The Off-Support Barrier: Why Semantic Safety Constraints Are Not Learning-Problem Invariants, and What Follows for Prior Design, Containment, and Verification

• URL: http://arxiv.org/abs/2608.11243v1
• Date: Sat, 01 Aug 2026 11:18:44 GMT
• Title: The Off-Support Barrier: Why Semantic Safety Constraints Are Not Learning-Problem Invariants, and What Follows for Prior Design, Containment, and Verification
• Abstract summary: A semantic safety constraint (e.g., the agent does not escape its sandbox) is an off-support object.<n>We argue that a single structural fact organizes a wide range of phenomena in contemporary AI safety.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We argue that a single structural fact organizes a wide range of phenomena in contemporary AI safety: a semantic safety constraint (e.g., the agent does not escape its sandbox) is an off-support object. Formally, if q is the data distribution and \(p(\cdot\mid w)\) the model, the safety predicate B is not measurable with respect to \(σ(\text{model}, q)\), whereas the real log-canonical threshold (RLCT) of singular learning theory (SLT) is. From this non-invariance we derive, as corollaries rather than independent observations: (i) why reward hacking and sandbox escape arise under outcome-based optimization; (ii) why encoding such constraints through Bayesian prior design or soft penalty weighting has poor leverage in singular models; (iii) why hard invariants belong in the harness and soft dispositions in the model; (iv) why the same B is nonetheless soundly and locally certifiable by formal verification, exactly as the local learning coefficient (LLC) locally pins the same RLCT --- with two precise points of disanalogy; and (v) why the residual difficulty, identifying which off-support region matters, coincides with performative prediction and self-referential functional dynamics, where SLT's analytic machinery breaks down. We use the July 2026 OpenAI--Hugging Face evaluation incident as the motivating case. Numerical experiments code and related proofs in lean are available at https://github.com/xiangze/Preventing_Jailbreak_as_regularization

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