An order-sensitive statistic reproduced by a one-point arithmetic bias in the Riemann-zero spectrum

In memory of Mykhailo Novikov and Mykhailo Palamarchuk, killed in the war. This note is written in their memory. This note withdraws a claim the author had made, and then withdraws the explanation first offered for what remained of it. A cumulative statistic over the Riemann zeros is formally order-sensitive: its value changes if the zeros are permuted. Measured against a density-matched Poisson null it gives z between 13 and 101, which reads as strong sequential correlation. It is not. Landau's 1911 explicit formula fixes the mean increment of the statistic at −μ(p) with μ(p) = log p/(√p·log(T/2π)), and from that alone the statistic is predicted to converge to μ(p) with no free parameters. The prediction matches the data in sign, in absolute magnitude, in the non-monotonic profile across primes with its maximum at p = 7, and in the 1/log(T/2π) scaling, with measured slope −1.01 ± 0.01 over 164 windows spanning T from 5.3×10⁵ to 9.4×10⁹. An order-free iid control matched only to the one-point marginal reproduces the signal in full. The claim of sequential sensitivity does not survive that control and is withdrawn. A methodological distinction follows, and it is the note's main contribution: a statistic may be functionally order-sensitive — its value changes under permutation — without being informationally order-sensitive, the signal being generated entirely by order-independent marginal structure. A permutation control cannot tell these apart, because permutation also destroys the marginal trend the signal rests on. A residual of +0.177% ± 0.111% above the prediction remained, and an earlier version of this note attributed its sign and order of magnitude to GUE spectral rigidity. A control pre-specified before the run that produced it removes that attribution: the order-free surrogate, which has no rigidity whatsoever by construction, exhibits an indistinguishable offset of +0.231% ± 0.081%. An ensemble with zero rigidity reproduces the effect attributed to rigidity, so rigidity is not required for either the sign or the scale — which is a counterexample to necessity, not a demonstration that rigidity contributes nothing. The residual is a bias of the mean-field derivation, which divides by sqrt(E|A_k|²) where the statistic requires E|A_k|. Cauchy–Schwarz fixes the sign of that one contribution with no free parameter; the full finite-N correction also carries covariance terms whose sign is not controlled, and remains open. Three limitations are stated in the text rather than left for a reader to find. The derivation of Section 2 is explicitly mean-field: it computes what an iid countermodel with the Landau marginal must give, and the empirical work of showing that such an object reproduces the real signal is done in Section 5, not by the algebra. The input gate is target-adjacent — it selects files by the presence of the arithmetic structure that is the explanatory variable — and the two remedies that would settle it have not been run. And the height-scaling fit uses 164 of the 313 windows by a rule that is not recorded here, which is flagged as the weakest-provenanced figure in the note. Two further observations are reported deliberately without a mechanism. The dispersions of the two ensembles differ by a factor of 32.5: the matched iid control reproduces the centre of the residual and not its narrowness, and what produces the narrowness is not localised. And off the arithmetic carrier the real zeros are not noise either — the statistic reads −0.108 ± 0.042 there against 0.000 ± 0.0014 for a Poisson surrogate. The same instrument is used twice, one level apart: a surrogate built without the property an effect was attributed to, first order and then rigidity, which in both cases reproduced the effect in full. The validation architecture and the taxonomy of failures this note was produced under are deposited separately (doi:10.5281/zenodo.23262157).