bitsPerPlanckArea
plain-language theorem explainer
The declaration assigns the real number 1/4 as the information density per Planck area in the Bekenstein-Hawking entropy formula inside the Recognition Science ledger model. Quantum gravity researchers deriving the Ryu-Takayanagi area law from two-dimensional ledger projections would cite this constant when converting between geometric area and bit count. The definition is a direct one-line assignment of the constant, motivated by the factor of four in the area law and the eight-tick periodicity.
Claim. The coefficient such that the entanglement entropy satisfies $S = A / (4 l_p^2)$, where $A$ denotes boundary area in Planck units and each Planck area contributes exactly 1/4 bit of information.
background
The module QG-008 derives the Ryu-Takayanagi formula from Recognition Science ledger structure. Ledger entries live on surfaces, so entanglement entropy counts shared entries across a boundary and therefore scales with area. The standard expression is $S_A = Area(γ_A) / (4 G_N ℏ)$, and the coefficient 1/4 encodes that each Planck area supplies precisely 1/4 bit.
proof idea
Direct definition: the real number 1/4 is assigned by a one-line abbrev. No lemmas or tactics are invoked; the assignment simply records the bit density required by the area law.
why it matters
This supplies the numerical prefactor for the holographic bound inside the EntanglementEntropy module and is referenced by the bitsPerPlanckArea declaration in HolographicBound. The attached comment explicitly ties the 1/4 to the eight-tick octave (T7) via 8/2 = 4, linking the definition to the forcing chain T0-T8 and the ledger-projection argument for the Ryu-Takayanagi formula stated in the module doc.
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