Current approaches to AI-generated user interfaces treat them as disposable artifacts: each generation cycle produces a static snapshot that discards all previous state. We present PLASMA (Persistent Living Application Surface for Mutating Agents), an event-sourced protocol that enables conversational AI agents to create, evolve, and maintain interactive web applications through incremental mutations. In PLASMA, an agent does not generate a UI and deliver it as a finished product. Instead, it creates an organism that accumulates changes over time, preserving complete history while remaining responsive to conversational intent. The protocol defines a file-based representation where an initial application state (HTML, CSS, JavaScript, and activity declarations) is followed by a sequence of JavaScript-only mutation files, with periodic mechanical snapshots for loading performance. A bidirectional activity system routes user interactions from the rendered surface back to the agent as natural-language-formatted messages, closing the loop between visual interface and conversational context. We describe the protocol design, its implementation within two deployment environments (the Hera multi-channel agent gateway and Claude Desktop/Cowork), and report on a series of experiments conducted during real-world use, spanning data tools, enterprise integration, scientific analysis, and agentic self-tooling. PLASMA demonstrates that event sourcing, a well-understood pattern in database systems, transfers effectively to agent-generated interfaces, offering an alternative to the regeneration-based paradigm that currently dominates AI UI generation.