OpenAI · 356-01 · 2026-09-24 · Differential geometry

Gigli’s distributional curvature characterization of Alexandrov spaces

preprints/Giglis-distributional-curvature-characterization-of-Alexandrov-spaces-September-24-2026

Family 356. Gigli's characterization of Alexandrov curvature.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Proves Gigli's conjecture: in every integer dimension $n \geq 2$ , Alexandrov curvature at least $κ$ is characterized by the full-support $RCD ((n - 1) κ, n)$ condition with reference measure $H^{n}$ and distributional sectional curvature at least $κ$ in the original global test classes. The RCD condition is unreduced.

For every integer n ≥ 2 and κ ∈ ℝ, we prove that a complete separable metric space is an n-dimensional Alexandrov space of curvature at least κ if and only if, with reference measure $H^{n}$ , it is a full-support $RCD ((n - 1) κ, n)$ space whose distributional sectional curvature is at least κ in Gigli's original global test classes. This resolves Gigli's characterization conjecture in dimensions at least two.

Preprint source and Lean scope

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A Lean scope note is stored for family 356, but it does not name this preprint. It names 356-02. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.