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NS-IDRP

Navier–Stokes Impulsive Defect Recurrence Program · Cycle IX · 4/4 built · global regularity OPEN

NS-IDRP is the first sub-line in the relay to continue directly from NS-DCRP — its own opening line states "DCRP Cycle VIII closes with the surviving normal form 𝒦_IDR (diffuse impulse recurrence)," the first place confirming NS-DCRP is in fact Cycle VIII. The core new question is temporal: can every positive carrier exist only at isolated moments, keeping every spacetime budget summable? Four rounds carry this forward: IDRP-01 separates persistence from burst debt; IDRP-02 proves that rapid loss of a filtered trace is not mechanism-invisible; IDRP-03 partially closes the burst-to-defect-realization (BDR) problem; IDRP-04 completes the Cycle IX final audit.

IDRP-04 concludes that source transversality from pressure alone is generally impossible, that the stronger "forcing pairing implies source defect" theorem also fails, and that the universal weak source-action budget is summable in scale — so it cannot by itself supply a physical critical lift. Cycle IX thereby reduces the surviving obstruction to a tangential singular-impulse phantom (TSIP), formally handing off to "NS-TSKR: Navier–Stokes Tangent Singular Kernel Rigidity Program." 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).