Fractal-Temporal Model of Computational Hardness_

Abstract Background: The P vs NP problem resists formal resolution due to established proof barriers. We propose the Temporal Expansion Hypothesis (TEH): computational hardness emerges from differential time flow between verification paths (low-entropy "voids") and solution paths (high-entropy "clusters"), analogous to Timescape Cosmology's inhomogeneous expansion. Methods: Using the Constructive Fractal Methodology (CFF), we apply the Fractal Iteration Log (FIL) to restructure P vs NP and the Interdisciplinary Translation Protocol (ITP) to import Timescape architecture. Empirical validation uses seeded 3-SAT (n=5-13) and RSA factorization (20-36 bits). Results: Structural 3-SAT solvers empirically track Fibonacci geodesics (φ^n scaling, Gap Ratio 0.74-0.76). RSA Pollard's Rho demonstrates N^(1/4) vs N^(1/2) erosion (15-300× speedup). Both confirm void/cluster time dilation. Conclusions: TEH reframes complexity as continuous gradients rather than binary classes. While not resolving formal P≠NP, it provides actionable parameterization of hardness erosion for cryptographic engineering. Further empirical scaling and theoretical formalization required. Keywords: computational complexity, time dilation, fractal methodology, cryptographic erosion, analogical reasoning