Klein‑Horizon Information Invariance — A Non‑Orientable Boundary Proposal for the Black Hole Information Problem

We propose that the event horizon is effectively non‑orientable at quantum scales: an orientation‑reversing identification on a stretched horizon renders the interior/exterior split purely conventional. In this picture, information is never destroyed nor escapes; it always lives on a single 2D manifold with a parity twist. We encode the topological contribution to entropy by where is the horizon area (in Planck units) and is a dimensionless topological factor determined by the horizon’s effective metric class ("Klein index"). Orientable horizons recover Hawking’s law with ; small departures capture soft, parity‑twisted corrections without breaking unitarity. We outline a falsifiable analogue‑gravity experiment (BEC sonic black hole with twisted boundary conditions) to probe cross‑horizon correlations consistent with a non‑orientable boundary. The proposal is framed as a testable addendum to existing frameworks (complementarity, soft hair, holography), not a replacement.