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Current AI-assisted engineering workflows lack a built-in mechanism to maintain task-level verification and regulatory traceability at machine-speed delivery. Agile V addresses this gap by embedding independent verification and audit artifact generation into each task cycle. The framework merges Agile iteration with V-Model verification into a continuous Infinity Loop, deploying specialized AI agents for requirements, design, build, test, and compliance, governed by mandatory human approval gates. We evaluate three hypotheses: (H1) audit-ready artifacts emerge as a by-product of development, (H2) 100% requirement-level verification is achievable with independent test generation, and (H3) verified increments can be delivered with single-digit human interactions per cycle. A feasibility case study on a Hardware-in-the-Loop system (about 500 LOC, 8 requirements, 54 tests) supports all three hypotheses: audit-ready documentation was generated automatically (H1), 100% requirement-level pass rate was achieved (H2), and only 6 prompts per cycle were required (H3), yielding an estimated 10-50x cost reduction versus a COCOMO II baseline (sensitivity range from pessimistic to optimistic assumptions). We invite independent replication to validate generalizability.