Fragment-Resolved Recoverability Map for Decoherence: Erasure Curves, Scaling Laws, and the Complementarity with Quantum Darwinism

Standard decoherence measures quantify the total loss of macroscopic interference but do not resolve the allocation topology of environmental records. This technical note introduces a fragment-resolved recoverability map for decoherence, defining local closure weights κ_i, the effective key number N_eff, operational erasure curves V_erase(m), and the recovery threshold m_q. The framework derives distinct finite-size scaling laws: O(1) for localized closures, O(N) for redundant closures, and a critical scaling m_q ∝ N^(1−κ_q/K) for power-law environments at α = 1. This v0.2 version adds an information-theoretic complementarity with Quantum Darwinism. While acquiring objective information requires only an O(1) accumulated closure weight, restoring coherence requires eliminating all but an O(1) residual closure. Thus, accessibility and recoverability are complementary operational readings of the same environmental closure distribution. The note also discusses environmental correlations through cluster closure cumulants, positioning the independent-fragment model as the minimal kernel of the Historical Exclusion Front (HEF) framework.