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An AI-Assisted Formalization of the Poincaré Conjecture
Source-backed selection; publication and proof assessment are separate.
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
The team reports an AI-assisted Lean formalization of both the smooth and topological three-dimensional theorem, with public verification resources.
Passage ID: poincare-conjecture:entry:frenzy-formal:v1
Source item: Formal theorem endpoints and verification discussion
Source record: frenzymath-poincare@arxiv-2610.08329v1
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v13
Formal declaration
Topological theorem · FrenzyMath reported verified revision
Scope
The topological three-dimensional Poincaré theorem
Formal declaration
Smooth theorem · FrenzyMath reported verified revision
Scope
The smooth three-dimensional theorem
Research activity
Two public formalization projects
The selected 2026 projects report complete smooth and topological three-dimensional proofs, with exact release or verification revisions.
These source reports do not constitute OpenMath executions or independently reviewed mathematical correspondence.
History
An AI-assisted formalization account
Further reading
Inspect the formal statement, assumptions and reported checks.
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Complete formal proof reported externally
Project evidence reports successful statement comparison and Lean/Nanoda verification for this proof commit. The later report revision is cited separately; OpenMath has not rerun these checks or completed independent mathematical review.
Statement match: Candidate correspondence · not independently confirmed · checked Oct 12, 2026
PoincareConjecture.ComparatorTargets.topologicalPoincareSkeletonCommit 1876d7dc2c85325a3f62ce9776af98f910c5db04
Complete formal proof reported externally
Project evidence reports successful statement comparison and Lean/Nanoda verification for this proof commit. The later report revision is cited separately; OpenMath has not rerun these checks or completed independent mathematical review.
Statement match: Candidate correspondence · not independently confirmed · checked Oct 12, 2026
PoincareConjecture.ComparatorTargets.smoothPoincareSkeletonCommit 1876d7dc2c85325a3f62ce9776af98f910c5db04
Recorded authorship
Zhiyuan Zhang · Axel Delaval · Leheng Chen · Jinxuan Chen · Jie Xu · Yuxuan Liao · Jiedong Jiang · Chunlei Liu · Bin Dong
Zhiyuan Zhang; Axel Delaval; Leheng Chen; Jinxuan Chen; Jie Xu; Yuxuan Liao; Jiedong Jiang; Chunlei Liu; Bin Dong
Authors report automated assistance; OpenMath has not independently assessed that workflow.
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
An AI-Assisted Formalization of the Poincaré Conjecture
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