The Chamberland–Meisters eigenvalue conjecture is false

Disproof of the Chamberland–Meisters conjecture (1998): that a C1 map of R^n whose Jacobian eigenvalues are bounded away from zero must be injective. Combining the July 2026 Alpöge–Fable counterexample to the Jacobian Conjecture (independently verified in exact arithmetic) with the classical Bass–Connell–Wright reduction yields, in some finite dimension, a polynomial map whose Jacobian matrix is unipotent at every point — all eigenvalues identically 1 — yet which is not injective; realification gives the real C1 statement. The same argument refutes the "unipotent implies univalent" principle in general dimension. A complementary computational rigidity theorem shows that within the dimension-3 equivariant ruled families that produced the Alpöge–Fable map, no member has constant characteristic polynomial with nonzero determinant, so the failure genuinely requires higher dimension or a non-ruled mechanism. The record contains the note (PDF) and a snapshot of the accompanying repository with LaTeX source and exact-arithmetic verification scripts (Python/sympy), github.com/Liam-G/m at tag v1.2. Developed with AI assistance (Claude Fable 5, Anthropic). Not peer-reviewed; classical citations flagged for source-checking in the note.