A new algebraic route to holographic bulk-boundary reconstruction

Holographic duality requires reconstructing bulk quantum information from boundary data, but the standard algebraic reconstruction theorem left type III operator algebras — the kind that naturally arise in quantum field theory — unresolved. By showing that relative entropy in crossed product algebras splits cleanly into bulk and observer contributions, this work builds matching 'holographic' algebras for bulk and boundary and extends the reconstruction theorem to cover these cases. The result incorporates the Ryu-Takayanagi entropy formula at the semiclassical level, completing an intrinsic algebraic account of bulk-boundary correspondence.