Fragment-Resolved Closure Weights, Erasure Curves, and Recoverability Scaling in Decoherence

Standard decoherence measures quantify the total loss of interference but do not resolve the allocation topology of environmental records. This technical kernel formulates the Historical Exclusion Front (HEF) framework for decoherence by introducing fragment-resolved closure weights κ_i, the effective key number N_eff, and operational erasure curves V_erase(m). The recovery threshold m_q is analytically derived, revealing distinct scaling laws: O(1) for localized closures, O(N) for redundant closures, and critical scaling m_q ∝ N^(1−κ_q/K) for power-law environments at α = 1. The note also introduces a cluster closure expansion via Möbius inversion to address environmental correlations, positioning independent environments as the reference model for 1-body local erasure and interpreting inter-fragment correlations as a cascade of closure weights into higher-order joint-operation hierarchies.