A String-Theoretic Resolution of the Vacuum Energy Problem from Crossing Symmetry, Entanglement, and Bulk Backreaction

A complete and explicit derivation of the observed vacuum energy density is presented entirely within string theory, formulated through the Anti--de Sitter/Conformal Field Theory correspondence. The construction uses only standard string-theoretic structures: Virasoro conformal blocks, exact crossing symmetry at finite central charge, unitary fusion matrices, entanglement entropy as defined by the Ryu--Takayanagi relation, and the bulk Einstein--Hilbert gravitational response. A finite, nontrivial fixed point arises from a local balance between boundary entanglement redistribution and bulk gravitational backreaction. All algebraic steps are shown explicitly, including the construction and unitarization of the crossing matrix, the derivation of the entanglement entropy expansion, the fixed-point equation, and the full numerical evaluation yielding the Hubble scale and vacuum energy density. No landscape statistics, anthropic assumptions, or phenomenological parameter tuning are invoked.