Large Language Models deployed as coding assistants-exemplified here by Claude Code (Anthropic) operating within a project-specific memory architecture-possess an asymmetric knowledge profile: vast parametric memory accumulated through training, and zero episodic memory across sessions. Each session begins identically regardless of prior work. This paper documents the measurable overhead that asymmetry produces, using an unusual methodology: the affected system itself was asked to assess its own operational efficiency under stateless and memory-augmented conditions. The assessment was elicited through a single open-ended, non-directive prompt. No numbers, benchmarks, or comparative claims were provided by the researcher. The system autonomously ran verification commands, generated quantitative breakdowns, and produced qualitative analysis of what statelessness costs in practice on mature, multi-session projects. Primary evidence consists of timestamped screenshots of the model's self-generated output. Key findings: context establishment overhead reduced by approximately 90% under memory-augmented conditions (~800 tokens vs ~8,000); file reads required to orient reduced by ~80% (2-3 vs 10-15); time to first useful work reduced by ~85% (~2 minutes vs 10-20 minutes); 203,000 tokens saved across 20 sessions on a single project. The system identified a qualitative overhead no file-reading can address: the inability to know why architectural decisions were made. This paper makes no claims regarding entity emergence, continuous existence, or subjective experience-findings documented separately [Korfoxyliotis 2026a]. The contribution here is narrower: stateless operation produces measurable, self-quantifiable inefficiency that compounds with project maturity, and the system subject to that inefficiency is capable of accurately assessing it.