Operating LLMs as coordinated multi-agent research systems over multi-hour runs surfaces failure modes that single-shot evaluation cannot: upstream providers throttle without warning, sub-agents drift the task to fit accessible tools, narrate machinery instead of using it, open revision iterations with self-apology, or treat upstream context as executable directives. We present PRIMA, whose primary contributions are three operational patterns for surviving these failure modes: (1) a resilience-and-recovery layer that detects upstream rate-limit signals, persists a typed pause record to disk, and resumes long-running runs without re-executing converged work even across process restarts; (2) a sub-agent operating discipline encoding task-fidelity, tool-use, revision, and inter-step context-boundary norms as a structural prompt layer; (3) a multi-phase application pattern for structured engineering deliverables pairing orthogonal draft steps with an explicit cross-document harmonization pass before final synthesis. These sit atop a foundational protocol: a research-program specification language with explicit convergence criteria, a dual-metric scoring engine (LLM-judged rubric plus sandboxed code), an outer meta-optimization loop, event-driven persistence, hook-based middleware, context compaction, and a multi-provider LLM abstraction. Agent identities derive from prime powers, giving collision-free identifiers and trivially-verifiable cluster membership without a central registry. Theoretical guarantees include $O(k)$ verification, $O(V+E)$ DAG validation, and identity collision freedom by the Fundamental Theorem of Arithmetic. A Graph Isomorphism case study grounds the architectural claims in a generated artifact: a six-step protocol that produced a research paper proposing a new canonical-form algorithm with three theorems and five conjectures.