coherenceExponent
The coherence exponent k is fixed at the natural number 5 to set the RS-native Planck constant ħ = φ^{-5}. Derivations of fundamental constants from the forcing chain at D=3 cite this pinning to obtain G = φ^5/π and κ = 8φ^5. The declaration is a direct constant assignment that propagates algebraically through uniqueness and positivity results.
claimThe coherence exponent equals the natural number 5, so that ħ = φ^{-5} in RS-native units.
background
The module derives the Planck constant from Recognition Science by pinning the coherence exponent k at D=3. Module documentation states that k=5 follows from the Fibonacci route k_fib(D)=2^D - D =5 and the integration route k_int(D)=D+2=5. Upstream definitions include ħ = E_coh · τ₀ = φ^{-5} · 1 from Constants and the uniqueness result that forces this exponent from the J-cost functional equation.
proof idea
The declaration is a direct definition assigning the natural number 5. It is referenced by the reflexivity theorem coherenceExponent_eq_5 and supplies the exponent for the algebraic definitions of hbar_RS and G_RS.
why it matters in Recognition Science
This definition supplies the exponent required by the parent results in CoherenceExponentUniqueness and the derivations of hbar_RS, G_RS, and kappa_RS. It fills the forcing-chain step where the eight-tick octave and D=3 determine k=5, as stated in the module documentation. The pinning closes the algebraic path to the RS-native constants with zero sorry statements.
scope and limits
- Does not derive k=5 from the J-uniqueness equation.
- Does not prove uniqueness of the exponent.
- Does not convert the RS-native constants to SI units.
formal statement (Lean)
29def coherenceExponent : ℕ := 5
proof body
Definition body.
30
31/-- hbar = φ^(-5) in RS units. -/