OpenAI · 260-13 · 2026-09-27 · Mathematical physics
Area-controlled end replacement and the Bondi Penrose inequality in the CKS class
preprints/Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026
Family 260. Spacetime Penrose inequalities and rigidity.
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
Expanding universe. Language of an expanding universe or a Penrose inequality is not a de Sitter state, not Em02-E's relational lapse, and not XVI-P's QdS external-leg scheme. 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. Em02-E · XVI-P
Proves the sharp enclosing-area spacetime Penrose inequality for smooth one-ended asymptotically flat initial data in every spatial dimension , under dominant energy, weak future trapping, positive enclosing area, and the stated decay assumptions. It bounds invariant ADM mass below using minimum enclosing area, with equality rigidity under additional horizon hypotheses. Charged upper-area bounds treat dyonic three-dimensional data; the higher-dimensional purely electric extension uses the matched neutral theorem.
We replace a three-dimensional Cha–Khuri–Sakovich hyperboloidal end by an asymptotically flat end while preserving the dominant energy condition and each fixed compact interior. For strictly future-timelike CKS initial-data charge, the replacements lose asymptotically no enclosing area and their ADM masses tend to the invariant Bondi mass. Combining this construction with the companion numerical spacetime Penrose theorem yields the sharp Bondi bound for possibly disconnected weakly future trapped boundaries in this class. Horizon-regular Schwarzschild exteriors attain equality at every positive mass.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 260: Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensions. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
CKSBondiPenrose.lean · CKSBondiPenrose.lean
Expanding universe
Anti-de Sitter Penrose inequalities are not a de Sitter state
Family 260 records spacetime Penrose inequalities. Those preprints are anti-de Sitter or asymptotically flat. That is not a de Sitter state, not Em02-E's relational lapse, and not XVI-P's QdS external-leg scheme. The authors are OpenAI. The companion does not verify those proofs. O.1 stays NOT_CLOSED.