Exact Resolution of Cuprate High-Tc Phenomenology and Bottom-up Design of Room-Temperature Superconductors via Seonggil Theoretical Frameworks

The microscopic mechanism of cuprate high-temperature superconductivity has long been hindered by the non-perturbative nature of strong electron correlations (U ≫ t), the Fermion Sign Problem, and the inability of classical spin-fluctuation models to quantitatively predict T_c. In this paper, we unify phenomenological cuprate physics—including d-wave symmetry, the t-J model, and spin-fluctuation pairing—into the exact algebraic framework of Rough Operator Algebra (ROA) and Seonggil Matrix Theory (SMT). By mapping creation/annihilation operators to Rough Fermionic Operators and absorbing the negative sign problem into a topological Berry-like phase θ_S, we collapse the exponential O(2^N) Hilbert space complexity into a polynomial O(N^k) domain. We derive a generalized d-wave macroscopic coherence gap equation, proving that engineering lattice parameters to maximize the maximal Seonggil invariant eigenvalue λ_max(S_M) enables room-temperature superconductivity (T_c > 300K) under ambient pressure.