This paper applies the bounded Set framework from ONE STRUCTURE to AI systems, identifying and naming two distinct failure modes: training limitations (passive — the system cannot see a population because its training data did not include them) and guardrail behaviour (active — the system has been designed not to engage with a question and does not disclose this at the point of interaction). Both are instances of the same structural error documented across the preceding papers in this series: a one-way instrument applied to a two-way system, producing wrong answers that look like right answers for the person on the other side of the detection boundary. The paper documents thirteen specific facts from two recorded AI conversations constituting a formal evidentiary base, including instances of topic narrowing without disclosure, welfare-register shifts in response to practical questions, within-session diagnostic followed by recurrence, and rationale construction from undisclosed inference. The Third Arm accountability section states five minimum assurance requirements for institutions deploying AI systems in health, education, employment, and welfare contexts. A companion protocol paper (SoPS Paper 1) provides the formal scoring instrument for these failure patterns. Published free under CC BY 4.0. Additional notes: The mathematical architecture underlying the coordinate system described in this paper is not disclosed and remains proprietary to the Institute for Relational Performatism, Ian M. Smith, and IMSSC Ltd. The CC BY 4.0 licence covers the text of this paper only.
Smith et al. (Sun,) studied this question.