IndisputableMonolith.Foundation.CoherenceExponentUniqueness
The CoherenceExponentUniqueness module defines the Fibonacci deficit k_fib(D) = 2^D - D and proves that the coherence exponent equals 5 uniquely at D = 3. Researchers deriving the phi-ladder mass formula or RS-native constants cite it to fix the scaling after the eight-tick octave. The structure consists of auxiliary deficit functions, agreement lemmas at D = 3, disagreement lemmas at neighboring integers, and a final uniqueness statement.
claimThe Fibonacci deficit is given by $k(D) = 2^D - D$. The coherence exponent is the unique value equal to 5 at spatial dimension 3, with the integer counterpart agreeing only at that point and disagreeing at D = 1, 2, 4.
background
This module belongs to the Foundation layer and supplies the uniqueness step after the forcing chain reaches the eight-tick octave and three spatial dimensions. It introduces the Fibonacci deficit k_fib(D) = 2^D - D as a measure of deviation from self-similarity between exponential base-2 growth and the linear term D. Companion definitions include the integer deficit k_int together with coherenceExponent and einsteinKappaExponent, all placed in the context of the Recognition Composition Law and J-uniqueness.
proof idea
The module first declares the two deficit functions. It then proves agreement at D = 3 by direct substitution, showing both versions equal 5. Separate lemmas establish explicit mismatch at D = 1, 2 and 4. The uniqueness result coherenceExponent_eq_5 is obtained by combining the single agreement point with the surrounding disagreements; k5_forced_at_D3 is an immediate corollary.
why it matters in Recognition Science
The module fixes the coherence exponent at 5, which is required for the mass formula yardstick times phi to the power (rung minus 8 plus gap(Z)) and for the constants G = phi^5 / pi together with hbar = phi^{-5}. It supplies the input to einsteinKappaExponent and supports the alpha inverse interval (137.030, 137.039). The result closes the T7 octave and T8 dimension steps in the forcing chain.
scope and limits
- Does not extend uniqueness to non-integer D.
- Does not derive the numerical value of phi.
- Does not compute alpha or its bounds directly.
- Does not treat the Berry creation threshold or Z_cf.
declarations in this module (16)
-
def
k_fib -
def
k_int -
theorem
agreement_at_3 -
theorem
both_equal_5_at_3 -
theorem
disagreement_at_1 -
theorem
disagreement_at_2 -
theorem
disagreement_at_4 -
theorem
exponent_unique_at_D3 -
theorem
k5_forced_at_D3 -
def
coherenceExponent -
theorem
coherenceExponent_eq_5 -
def
einsteinKappaExponent -
def
einsteinKappaPeriod -
theorem
kappa_eq_8phi5 -
structure
CoherenceExponentCert -
def
coherenceExponentCert