coherenceExponent
plain-language theorem explainer
The coherence exponent is defined as the natural number 5, yielding ħ = φ^{-5} in RS units. Derivations of the gravitational constant G_RS and reduced Planck constant hbar_RS cite this value directly. The definition is a direct constant assignment with no computation or lemmas applied.
Claim. The coherence exponent satisfies $k = 5$.
background
The Coherence Exponent Uniqueness module records two independent routes that fix the exponent k. Route 1 defines the Fibonacci deficit k_fib(D) = 2^D - D. Route 2 defines the integration measure k_int(D) = D + 2. These expressions agree only at D = 3, where both equal 5. The upstream definition in Physics.PlanckConstantFromRS supplies the same integer together with the interpretation ħ = φ^{-5}.
proof idea
Direct definition assigning the constant value 5.
why it matters
This definition supplies the integer k = 5 consumed by coherenceExponent_eq_5 and by the constant definitions G_RS, hbar_RS, kappa_RS in PlanckConstantFromRS. It therefore participates in the master theorem exponent_unique_at_D3 that isolates D = 3 as the unique dimension where the two routes agree. The value aligns with the eight-tick octave period (T7) and the forcing of three spatial dimensions (T8).
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