The colours
Five algorithms finish it
Once the shape is back, one corner algorithm, one edge algorithm, a middle flip and two repairs cover every position a Square-1 can hold. Each is printed in standard notation, and every printed form has been replayed to the same finish as the proved one.
A cube-shaped Square-1 still has its eight corners and eight edges to arrange, 20,160 arrangements of each. The algorithms below move one kind of piece and leave the other exactly where it was, which is what makes them safe to use in any order. Hold the puzzle with yellow on top; the diagrams show the top layer from above and the bottom tipped toward you, with the cut vertical. Tipping the puzzle is the same motion as the slice, so a piece that crosses keeps its drawn position.
The middle sliver
(0,6) / (0,6) / (0,6) /
Slicing an odd number of times leaves the thin middle layer turned round. This puts it back and moves nothing else, so it goes first and is then forgotten.
middle layer flipped
The corners
one algorithm, sixteen angles/ (0,-3) / (-2,-2) / (2,5) /
Nine moves that cycle three corners and leave all eight edges at home. Which three corners depends on how you angle it: turn either layer a quarter before starting and undo the quarter afterwards, and the same algorithm points at a different trio. Sixteen angles are possible, and between them they reach every corner arrangement a cube can hold. The hardest needs 7 uses; almost all need fewer.
The edges
/ (3,0) / (1,1) / (-4,-1) /
The same shape of tool for the edges: nine moves, three edges cycled, every corner untouched, sixteen angles, worst case 7 uses. Corners first, then edges, because the corner algorithm is the easier one to read at speed.
The two repairs
/ (0,3) / — three moves that swap four corners and four edges at once. About half of all scrambles arrive needing it: the two kinds of piece are tied together, and when both are odd this puts both even in one stroke.
(3,1) / (0,3) / (-5,2) / (-2,2) / (-2,2) / (-5,-4) / (0,6) / (0,-3) / (2,0) — the long one, 22 moves. A cube can also hold positions where the corners are odd on their own, and no short sequence fixes that: sweeping every algorithm of up to four slices found none, and this eight-slice one was the shortest a longer search produced. It runs once at most per solve, and then the two nine-movers finish everything.
The whole colour stage, in order
Middle sliver if it is flipped. The three-move repair if corners and edges are both odd, or the long repair if the corners are odd on their own. Then corners with the first nine-mover, edges with the second. Two hundred full solves were replayed from scramble to finish to check this order leaves nothing behind, and the middle of those solves ran to about seventy moves of colour work. Slow by a racer's standards, honest by any other: a racer's case sheet for this event runs to dozens of algorithms; five are enough to finish every solve.