Observable systems with divergent isolated Kalman covariances: a counterexample to the isolated Kalman filtering convergence conjecture

Unrefereed research candidate. The isolated Kalman filter (IsoKF) of Jung, Luft and Weiss (Autonomous Robots, 2025) lets the nodes of a robot or sensor network share an estimation task cheaply: only the nodes involved in a measurement update, and their correlations with everyone else are rescaled by a correction factor. Its authors conjectured that for any completely observable and controllable system the covariance it reports converges to a finite, unique, stable steady state. Result: the conjecture is false. A three-node system with pair-sum observations x1+x2, x2+x3, x3+x1 and dynamics A = 3I is observable from one epoch and controllable, every local block the filter uses stays positive definite, yet the reported marginal variances satisfy m_k ≥ (5/4)(9/5)^k − 1/4, while the centralised Kalman filter keeps every variance at most 3/4. A Perron-root comparison extends divergence to every connected non-bipartite pair-sum graph when a^2 is large enough; extra attenuation or deletion of cross-covariances does not help. Schur-stable dynamics always give bounded marginals (proved). Computer-assisted proofs (outward-rounded interval arithmetic) show that for a^2 in (1, 1.38] large priors diverge at rate a^(2k), entry certified from 10^12 I at eight values down to a^2 = 1 + 10^-8, and that at a^2 = 21/20 the prior I converges while 10^12 I diverges: there is no globally attracting steady covariance. Also: exact classification of participant overlaps (|U ∩ V| ≤ 1) that keep every local block positive definite, and a bounded regime for anchored relative measurements. Scope: in high-precision numerical tests the actual estimation error stays bounded; the failure is gross pessimism of the reported covariance, not divergence of the estimate. The counterexample uses pair-sum measurements, not plain differences. Nothing is proved for a^2 in (1.38, 2+√5); uniqueness for stable dynamics remains open. The ikf_lib software was inspected but not run; no software failure is claimed. Version 0.2.0 (correction). Version 0.1.0 compared this work with Luft, Schubert, Roumeliotis and Burgard (2018, IJRR, doi:10.1177/0278364918760698) at abstract level only. This version compares it with the full text: Luft et al. introduce the correction factor (their eq. 26) and a scaled variant (eq. 28), and prove that two-robot blocks stay positive definite (Proposition 1, now credited at Theorem 8.1 and Corollary 5.3); they make no claim about boundedness or convergence of the covariance and give no divergence example. The two citing works are now also compared in full text. No theorem, proof, certificate, computation or numerical finding changed. Archive: LaTeX manuscript and PDF, bibliography with registry records, exact rational verifiers, interval certificates C1–C3, numerical scripts and their outputs (normal and python -O), figures, CI and SHA-256 manifest. Assurance: internal AI-assisted review only (not human peer review, independent reproduction or formal verification); certificates are computer-assisted, not formal proofs. Creator: Anonymous. Text CC0-1.0; code MIT.