kappa_fibonacci_form
plain-language theorem explainer
kappa_fibonacci_form establishes that the Einstein coupling equals 8(5 phi plus 3) in RS units. Unification researchers cite it to recast gravitational strength via the golden-ratio Fibonacci sequence. The proof is a short term reduction that substitutes the power definition of kappa and applies the upstream Fibonacci identity for phi to the fifth.
Claim. In RS-native units the Einstein gravitational coupling satisfies $kappa = 8(5 phi + 3)$, where $phi$ is the golden ratio obeying $phi^2 = phi + 1$.
background
The QuantumGravityOctaveDuality module proves that kappa times hbar equals the octave factor 8. kappa_einstein is introduced as 8 phi^5 via the constants module, using G = phi^5 / pi and hbar = phi^{-5}. The upstream lemma phi_fifth_eq records the identity phi^5 = 5 phi + 3, obtained from the recurrence phi^{n+2} = phi^{n+1} + phi^n and the defining equation phi^2 = phi + 1.
proof idea
The term proof first rewrites via kappa_einstein_eq to replace kappa with 8 phi^5. It then applies congr 1, converts the natural-number exponent with norm_cast and Real.rpow_natCast, and finishes by exact application of phi_fifth_eq.
why it matters
The result supplies the Fibonacci form required by the downstream QG Octave Certificate qg_octave_cert. It realizes the eight-tick octave (T7) of the forcing chain by writing kappa as F_6 times (F_5 phi + F_4). The declaration thereby links the phi-ladder mass formula directly to the gravitational coupling inside the single J-cost framework.
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