The search of super-rare decay $K^+ \to \pi^0\pi^0\pi^0 e^+ \nu$ is performed by the OKA collaboration. No events of the searched process observed, the upper limit set:
$Br < 5.4 \times 10^{-8} ~ 90\%$ C.L. is currently the world's best one. The previous value listed in Particles’ Table (PDG) is 65 times worse. The decay is sensitive to New
physics. The search of this decay turned out background-free which paves the road for future high-statistics experiments. The result will be published in JETP Letters
and presented at the international conference ICPPA-2024.The upper limit on the $K^+ \to \pi^0\pi^0\pi^0e^+\nu$ decay

Search for the $K^+ \to \pi^0\pi^0\pi^0e^+\nu$ decay.   Missing momentum and missing energy in the $K^+$ rest frame: data (red bullets),   MC simulation of backgounds (blue stars) and MC simulation of signal (dots).
  The vast majority of the decay events are expected within the area marked with the rectangle.

A. V. Artamonov, V. N. Bychkov, S. V. Donskov et at.,
JETP Letters 120, issue 8 (2024)