hbar_rs
plain-language theorem explainer
In RS natural units ħ equals φ^{-5}, where φ is the golden ratio fixed point forced by J-uniqueness. Derivations of the Bekenstein-Hawking bound from the ℤ³ ledger cite this identity to obtain Għ = 1. The definition is a direct power expression with no lemmas or tactics applied.
Claim. In RS natural units, the reduced Planck constant satisfies $ħ = φ^{-5}$, where $φ$ is the golden ratio satisfying the self-similar fixed-point equation from the recognition composition law.
background
Recognition Science derives all constants from the forcing chain T0-T8, with φ the unique positive solution to the J-cost equation J(x) = (x + x^{-1})/2 - 1. This module works on the simplicial ledger on ℤ³ (D = 3 from T8), where each voxel carries one information unit and accessible information scales with boundary area rather than volume. Upstream, Constants.G supplies the RS-native form G = λ_rec² c³ / (π ħ) that becomes consistent once ħ = φ^{-5} and G = φ^5 are imposed so that Għ = 1.
proof idea
Direct definition: ħ_RS := φ^{-5}. No tactics or lemmas are invoked; the body is the exponentiation itself.
why it matters
This definition supplies the RS value of ħ that feeds G_hbar_product_eq_one and bekenstein_hawking_from_rs, establishing S_BH = A/4 in natural units. It supports the area-not-volume certificate and closes the natural-unit scaling step in the brain holography forcing chain. The parent result is area_not_volume_certificate, which chains this identity with the boundary exponent 2/3 forced by D = 3.
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