2 problems

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Bergelson–McCutcheon IP-limit positivity conjecture for VIP-systems
Bergelson–McCutcheon IP-limit positivity conjecture. For every $f\in\mathcal H$ ,
Conjectureopenergodic-theory hilbert-spaces vip-systemsarXiv posted 2 days ago
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The VIP-system nice recurrence conjecture
VIP-system recurrence conjecture. The VIP-system $v$ is good for nice recurrence.
Conjectureopenergodic-theory recurrence vip-systemsarXiv posted 2 days ago

Bergelson–McCutcheon IP-limit positivity conjecture for VIP-systems