BU75 AAI-07 | Full-Domain Surjective Closure Ecology Interface Demand Streams, Concurrent Windows, and Continuous Settlement of Real-World Chains

This paper develops BU75 AAI-07|Full-Domain Surjective Closure Ecology Interface as the seventh file in the B_U-based Agentic AI series. Its central claim is that the next phase of Agentic AI will not be defined by isolated agents, single-app automation, or local workflow orchestration, but by a full-domain surjective closure ecology interface that maps real-world demand streams into multiple concurrent closure windows and settles them continuously in reality. The paper defines a demand stream as a sequence of user intentions, time windows, locations, resources, preferences, permissions, risks, costs, and feedback events. A simple user request—such as taking a flight, shopping, dining, and checking into a hotel—already contains a multi-window scenario graph: transport, routing, booking, reservation, arrival, reception, payment, exception recovery, and user confirmation. In this structure, the user no longer manually assembles separate software operations. The user expresses high-level intent and confirms key nodes, while the closure ecology aligns people, goods, places, time, money, permissions, routes, bookings, feedback, and contingency handling in one continuous settlement surface. BU75 further distinguishes this process from ordinary prediction. Pre-arrangement is not mystical foresight or speculative forecasting. It is pre-settlement: known constraints, available resources, route options, reservation slots, time buffers, risk gates, and confirmation nodes are projected into the same closure ecology before the activity occurs. Uncertain parts remain as dynamic reconfiguration windows. This reduces time residuals, resource conflicts, route errors, booking mismatches, and coordination costs before they become operational failures. The paper reframes Agentic AI from software operation to real-world chain settlement. Full-domain surjection means that every admissible demand node can be mapped to at least one closure or closure composition. Continuous settlement means that each action, feedback signal, delay, confirmation, and exception updates the scenario graph and the shared ledger. The final judgment is that Agentic AI’s real-world value lies in moving requirement–production alignment toward finer granularity, real-time responsiveness, and co-temporal settlement across the full activity chain.