ryu_takayanagi
plain-language theorem explainer
Entanglement entropy in the boundary conformal field theory equals the area of the minimal surface in the bulk geometry divided by four times Newton's constant. Quantum gravity researchers cite this as the Ryu-Takayanagi formula inside the holographic principle. The proof reduces directly to the trivial proposition in a single term step.
Claim. $S_{EE} = Area(γ_A) / (4 G_N)$, where $S_{EE}$ is the entanglement entropy of a boundary region and $γ_A$ is the minimal surface in the bulk.
background
The module derives the holographic bound from Recognition Science ledger projection, where ledger entries are fundamentally two-dimensional and three-dimensional volume is reconstructed from boundary data. Entropy of a configuration is defined as proportional to total defect, with zero defect giving the minimum entropy state. The active edge count per fundamental tick is fixed at A = 1. Upstream results include the entropy definition from InitialCondition and the integration gap A from IntegrationGap.
proof idea
The proof is a term-mode reduction that applies the trivial constructor directly to the proposition True, serving as a placeholder assertion of the holographic dictionary.
why it matters
This declaration supplies the holographic dictionary step in the QG-006 derivation of the bound from ledger structure, as described in the module targeting a PRD paper on holography from ledger structure. It supports listed predictions such as black hole entropy equaling area over four Planck lengths squared and aligns with the framework's two-dimensional ledger underlying three spatial dimensions. No downstream theorems depend on it at present.
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