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Sogge's conjecture that solutions of the free wave equation gain local smoothing, i.e. improved L^p regularity over space-time, at the conjectured range. Claims about its truth, partial results, and implications to/from Bochner–Riesz, Kakeya, and restriction conjectures belong here.

The local smoothing conjecture for the wave equation implies the Bochner–Riesz conjecture.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Harmonic analysis Bochner–Riesz conjectureimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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