To untransform is to apply the inverse of the map that transformed a cell: the transform doubled the core to 8; the untransform halves it back to 4. When a function is invertible, transform-then-untransform is the identity — the cell returns exactly to where it began. This is the logic of reversible computing: an operation you can run backwards, losing nothing. It is the mirror of dart 332 across the palindrome — the coming-out map that undoes the going-in map — and a small proof that the batch's value-changes, like its place-changes and its masks, all leave a way back to the original cell.
The demo transforms (double) then untransforms (halve) the core — and it returns to 4: live demo
“Computation throws information away.” — a reversible operation keeps enough to run backwards; f then f-inverse loses nothing and returns the input. cited
Double on the way in, halve on the way out, and the cell is 4 again. To untransform is to prove the map kept a way back. reversible computing
On the canonical compiler, doubling then halving the core returns 4 — identity: