Is Retraining Enough? Coordinated Local Editing for Certified Vertical Federated Unlearning

Vertical federated unlearning (VFU) removes a departed party's feature block from a model jointly trained by institutions holding different features of one population. VFU faces a distinctive obstacle: feature blocks are correlated across institutions, so retraining leaves a predictable share of the departed signal in the retained encoders. Current methods edit inside the task objective and settle at the level retraining attains, and they certify model parameters rather than the embeddings, read-out and caches an auditor reads. To address these, we first establish a two-floor separation: the recoverable share splits into a task-required part and a free part whose removal locates an encoding-layer floor beneath the task-objective floor. We then design CLEAVE, a Coordinated Local Editing framework for Attested Vertical Erasure. Within this framework, Residual Splitting measures the joint residual from statistics the active party already holds and separates task-required from removable directions. Coordinated Local Editing then solves one block-diagonal edit that hands each retained party a local adapter, so no party combines features held by others. In addition, State Purge and Certification refits the read-out, purges the requested state and certifies leakage for a declared decoder class and audited interface. Across three datasets, four deletion granularities and thirteen published baselines, CLEAVE most consistently lowers the recovered share and the issued level while retaining utility close to retraining in one communication round. For example, on Letter under party unlearning, CLEAVE lowers the recovered share from 0.727 under retraining to 0.331 at higher utility.