A Formal Model for Corrigibility

This paper presents a unified, recursive framework for modeling both intentional and unintentional corrigibility (and incorrigibility) of intelligent systems at arbitrary orders of intelligence (denoted N). We ground the model in a well‑scoped domain object D, define a single functional state‑space X and a tagged family of update operators F with order labels, introduce user and agent fitness functions, and give a parametric definition of Corrigibilityₙ. We then distinguish unintentional vs. intentional incorrigibility, embed the model fractally so it applies to its own revisions, and outline theorems (base case, inductive step, alignment, intentionality lemma, resource‑failure detection) that underpin formal proofs of closure and stability at every order.