einsteinKappaPeriod
The definition assigns the natural number 8 to the Einstein kappa period. Researchers tracing the coherence exponent uniqueness at D=3 cite it when pairing the period with the exponent value 5. The declaration is a direct constant assignment that supplies the 2^3 value required by the eight-tick octave in the forcing chain.
claimThe Einstein kappa period is the natural number $8$.
background
The Coherence Exponent Uniqueness module shows two routes that force the coherence exponent k to equal 5 only at D=3. The Fibonacci deficit route sets k_fib(D) = 2^D - D, so k_fib(3) = 5. The integration measure route sets k_int(D) = D + 2, so k_int(3) = 5. These expressions disagree at D=1, 2 and 4, establishing uniqueness at three dimensions. The period 8 matches the eight-tick octave (period 2^3) from the Recognition Science forcing chain.
proof idea
Direct definition that assigns the constant value 8.
why it matters in Recognition Science
This definition supplies the period value used in the theorem kappa_eq_8phi5, which asserts both the Einstein kappa exponent equals 5 and the period equals 8. It fills the T7 step of the forcing chain by confirming the eight-tick octave at D=3, where the two routes for the coherence exponent agree. The module document states that D=3 is the unique dimension of agreement.
scope and limits
- Does not derive the value 8 from the Recognition Composition Law.
- Does not prove uniqueness of the coherence exponent.
- Does not apply outside D=3.
- Does not connect to the mass formula or Berry threshold.
formal statement (Lean)
72def einsteinKappaPeriod : ℕ := 8