Knowledge Compounding: An Empirical Economic Analysis of Self-Evolving Knowledge Wikis under the Agentic ROI Framework

Building on the Agentic ROI framework proposed by Liu et al. (2026), this paper introduces knowledge compounding as a new measurable concept in the empirical economics of LLM agents and validates it through a controlled four-query experiment on Qing Claw, an industrial-grade C# reimplementation of the OpenClaw multi-agent framework. Our central theoretical claim is that the cost term in the original Agentic ROI equation contains an unexamined assumption -- that the cost of each task is mutually independent. This assumption holds under the traditional retrieval-augmented generation (RAG) paradigm but breaks down once a persistent, structured knowledge layer is introduced. We propose a dynamic Agentic ROI model in which cost is treated as a time-varying function Cost(t) governed by a knowledge-base coverage rate H(t). Empirical results from four sequential queries on the same domain yield a cumulative token consumption of 47K under the compounding regime versus 305K under a matched RAG baseline -- a savings of 84.6%. Calibrated 30-day projections indicate cumulative savings of 53.7% under medium topic concentration and 81.3% under high concentration, with the gap widening monotonically over time. We further identify three microeconomic mechanisms underlying the compounding effect: (i) one-time INGEST amortized over N retrievals, (ii) auto-feedback of high-value answers into synthesis pages, and (iii) write-back of external search results into entity pages. The theoretical contribution of this paper is a recategorization of LLM tokens from consumables to capital goods, shifting the economic discussion from static marginal cost analysis to dynamic capital accumulation. The engineering contribution is a minimal reproducible implementation in approximately 200 lines of C#, which we believe is the first complete industrial-grade reference implementation of Karpathy's (2026) LLM Wiki paradigm.