The paper distinguishes:
-
Exact Haar kernels: P_K^{Haar}
-
Lift-averaged empirical kernels: P_{K,M}
The exact AP geometry and exact TV formula apply to P_K^{Haar}.
The numerical spectral observations concern P_{K,M}.
This distinction is mathematically essential.
The exact support geometry is rigorous.
The support evolves as a dyadic arithmetic progression.
This yields:
T_mix(K)=K-1
exactly.
The observed exponent:
alpha ≈ 0.39
is numerical only.
No theoretical asymptotic spectral theorem is claimed.
The remaining obstruction is orbitwise lifting:
population mixing ≠ orbitwise arithmetic decorrelation.
A divergent orbit would require coherent arithmetic correlations across infinitely many 2-adic scales simultaneously.