Resolution of UV/IR Mixing and Cosmological Constant via Non-identity Calculus in Rough Operator Algebra

One of the most critical contradictions faced by modern quantum field theory and noncommutative geometry is the Ultraviolet/Infrared (UV/IR) mixing phenomenon. Specifically, the translation of ultraviolet divergence at extreme microscopic scales into infrared divergence at macroscopic scales, governed by the θ^4p^8 denominator term in the propagator, causes a topological collapse that conventional renormalization techniques cannot control. To overcome this anomaly, this paper introduces ’Non-identity Calculus’ anchored in Rough Operator Algebra (ROA). The divergence occurring at the ultraviolet cutoff limit (Λ_UV →∞)is geometrically canceled through the ’extreme asymmetric operation’ axiom of the non-identity derivative operator (∇_non-identity) without relying on inverse operations or arbitrary fine-tuning. Consequently, this study proves the isomorphism of macroscopic and microscopic scales within a single tensor field and reveals that the residual effective densityof dark energy, corresponding to the cosmological constant (∼ 10^−47 GeV^4), is naturally derived as an algebraic inevitability.