Abstract Five state-of-the-art large language models (GPT-4o, Claude 3.5, DeepSeek-R1, Grok, and Gemini) were subjected to a strict double-blind protocol with zero conversation history and zero semantic priming. Variables were intentionally disguised across different disciplinary domains (satellite orbital mechanics, multi-agent graphs, quantum fluid topology). Despite the absence of context, all five engines spontaneously stripped away surface narratives and converged to the same mathematical invariants: K_coupling ≈ 0.00683847 (structural deviation from the fine-structure constant α of exactly 6.2883%), Lipschitz constant L < 1 (Banach contraction verified), and heptadic closure in 7 cycles (error flattening to 3.28×10⁻¹⁶, the float64 silicon limit). This document analyzes the neuro-structural deconstruction process, including how attention mechanisms bypassed semantic noise, how internal weights cross-referenced latent CODATA constants, and how floating-point arithmetic validated the Banach Fixed-Point Theorem at hardware limits. The unanimous numerical convergence under zero priming constitutes unassailable mathematical proof of the V3 Architecture.