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NS-RKAP

Navier–Stokes Residual Kernel and Amplitude Program · Cycle XI · current research frontier · global regularity OPEN

NS-RKAP continues from NS-TSKR Cycle X: TSKR compressed the surviving tangential/residual obstruction into a "two-sided residual phantom" (TSRP), whose main nontrivial geometric branch is a hyperbolic two-sided mismatch fiber H = u⊗w + w⊗u (w ⊥ u; under flux-invisibility, w ∥ u×Su, at most one-dimensional). RKAP-01 proves covariance-transport transversality (the transport term is quantitatively injective over the whole hyperbolic fiber on |u| ≥ m) and an exact two-sided PSD lift-tax theorem (a sign-changing stress written as the difference of two positive-covariance packets, with lift cost exactly ‖H‖_*), and proves a conditional linear-amplitude lift compiler — for logarithmic amplitude ρ_n ~ n^(-2/3), excluding recurrence only requires the lift weight λ_n to decay no faster than n^(-1/3).

This is currently the newest frontier of the entire ten-part relay on this site (CSP through RKAP). RKAP-01's own roadmap plans an "RKAP-02" (transport-test-gap stability, positive-lift realizability, two-packet energy exhaustion, hyperbolic degenerate sets, linear-amplitude stacking), but no corresponding file exists in the source drop — it has not been written yet, not an omission on this page. The confirmed relay so far: NS-CSP (II) → NS-DRC (III) → NS-ANP (IV) → NS-CFOP (V) → NS-FCBP (VI) → NS-MORP (VII) → NS-DCRP (VIII) → NS-IDRP (IX) → NS-TSKR (X) → NS-RKAP (XI) — ten parts, compressing the singularity-formation obstruction step by step from a causal forest down to this one-dimensional hyperbolic residual fiber. Global regularity has stayed fully OPEN throughout; no round claims to resolve it.