DCRP62 / X72R45: Aligned Neutral Pressure Compatibility and Convergence of the N Branch

Building on the invisible eigen-aligned Floquet equality mode DCRP61 found (neutral averaging rate λ*=(2−3γ)/2), this round asks whether that mode can simultaneously sustain a perfect pressure response. Differentiating the eigenvector relation along the material derivative yields the proper pressure–Hessian compatibility condition E_pΩ=−(λ'+λ+|Ω|²/6)Ω, and proves that under neutral Floquet averaging, the single-period directional integral of this pressure defect is strictly positive — meaning the mode cannot satisfy zero turnover, perfect pressure, and cognate periodic recurrence all at once. The non-affine-stretching 'N branch' that DCRP61 had opened is therefore closed as an independent terminal branch, converging fully into X∨T. STOP-D62 compresses the rank-two continuation down to just two global exits — X (X72 pressure/projection defect) and T (cognate turnover) — and hands to DCRP63 the task of judging which carries sharper new structure and should be attacked first.