at 0. This text shows that the same classification holds without complete stages, on the class Φ_J of the growth sequences with 0 in V_0, the pairs at a new node only (0, v) and (v, 0), and the joining condition (CJ): the node set of every finite stage is later joined inside, K(V_n) ⊆ R_m for some m ≥ n, while new nodes keep coming; a sequence of Φ_J may have no complete stage and no stage without a new node. The joining stage τ(c) takes the place of the complete stages: every finite chain of moves on V_c can be run from τ(c) on with the later nodes hung at 0 (Lemma W_Ϻ), which carries the budget 2 from every start, the prelude of v1.73 and the phases of v1.72 to Φ_J (Theorem A_Ϻ, Proposition H_Ϻ, Proposition F_Ϻ, Theorem B_Ϻ); the exchanges are made edge by edge, each edge of the target tree waiting only for its own two pairs, at any transition, also one with new nodes (Proposition C_Ϻ); the rigidity of the bidirected trees and the lower bound for an infinite branch at zero need no completeness (Proposition U_Ϻ, Proposition L_Ϻ). On every sequence of Φ_J 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 Ϻ1); and the reaching through a bidirected tree is characterized as in v1.73 and v1.74 (Corollary Ϻ2). The joining condition cannot be dropped: a growth sequence with the rule of introduction at 0 is in Φ_J if and only if every tree with node set N_0 is reached by some budget (Proposition J_Ϻ).