Dependency-Preserving Direct-Area Compiler and First-Order Renormalized Residual: From a 10⁻⁹ Raw Margin to R₂^fin ≈ 0.106, Rewriting the B01 Hard Core as a Conditionable Finite-Radius Residual Problem

Writes the B01 target as the exact identity A − A0 − 0.1ρ² = ρ·Φ1 + ρ²·(R2fin − 0.1). With Φ1 ≥ 0 (cited from LESR 09E) the problem reduces to inf R2fin ≥ 0.1. A global counter-search (10 DE seeds, 32,768 Sobol points) finds min R2fin ≈ 0.10608: a search, not a certificate.