Can changing the field around each spin restore a hidden conservation law? This research candidate asks that question for a quantum chain whose neighbouring spins interact in the same way, while the local fields can differ from site to site. A local conservation law is built by adding terms that each act within a short stretch of the chain. Such laws can make quantum models unusually constrained. Rather than trying countless fields, the paper removes every field from a small set of equations. If an exact obstruction remains, no permitted field choice can restore the conservation laws covered by the theorem. The sharpest application concerns a standard spin-one family with two interaction strengths. Three straight lines in its parameter plane admit a conserved three-site current when the fields are zero. Everywhere else, arbitrary local fields cannot produce the specified higher-range charges. The exclusion applies on periodic chains with at least six sites, to charges extending from three sites up to half the chain. It does not exclude every conceivable conserved operator. The method also detects cases missed by an older, cheaper test. At the familiar AKLT interaction, that older test returns zero, while the new obstruction is strictly nonzero. Earlier research already classified important zero-field models and used symmetry to constrain corrections. The extension here is to average the local equations even when the actual fields break those symmetries. The package contains written proofs, exact calculations and small rational witnesses that can be checked by multiplication. It remains an unrefereed candidate, without formal proof verification or authenticated independent peer review. Nor does the absence of these local charges prove chaos or thermalisation. This is Evidence Press, field-uniform nonintegrability of spin chains, released on the twenty-eighth of September twenty twenty-six. The paper and evidence are linked on this page. This synthetic AI voice explains the result; it is not additional scientific evidence.