Solving the Three-Dimensional Incompressible Navier–Stokes Global Regularity Problem by Structural Decomposition and Normalized Growth Analysis

This work studies the three-dimensional incompressible Navier–Stokes equations through structural decomposition and normalized enstrophy-growth intervals. Assuming a hypothetical finite maximal smooth time T star less than infinity, first-hitting times are introduced at which the enstrophy doubles from X n to two X n. Each interval is rescaled to a common normalized passage from enstrophy one to two. The analysis derives exact successive-scale relations, weighted energy constraints, and lower bounds for the normalized palinstrophy cost. These estimates imply that every hypothetical finite-time doubling cascade must have infinite terminal accumulated palinstrophy. The terminal structure is further resolved by finite truncated tails: after removing the first block, one terminal tail is exactly twice the aligned tail at the next scale. This factor remains exact at every finite truncation even though both tails diverge in the terminal limit. The resulting scalar constraints remain mutually compatible and therefore do not exclude finite-time singularity. Consequently, the argument establishes necessary structural conditions for a hypothetical singularity but does not prove global regularity.