Navier–Stokes Volume III: A Type-I No-Go Theorem via Strip Palinstrophy Scaling (H3)

Volume III (companion to Volumes I–II) reframes the boundary-layer palinstrophy non-concentration hypothesis (H3) as a Type-I blow-up no-go condition. We introduce the scale-invariant strip observable Φ(ε) measuring the fraction of palinstrophy captured in an ε-thin neighborhood of the high-vorticity interface. Main result (Type-I no-go): under mild tubular-neighborhood and non-degeneracy assumptions, one must have Φ(ε) ≳ ε, hence any uniform strip law Φ(ε) ≤ C ε^θ can hold only for θ ≤ 1. Implication: empirical evidence for θ > 1 (e.g., DNS measurements around θ ≈ 1.27 in Volume II) excludes standard Type-I self-similar blow-up routes, pushing any potential singularity into more exotic regimes (fractal interfaces, energetic pathologies, or Type-II / non-self-similar behavior).