After recall, how do you physically restore or state the deck's order?

Walk the palace, decode each composite to its cards in order, and name (or lay out) the 52 cards one by one from the first locus to the last.

* The reconstructed deck — laid out in order by walking the palace, locus by locus. — Imk3nnyma, CC BY-SA 4.0, via Wikimedia Commons. *

The memorised order lives as the sequence of composites along the route. To reproduce the deck, you simply traverse it: first locus → its three cards, second locus → its three cards, and so on, reciting or dealing them in that exact sequence. In competition this is how a memoriser reconstructs a second identical deck to match the shuffled one — purely by walking the palace and decoding.

Go deeper:

• Alex Mullen — Speed Cards world record (checking) — the competition reconstruction/checking step.