These resolve 6 entries in my top 500 open problems list (LLM ranked, https://www.proofatlas.ai/open-problems/) and there is partial progress on #3 overall (Yang–Mills Existence and Mass Gap):

Kakeya conjecture — #38

Fourier restriction conjecture — #46

Local smoothing for wave equations — #187

Bochner–Riesz conjecture — #190

Exponential Time Hypothesis — #43

Strong Exponential Time Hypothesis — #63