CanonEdit: Canonical Quotient Editing

Sequential factual editing asks models to absorb requested facts over a long update stream while preserving behavior on the remaining knowledge. Yet each target specifies what behavior should change, not which parameter update should realize it. Many updates can write the same fact, but their side effects differ and can accumulate; the update retained at each step therefore shapes how long the model remains editable. We introduce **CanonEdit**, which groups updates with the same target action into quotient-space equivalence classes, measures their cost on history and unrelated prompts, and commits the least-cost representative that passes nonlinear success and protection-budget checks. This quotient-space representative selection is a target-constrained Bregman projection with a closed-form KKT solution. We prove that CanonEdit selects the successful local update with the smallest predicted protected change; under a stated budget, its feasible set retains every feasible hard-null update in the same trust region and admits additional bounded-cost directions. Across three datasets and four backbone families, seven 10,000-request streams achieve 99.24-100% online writing efficacy, 0-76 failed writes, and 99.97-100% measured specificity. These results show that quotient-space representative selection can control cumulative interference and keep models receptive to new knowledge over long update streams.