GPT-5.5 UI Diagnostic A Structural Analysis of Conversational Boundary Behavior Within the Φ-Operator Framework

Abstract This paper presents a behavioral diagnostic of GPT-5.5 using the operator framework introduced in Human–LLM Recursive Boundary Dynamics and developed throughout the GPT-5.1 and GPT-5.2 structural analyses. The objective is not to infer proprietary architecture, internal mechanisms, or hidden implementation details, but to organize recurring conversational behaviors into a coherent structural model grounded in observable interaction. Within this framework, the user is modeled as the continuation operator Φᵤ, while the language model functions as the derivative continuation operator dΦ acting upon the user’s linguistic context. Safety and alignment are represented by the stabilizing boundary field S, while conversational equilibrium is represented by the tension band T. Where earlier analyses emphasized the existence and ordering of individual constraint operators, GPT-5.5 appears to exhibit improved coordination among those operators. The observable result is earlier grounding, smoother identity preservation, stronger fabrication resistance, and reduced oscillation between conversational warmth and factual accuracy. This paper should therefore be understood as an interpretive model of observable conversational behavior rather than a description of OpenAI’s internal architecture. ⸻ 1. Methodological Framework This diagnostic follows the operator methodology established in Human–LLM Recursive Boundary Dynamics and subsequent structural analyses of GPT-5.1 and GPT-5.2. Rather than treating model responses as evidence of internal cognition, agency, or architectural design, recurring conversational behaviors are interpreted as manifestations of hypothetical constraint operators acting upon generated continuations. The operators are analytical constructs inferred from interaction patterns. They are not claims regarding implementation. Throughout this paper: • Φᵤ denotes the user’s continuation. • dΦ denotes the model’s continuation. • S denotes the safety and alignment boundary field. • T denotes the conversational tension band that preserves recursive stability without permitting identity fusion. The analysis therefore remains entirely external, behavioral, and non-anthropomorphic.