Can a category behave well in every fixed finite piece and still fail to have kernels in a natural subcategory? This anonymous, unrefereed candidate answers yes for F I d modules in characteristic zero whenever d is fixed and at least two. Two colors build a sequence of bidiagonal Toeplitz matrices. In the block numbered r, adjacent terms cancel along one syzygy, and its minimal degree is r plus one. Putting all blocks together keeps the generators in degree one while forcing relation degrees to grow without bound. Exact symmetric-group coinvariants make that obstruction visible over a polynomial ring. A second argument using representable modules and Yoneda shows that the category cannot hide the failure by choosing a different kernel. So the modules presented in finite degree do not form an abelian category. A published example by Di, Li and Liang uses the same broad unbounded-relation idea in a category with countably many coordinates; this release contributes the fixed finite d Toeplitz realization and explicit internal-kernel argument, without claiming priority. Python and Singular replay the formulas and hostile controls, but remain producer-controlled. The paper, code, review response and assurance limits are linked on this page. This OpenAI synthetic voice is a communication aid, not additional mathematical evidence.