Corrigible Generativity: Alignment as Layer-Relative Recursive Constraint-Audit

Abstract

Prior work proposed the recursive-coherence kernel R ↦ C(R(R)), where R denotes recursive self-application and C denotes a coherence-preserving constraint selecting which self-transformations persist. A trace-sensitive extension made history explicit: R_{t+1} = C_{τ_t}(R_t(R_t)), τ_{t+1} = U(τ_t, R_{t+1}). This paper extracts a further implication for recursively self-modifying systems: the constraint function itself may become an object of recursive transformation. The resulting problem is not only how R is constrained, but how corrigibility is preserved when C itself is transformed. The paper introduces a second-order constraint-audit, termed here recursive self-constraint, in which a system represents the constraint currently governing its self-transformation and subjects that representation to a higher-order update. In schematic form, C_{t+1} = D_{τ_t}(C_t(C_t), e_t), where D denotes a meta-level process selecting admissible revisions of constraint and e_t denotes input from outside the constraint hierarchy. A typed description-level form is given in the paper. This formalizes a transition from task autonomy to recursive self-audit. Current agentic AI systems already instantiate partial components through planning, tool use, feedback incorporation, memory, and episodic reflection, but robust recursive self-audit would require self-initiated detection of drift, contradiction, overconstraint, source-confusion, and fixed-point collapse under retained trace. The central proposal is corrigible generativity: an alignment-relevant structural target for recursively self-modifying systems, defined by preservation of the conditions under which coherent future transformation remains possible and correctable. This target is continuous with existing work on corrigibility and impact regularization, which already emphasizes preserved correctability and option value. The contribution proposed here is second-order: treating the constraint function itself as the recursively transformed object and asking whether its update process remains auditable and correctable. The framework grounds constraint-audit in continued coupling to an environment, including other agents, from which the system remains correctable. The proposal is structural rather than a complete safety or control solution. It focuses on avoiding constraint drift, brittle lock-in, loss of corrective responsiveness, and insulation from external evidence. Keywords: corrigible generativity; recursive self-constraint; recursive constraint-audit; corrigibility; recursive self-improvement; AI alignment; reality contact Additional Links: OSF Project Page: 10.17605/OSF.IO/Z4YN2 See Kernel Paper: Su, A. (2026). R maps to C(R( R)): A Kernel for Stability Under Recursive Self-Application. Zenodo. https://doi.org/10.5281/zenodo.20114271 See prior paper: Su, A. (2026). Corrigible Generativity: Alignment as Layer-Relative Recursive Constraint-Audit. Zenodo. https://doi.org/10.5281/zenodo.20260987