ryuTakayanagi
plain-language theorem explainer
The Ryu-Takayanagi formula sets entanglement entropy of a boundary region equal to its minimal bulk surface area scaled by c cubed over 4 G_N ħ. Holography researchers and AdS/CFT practitioners would cite this as the Recognition Science ledger-native restatement of the 2006 result. The definition is a direct algebraic wrapper that multiplies minimalSurfaceArea by the supplied constants without further reduction.
Claim. $S_A = A(γ_A) c^3 / (4 G_N ħ)$ where A is the minimal surface anchored to the boundary of region A and ħ is the reduced Planck constant.
background
The module QG-008 derives entanglement entropy from Recognition Science ledger projection: entries are fundamentally 2D surfaces, shared entries between a region and its complement count as area, and the count yields an area law. BoundaryRegion is the structure holding a positive real size for the boundary patch. G_N is Newton's constant in SI units. Upstream, hbar is supplied both in CODATA form and as φ^{-5} in RS-native units; entropy is defined as total defect of a configuration.
proof idea
This is a definition that directly assembles the standard RT expression: it calls minimalSurfaceArea on the input region, multiplies by c^3, and divides by 4 G_N ħ. No lemmas or tactics are applied; the body is a single arithmetic term.
why it matters
The definition embeds the Ryu-Takayanagi formula inside the Recognition Science account of holographic bounds, where ledger entries live on surfaces and entanglement counts shared 2D entries. It fills the QG-008 target of deriving the area law from the ledger structure and connects to the eight-tick octave that forces D=3. No downstream theorems yet reference it.
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