Remark: 260-01. The spacetime Penrose inequality with charge and original-data rigidity

Authors: OpenAI. Family 260.

Title: The spacetime Penrose inequality with charge and original-data rigidity.

Abstract: Under the stated energy, decay, and trapping hypotheses, we prove the sharp charged spacetime Penrose upper-area inequality for one-ended three-dimensional initial data with source-free electric and magnetic fields. The theorem allows arbitrary second fundamental form, nonzero ADM momentum, and disconnected boundary. Writing m for invariant ADM mass, Q for total charge magnitude, and rA for the minimum-enclosing-area radius, the bound is m ≥ Q and $r_A{}le m+{}sqrt{m{}2-Q{}2}$. The polynomial mass bound $m{}ge(r_A+Q{}2/r_A)/2$ is asserted only when $r_A{}gt Q$. When m > Q, equality under the stated connected, outermost, outer-area-minimizing future-horizon hypotheses identifies the original data as a smooth spacelike slice of dyonic Reissner–Nordström, including smooth attachment at the future horizon.

This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.