In homotopy theory, Goodwillie-Weiss embedding calculus approximates a space of smooth embeddings by a diagram of configuration spaces of disks. For the space of long knots, this leads to the introduction of a cohomology spectral sequence by Sinha. This sequence is closely related to Vassiliev’s sequence containing finite type invariants of knots. In rational coefficient, together with operad formality, this relation was used in the proof of a conjecture of Vassiliev claiming E1-collapse of his sequence. In this talk, we compute some higher differentials of Sinha’s sequence in codimension one in characteristics 2 and 3. The geometric meaning of this codimension case is unclear, but we give some application to non-formality of an operad. The idea of computation is to replace the diagram of configuration spaces with that of Thom spaces over fat diagonals and resolve it by Cech complexes, using a space-level realization of Alexander duality by Dold-Puppe and Atiyah. This talk is based on arXiv:2303.08111.