Queue Isomorphism and the Local Lipschitz Reduction for Selection Cost / 选择代价的排队同构与局部 Lipschitz 归约

Full bilingual text and framework available at self-as-an-end.net Paper XXI in the ZFCρ series establishes an exact algebraic isomorphism between the DP recursion defining ρ_E and the Lindley equation of G/G/1 queueing theory, and reduces the Local Lipschitz property (Var(A | Ω(n) = k) = O_k(1)) to three explicit input conditions. Core discovery (Theorem 1): the defect D_n = M_n − ρ_E(n) satisfies exactly D_{n+1} = max(D_n + ΔM_n − 1, 0). This transforms variance analysis of the DP recursion into a classical queue stability problem. Conditional Theorem (Theorem 3): if (0) the global Lindley process has bounded variance, (I) the shell-sampled one-step global gradient has bounded variance, and (II) the predecessor defect has bounded variance on Ω-shells, then Var(A | Ω = k) = O_k(1). All three conditions have overwhelming numerical support (N = 10^7, 11 shells cross-validated) but their complete analytic proofs are deferred. Key results: Theorem 1: Lindley Identity — exact algebraic isomorphism (proved) Corollary 2: Memory Wipe — queue empties at every jump point (proved) Theorem 3: Conditional Local Lipschitz (proved, conditional on (0)(I)(II)) Discovery: Cov(ΔM, D) < 0 across all shells — anti-correlation engine at the gradient level Consistency verification: Var(G) = Var(ΔM + D) confirmed to 4 decimal places across 11 shells The definitive contribution is the queue isomorphism itself and the precise reduction framework. Together with Paper 20 (B-bound, M10), this paper completes the architectural framework for G_spf variance control. Keywords ZFCρ, remainder theory, selection cost, Local Lipschitz, queueing theory, Lindley equation, variance boundedness, DP recursion, conditional theorem, Kingman stability, prime factorization Related identifiers Paper 1: 10.5281/zenodo.18914682 (IsPartOf) Paper 2: 10.5281/zenodo.18927658 (IsPartOf) Paper 16: 10.5281/zenodo.19013602 (Continues) Paper 19: 10.5281/zenodo.19026991 (Continues) Paper 20: 10.5281/zenodo.19027893 (Continues)