Traversable Multi-Mouth Wormholes in 4D: Entanglement, Free Group Topology, and Negative Energy — E8 Intelligence Research

FINDING: Traversable wormhole construction in the lab is a real theoretical program, with multi-mouth generalizations in 4D spacetime tied to quantum entanglement and free group topology. | MATH: The multi-mouth wormhole spacetime has fundamental group \(F_2\) (free group on two generators) for the three-mouth case; traversability between any pair of mouths requires negative energy (quantum null energy condition violation) — the key constraint is the integrated null energy \(\int T_{\mu\nu} k^\mu k^\nu d\lambda < 0\) along the throat. The eternal traversable wormhole solution (Freivogel/Maldacena) relies on a double-trace deformation coupling two CFTs, with coupling \(g\) tuned to overcome the Casimir energy; the throat radius scales as \(r_0 \sim (g N)^{1/3} \ell_{\text{AdS}}\) in the large-\(N\) limit. | CONNECTION: The three-mouth case's \(F_2\) fundamental group is directly related to the free group structure underlying the binary tree of the hyperbolic plane — a lattice with const Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com