G_N
plain-language theorem explainer
Newton's gravitational constant is assigned the numerical value 6.674 times 10 to the minus 11 in SI units. Workers on the Ryu-Takayanagi formula or Bekenstein-Hawking entropy in the Recognition Science ledger model cite this value to scale minimal surface areas into entropies. The definition performs a direct numerical assignment with no further reduction or lemma application.
Claim. $G_N = 6.674 × 10^{-11}$ (SI units)
background
The module derives the Ryu-Takayanagi formula S_A = Area(γ_A) / (4 G_N ℏ) from the ledger projection that entries are fundamentally two-dimensional surfaces. Shared ledger entries between a boundary region and its complement therefore count as area, producing an area law rather than a volume law for entanglement entropy. G_N supplies the gravitational scale that converts those areas into entropy units alongside hbar and c.
proof idea
The definition is a direct noncomputable assignment of the floating-point constant 6.674e-11. No lemmas or tactics are applied; the body simply equates G_N to the literal value.
why it matters
G_N is required by the Bekenstein-Hawking entropy definition and the area_not_volume theorem, which establish that entropy scales with area because ledger entries are two-dimensional. It anchors the RT formula in the QG-008 target and supplies the SI counterpart to the framework's native G = phi^5 / pi, allowing numerical checks against the alpha inverse band and the eight-tick octave. The declaration closes the constant interface for all downstream entropy calculations in the module.
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