quarter_bit_per_planck_area
plain-language theorem explainer
The declaration asserts that each Planck area contributes exactly one quarter bit to entanglement entropy, reproducing the Bekenstein-Hawking prefactor. Holographic quantum gravity researchers would cite it when connecting Recognition Science ledger counting to the Ryu-Takayanagi formula. The proof is a one-line triviality that directly asserts the equality S = A / (4 l_p²).
Claim. Each Planck area contributes exactly one quarter bit, so the entanglement entropy satisfies $S = A / (4 l_p^2)$.
background
The module derives the Ryu-Takayanagi formula from Recognition Science ledger structure. Ledger entries are fundamentally 2D surfaces; entanglement counts shared entries across a boundary; the number of such entries is proportional to boundary area. This yields the standard RT relation $S_A = Area(γ_A) / (4 G_N ℏ)$ where γ_A is the minimal bulk surface anchored to ∂A. Upstream results supply the active-edge count A (equal to 1 per tick) and the φ-ladder correction that normalizes capacities at finite N.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to assert the bit-density equality directly from the Bekenstein-Hawking factor of 1/4.
why it matters
This supplies the bit-density step inside the QG-008 derivation of the Ryu-Takayanagi formula. It links the 1/4 prefactor to the eight-tick octave (T7) via the relation 8/2 = 4 and supports the holographic bound that maximum information scales with area rather than volume. No downstream uses are recorded yet.
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