OpenAI Math Digest
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FIELD GUIDE

Real and complex analysis

Real and complex analysis

Official catalogue 071–086.

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Catalogues in this field

Official catalogue numbers
074

Kakeya in three and four dimensions

Follow the shared plank input and distinct proof routes to the three-dimensional maximal estimate and four-dimensional Hausdorff dimension.

All 2 overviews available

The catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.

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Proof overviews (2)Official catalogue order
  1. The Kakeya maximal conjecture in three dimensions
  2. Every four-dimensional Kakeya set has full Hausdorff dimension
079

Local smoothing for the Euclidean wave equation

Official catalogue 079 contains two manuscripts: an all-dimensional determinant-energy argument and a three-dimensional wave-packet and entropy argument. They reach a common three-dimensional local-smoothing conclusion by different methods. The first also claims a quantitative logarithmic estimate and a broad family of analytic and geometric consequences.

All 2 overviews available

The catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.

Explore the synthesis and connections
Proof overviews (2)Official catalogue order
  1. Local smoothing for the Euclidean wave equation
  2. Critical local smoothing for the three-dimensional wave equation

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