An explicit counterexample to three-summand Kato-kernel splitting

An explicit full negative instance of Question2 in Laghribi's OWR5/2016 contribution, printed251 (problem30003045). In characteristic two, a degree-four exponent-two purely inseparable extension, a separable quadratic extension and an anisotropic binary bilinear Pfister form give a class in the composite Kato kernel outside the sum of all three individual kernels, at original index1. A direct all-parameter cyclic-norm and residue square-class argument proves nonmembership. The original n=0 equality is separately positive for positive-fold forms; failure at every index is not claimed. The mixed class is exactly a specialization of Aravire-Laghribi-O'Ryan2019 Definition1.3/Lemma3.1/Theorem1.4, published Journal of Algebra542(2020),249-276, DOI10.1016/j.jalgebra.2019.09.012. The generator and mixed vanishing mechanism are prior work. This four-page note gives the explicit survival argument after the third Pfister kernel is added. An auxiliary exponent-one shortcut in the earlier draft is repaired by proving membership in the inseparable-plus-separable kernel sum rather than an unjustified base-field symbol equality. Extensive bounded primary priority audits did not verify an earlier recorded full three-summand answer in inspected bodies. They do not certify firstness, novelty, causal independence or continued global openness. Final mixed2020 typeset-body comparison and the adjacent nonnormal2020 and transfer2022 full bodies remain access limits; other precise read/version limits are documented. The source archive includes the operative proof, repaired16-file PR edition, clearly historical original inputs, three mathematical and three priority approaches, root verification and portable standard-library exact diagnostics. Both algebra programs run ordinarily and with optimization, comparing complete outputs; nine wrong-result controls fail in both modes,18 actual failures. Finite diagnostics supplement the universal proof and do not decide Kato cohomology. Third-party source bodies are excluded. AI tools were used extensively in developing, writing, researching, reproducing and adversarially verifying the work. Initial review families had parent history available, with no perfect information isolation claimed. This preprint and package are unrefereed; internal AI reviews do not constitute external human peer review, journal acceptance or formal proof-assistant certification.