This arXiv preprint (not yet peer-reviewed) employs a fully analytical Fourier-based method on the infinite square well to derive closed-form asymptotics for interference in equiprobable high-n eigenstate superpositions. Unlike numerical simulations common in prior studies, the authors expand quantum Fourier coefficients into geometric series, proving that individual rho_alpha^a(x) envelopes persist but converge uniformly to the classical uniform distribution as Delta approaches infinity for 2Delta+1 states. Dynamically, position expectation values recover the exact triangular classical trajectory, with quantum residuals confined to vanishing boundary layers under macroscopic scaling. This rigorously realizes Bohr's correspondence principle in an isolated bound system at high energies, a regime often overlooked in decoherence-focused literature such as Zurek's 2003 work on environment-induced transitions. What prior coverage misses is the absence of external mechanisms here: the emergence is intrinsic and exact in the asymptotic limit, challenging assumptions that classicality always requires many-body interactions or measurement. Limitations include restriction to one-dimensional infinite wells and the mathematical large-n idealization, with no experimental validation provided.