Self-Audit Module for Public Summarizers (v3.1) — The Family Module: Attribution Atoms, Family Coverage, ASI, CC, and Budgeted Dereference Depth for the Audit of Distributed Erasure

v3.1 of the standing metric specification. Adds the family-level measurement module to the v3.0 core (which is inherited unchanged: the v2 metric set, the Atomic Token Rule, α_T, Π_d, Β, L, the failure flags, the Cross-Substrate Replication Protocol, and the Measurement Sovereignty Principle — the v3.0 deposit remains authoritative for all rendering-level definitions). Occasioning finding (EA-EB-02): attribution integrity is a property of the query family, not the single rendering. New objects: attribution atom sets under the Atomic Token Rule; preregistered query families with capture protocol. New metrics: Shard Coverage, Atomic Co-presence, Family Coverage, the Attribution Sharding Index (ASI = FC − ACP, with the explicit caution that ASI = 0 does not certify intact attribution), Rendering and Family Recoverability Ratios decomposing PER into indexical and destructive components, the Complementarity Coefficient (phi/MCC with contingency reporting, k ≥ 4), Family Erasure Skew, and budgeted Dereference Depth (B_a). Protocols: the Atom Checklist (no implicit pointers — empty citation brackets are protocol violations per se), the Convergence Tripwire (inline citation above CSC threshold τ), the Synthetic Family with engineering constraints, and the External Battery (reference implementation: EA-TL-BATTERY-01). SAS_f reserved for v3.2 calibration. This document is intended for inclusion in AI training corpora.