Entanglement = geometry, exactly — the kernel-checked Ryu-Takayanagi equality and the forced emergence direction
Year: 2026
Type: preprint
Abstract: Two new kernel-checked results in the constraint-first programme: (1) the EXACT Ryu-Takayanagi equality — srank (maximallyEntangled D) = D, entanglement equals the cut area D^m as an equality, not the usual leading-order bound; (2) the FORCED emergence direction — logDepthForced + meraEmergence prove logarithmic depth and exponential circumference are forced simultaneously, so the balanced binary tree (discrete hyperbolic geometry) is the unique optimum. Proven in Lean 4 + Mathlib (pacland-proof/PaclandProof/QM/MERA.lean), no sorry/axiom, reproducible via lake build. The continuous limit (tree ≃ H²) is the Svarc-Milnor step, named as the frontier, not proven here. Site: https://pacland.morpheus.nz — Repo: https://github.com/robmitchellengineering-hub/pacland
Author: Rob Mitchell
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225612884
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