The arithmetic pole

• 2026-09-06 [Proved] The comb zeta of base 3 digits {0,1} has a genuine pole at every s_(0,k) = log_3 2 + 2 pi i k/log 3, k = 1..10: the residue lambda_(0,1) lies in [0.231891517689918, 0.231891517689919] + i [-0.501067414481069, -0.501067414481068] by interval arithmetic on Burnol's Proposition 5.1 with every truncation bounded by a proved tail, and Res = s_(0,k) c_k ties it to the k-th Fourier coefficient of the log-periodic profile of A(x); the profile control from exact counts and a second certified enclosure by the functional-equation route both meet the first. Witness: lab/py/burnol-residue, dimensions.md THE ARITHMETIC POLE.