G_rs
plain-language theorem explainer
Recognition Science sets the gravitational constant to G = φ^5 in its native units. This pairs with ℏ = φ^{-5} to give Gℏ = 1 and simplifies the Bekenstein-Hawking entropy to S = A/4 on the ℤ³ ledger. Researchers closing Gap G3 in the holography proof or deriving all constants from φ cite this assignment. It is introduced by direct assignment from the phi-ladder scaling.
Claim. In Recognition Science natural units the gravitational constant satisfies $G = φ^5$.
background
The module derives the Bekenstein-Hawking bound from ledger capacity on ℤ³. Each voxel carries one unit of information and the boundary scales as volume to the power 2/3, consistent with D = 3 forced by the upstream chain. In RS units this yields Gℏ = 1 so that S_BH reduces to A/4 where A counts boundary voxels.
proof idea
The declaration is a direct definition that assigns phi raised to the fifth power to G_rs. No lemmas or tactics are applied.
why it matters
This supplies the G value used by gravitational_constant_derived (which resolves C-002 with no free parameters) and by all_constants_from_phi. It enables the Gℏ = 1 step required for bekenstein_hawking_from_rs and aligns with the phi-ladder and T8 forcing of D = 3.
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