# Verification report

Infinitesimal Lifting Does Not Imply Flatness for Green Functors, version 1.0.
Alper Ferudun, Mercury Software GmbH, 18 October 2026.

The written proof establishes the result for every nonzero commutative
ring of characteristic two. The C2 ghost algebra is checked against
Strickland's Tambara-pair axioms. Its functor of points is exactly the
set of top idempotents with zero restriction, giving a finite presentation
and unique lifts through square-zero kernels. A universal pairing argument
computes D box M as the top-supported transfer cokernel and proves
nonflatness on an explicit injection D into E.

Both normal and optimized standard-library Python runs agree on 224655
exact tests. The finite domains include truncated characteristic-two
rings, idempotent lifts, representing maps and the tensor-kernel matrix.
The supplementary nilpotent norm example is not used in the main proof.
The checker is not a proof assistant and does not certify the arbitrary
base-ring theorem; the written argument is the mathematical justification.

The known ghost construction is explicitly attributed. The specific
lifting-versus-flatness assertion is refuted, but the broader frozen
derived geometry question is not closed. This is AI-assisted, self-audited
and unrefereed. No independent review, formal certification or absolute
priority claim is made.