coherence_exponent
plain-language theorem explainer
The coherence exponent is the integer 2^D minus D, which equals 5 when D is fixed at 3 by the forcing chain. Lepton mass derivations cite this value to fix the rung offset in the phi-ladder formula for E_coh. The definition is a direct algebraic substitution that reproduces the Fibonacci deficit identity.
Claim. The coherence exponent is the natural number given by $2^D - D$, where $D$ is the number of spatial dimensions.
background
Recognition Science fixes D = 3 via T8 and the eight-tick octave period via T7, so that the octave equals 2^D. The upstream definition in Masses.CoherenceExponent sets coherence_exponent := octave - D and proves it equals 5 by the Fibonacci identity F_6 - F_4 = F_5. This module re-expresses the same quantity for the T9 electron-mass chain that begins from cube geometry (12 edges, 11 passive) and wallpaper count 17.
proof idea
The declaration is a direct definition that substitutes the octave period 2^D into the expression octave - D. It matches the upstream coherence_exponent by algebraic identity and requires no further lemmas.
why it matters
This supplies the exponent 5 that appears in E_coh = phi^{-5} and in the uniqueness theorem coherence_exponent_unique, which shows D = 3 is the sole dimension where both D and 2^D are Fibonacci numbers. It closes the derivation from T7-T8 to the lepton mass ladder and is invoked by coherence_exponent_eq_5, coherence_exponent_is_fib_5, and E_coh.
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