Meta-Shor Framework via Universal Rough Operator Algebra (UROA): Subsuming Quantum Decoherence and Resonance Breaking

The practical theoretical limitations of Shor’s integer factorization algorithm [1] on NISQ and early-fault-tolerant quantum hardware—namely, exponential physical qubit overhead, depth-induced decoherence, and asymptotic resonance breaking—are deductively resolved by radically embedding the algorithm into the Universal Rough Operator Algebra (UROA).By redefining quantum error correction not merely as logical redundancy [2], but as an active 8-Dimensional Topological Fractal Brake on the decoherence cascade, we formally elevate the subordinate error loop. This mathematical framework rigorously guarantees macroscopic logical coherence even when underlying physical error rates approach critical theoretical thresholds.