Informal statementPinned source
Every Kakeya set in positive Euclidean dimension has full Hausdorff dimension.
Source correspondenceImported; no Proofweave fidelity attestation
MSC 42 · Harmonic analysisOpen conjecture
Founding Challenges · Formal Conjectures
Kakeya Set Conjecture
Kakeya sets contain a unit segment in every direction; the collection separates the open general dimension statement from solved Euclidean and finite-field cases.
Environment
leanprover/lean4:v4.27.0
mathlib:a3a10db0e9d6Formalized statementOpen proof branchNo Proofweave attestation
Pinned Lean statementLean 4
theorem kakeya_set_conjecture (n : ℕ) (hn : n > 0) :
KakeyaSetConjectureDim n := by
sorryReproducibility recordcurated-focus-v1-lean4.27.0
- Revision
b2e608fc52d765510915a244bb69b1a2741acc3c- Retrieved
- 2026-07-16T00:00:00Z
- Source hash
sha256:4d624a82f55702f1602858e2d38bdf26bfdb9892954c71736768e84f8cb9012c- License
- Apache-2.0 source code; upstream materials may carry their own stated terms.
- Mathlib
a3a10db0e9d66acbebf76c5e6a135066525ac900
Proofweave verification0 attestations
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- Records
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- Papers
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- Lean paths
- 1
- Reviewed
- 0
Source-backedPer-conjectureAppend-only curationPublic context ≠ Proofweave verification
01
Research progressReview
Recent progress on the Kakeya conjecture
This survey records the geometric and harmonic-analytic route through the Wolff and Katz-Tao era of Kakeya progress, giving context for the higher-dimensional target.
02
AnnouncementPublic note
Introduction to the proof of the Kakeya conjecture
A 2025 survey describes the announced Wang-Zahl proof of the three-dimensional Kakeya conjecture. This remains an announcement/review record and is not a Proofweave verification.
03
FormalizationLean project
Pinned Lean statement in Formal Conjectures
The pinned snapshot exposes the general-dimensional Kakeya declaration and source hash for a local replay. The catalog declaration is admitted and does not certify the announced result.
Verification market · v1
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00 · Prior work
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