Mixed-characteristic Cohen structure remains a cited boundary

The full Cohen structure theorem extends beyond the equicharacteristic case: if $(A,\mathfrak{m})$ is a Noetherian complete local ring of mixed characteristic, then $A$ is a quotient of a power-series ring over a Cohen ring.

This page does not prove that theorem. It records it only as the boundary immediately beyond the equicharacteristic results proved here.

The missing input is not cosmetic. Mixed characteristic requires two genuinely new pieces of machinery:

1. Cohen rings that lift the residue field in characteristic $p$ while the ring itself has characteristic $0$.
2. The mixed-characteristic lifting argument that replaces the field-valued coefficient-field step used on this page.

The equicharacteristic corollary A complete equicharacteristic Noetherian local ring is a power-series quotient is therefore the terminal proved-here result of this pair, not an incomplete first draft of the mixed-characteristic theorem.