AdaptiveResolver is a dynamic microservice architecture designed to address the limitations of static endpoint resolution for AI agent communication in distributed, heterogeneous environments. Unlike traditional DNS or static URLs, AdaptiveResolver enables context-aware, real-time selection of communication endpoints based on factors such as geographic location, system load, agent capabilities, and security threats. Agents advertise their Agent Name and context requirements through Agent Fact cards in an Agent Registry/Index. A requesting Agent discovers a Target Agent using the registry. The Requester Agent can then resolve the Target Agent Name to obtain a tailored communication channel to the agent based on actual environmental context between the agents. The architecture supports negotiation of trust, quality of service, and resource constraints, facilitating flexible, secure, and scalable agent-to-agent interactions that go beyond the classic client-server model. AdaptiveResolver provides a foundation for robust, future-proof agent communication that can evolve with increasing ecosystem complexity.

In equity markets, stocks are conventionally labeled by equity indices (company names). By relabeling stocks according to their ranks in capitalization, rather than their equity indices (company names), a different, more stable market structure can emerge. Specifically, we will gain a different perspective on market dynamics by focusing on the stock that occupies a certain rank in capitalization while the corresponding company name may change. We refer to a market labeled by the equity indices (company names) as a market in name space and one labeled by ranks in capitalization as a market in rank space . Market in rank space was explored by Fernholtz et al. who observed a stable distribution of capitalization across different ranks in the U.S. equity market over different time periods [11,16]. They further introduced an explanatory hybrid-Atlas model under stochastic portfolio theory, a framework that enables analyzing portfolios in rank space [5,15]. Empirically, B. Healy et al. analyzed the U.S. equity data and showed that the market in rank space is driven by a dominant single factor [14], in contrast to the multi-factor-driven market in name space [9,10,19]. While the primary market factor in rank space has been extensively studied, the residual returns - those not explained by this primary factor in stock returns - remain a fertile land of adventure.

The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main technical result is a completeness theorem for the proposed system.