Certified Knowledge Editing: Closed-Form Reachability Guarantees for Additive Edits to a Frozen Language Model

Abstract

Knowledge edits to language models are usually validated after the fact. This paper studies the reverse contract: a closed-form certificate, computed before an edit is applied, of exactly which single-token edits can succeed on a frozen decoder-only language model with an additive gated memory. The certificate reduces edit reachability to one-dimensional linear feasibility, doses each edit inside its certified interval, rescues certified-unreachable targets by residual synthesis, and emits verifiable receipts. All code, experiment scripts, and result artifacts: github.com/qriton/hlm5; model weights: huggingface.co/qriton/hlm5-1b-trunk. Version 1.1.0 (2026-10-02). Changes since 1.0.0:- Residual-synthesis rescue corrected from 17/17 to 15/17 (0.882) after the 2026-08-10 exact-sign certificate refresh; abstract and conclusion updated accordingly. A gate-matched logit bias is stronger on efficacy and matches on generalization and locality.- Certificate-predicts-editors: a registered confirmatory run on 600 untouched CounterFact records (gpt2-xl; ROME, MEMIT, FT) confirms all five registered tests after Holm correction, with small effects (|rho| = 0.11-0.18).- The earlier reading that certificate features predict neighborhood damage for ROME and GRACE is withdrawn: those correlations tracked the unedited model, not the edit. Collateral is now measured against the unedited model.