Local number variance as a causal handle in the one-dimensional Bose-Hubbard chain

We test whether the local occupation variance Fᵢ= nᵢ²- nᵢ² identifies causally effective intervention sites in a one-dimensional open Bose-Hubbard chain under Lindblad dephasing. Additional dephasing at the top-k highest-Fᵢ sites is compared against matched-budget random targeting across 100 independent trials per condition, using exact Lindblad evolution in the fixed-particle-number sector (L6, 7, 8, 1, 2, 3). The primary sweep reveals three regimes: at J/U=0. 12 targeted intervention is harmful; near J/U0. 20 there is a crossover sensitive to system size and horizon; and at J/U0. 30 targeted intervention is reliably beneficial, with 95% confidence intervals above zero at every tested (L, ) combination. Controls using disorder, shell-matched permutations, deterministic tilt chains, and extra-dephasing-rate scans show that the effect is not reducible to geometric centrality, shell position, mean occupation, disorder amplitude, or a tuned intervention strength. Because the systems are small enough for exhaustive enumeration, we rank the Fᵢ-selected subset against all Lk possible intervention subsets; in the positive-pocket regime it lies at the top of the subset-response distribution and the conclusion survives signed, absolute, and redistribution-based target definitions. Finite-difference susceptibility analysis shows that Fᵢ is not a local-depletion susceptibility but a redistribution susceptibility: high-Fᵢ sites are those where small extra dephasing most strongly perturbs the global occupation pattern. Thus, within the tested finite chains, local number variance functions as a regime-dependent redistribution handle for targeted dephasing.