The rota still works, the record of it is wrong
A printed chore grid with two heavy double-headed arrows drawn across it — nothing was reassigned, it was traded, and the sheet no longer says who does what.

A grey tee on a wooden hanger, hooked over the top of a door. THIS WEEK across the chest in black capitals, and a blue grid underneath it. Two columns, headed R and T. Bins, table, feed, sweep down one side; sweep, feed, table, bins down the other.
Across the middle, two heavy black arrows with a head at each end, crossing in a clean X.
The grid was printed. The arrows were added afterwards, and they are the part that decided anything.
Why are the two columns in exactly opposite order?
Because that is what an even allocation looks like before anybody touches it — the same four jobs, running top to bottom on one side and bottom to top on the other.
Reversal is the cheapest fairness device there is. Nobody ends up with the same job in the same position, the two columns are symmetrical, and the sheet can be checked at a glance by anybody who wants to check it. What it cannot do is account for the two people named in the columns rating the four jobs differently — symmetrical on paper and equal to the pair reading it are separate claims, and the doorway only ever shows you the first.
Why do the arrows have a head at both ends?
Because nothing was reassigned. It was traded, and a trade needs a head pointing each way.
One arrowhead is an instruction: this moves there. Two heads is an exchange, and an exchange requires both parties to prefer what they are getting to what they are giving up. Bins go one way, sweeping comes back the other, and both of them are better off by their own reckoning.
There is a price inside that even though no figure appears anywhere on the sheet. The version with the number written down is a ruled card with four services and their rates.
What does the marker say that the printed grid doesn't?
That the sheet was overruled by the two people named on it, in a heavier ink, without the sheet being reissued.
The blue rules are thin and even. The arrows are wider than the lines they cross, drawn freehand, and they sit on top of everything. One kind of authority written straight over another, with no request made of it.
What the arrows conspicuously do not do is erase. The original allocation is intact underneath, which is why the sheet can still tell you what was set out before it was traded. A corrected grid, reprinted clean, would carry far less information than this one does.
If all four jobs still get done, what actually changed?
The work is unchanged. The record broke — the sheet now describes an allocation that stopped happening the moment the arrows went on.
Bins get emptied, the table gets laid, the animal gets fed and the floor gets swept, on the same days as before. Anyone auditing the household from the grid alone reads off the wrong two names for every line of it.
That is the odd property of a document its subjects can write on: it keeps a true record of what was agreed and a false one of what happens. An object two of them bought together has the same gap the other way round — possession settled in practice, nothing on paper saying so.
Does this work for allocations other than chores?
Yes — any printed grid two people have written on carries the same double reading: what was set out, and what they did with it.
Revision timetables, shift rosters, a packing list, seats at a table. The device is the grid plus the overwriting, not the subject, and the marker has to be visibly a different hand from the print or the two layers collapse into one.
Fourteen journeys plotted as a grid of dots is the version where nobody drew the rota at all and the pattern has to be reconstructed afterwards from the record of turns.
Does printing a household's chore grid need anyone's permission?
No. Four jobs, two initials and a set of ruled lines are nobody's property, and nothing here reproduces a published chart or another artist's layout.
The R and the T were invented for the design and point at no particular household. If you wanted a real printed chart — a shop's wall planner, something with a character on it — that is somebody's work, and work of that kind gets licensed constantly; clearing it is part of the job when the real one is the point. A style belongs to nobody. A specific piece of artwork belongs to somebody.
Does it print well?
Yes — two flat inks, hard edges, and the largest element on the chest is a pair of black strokes.
The X is what has to survive, because it is the thing that reads from across a room. Heavy shafts, solid arrowheads, and no taper: a fine arrow at chest scale thins out to nothing and the swap stops being legible at the distance the design is actually seen from.
The blue rules are the most fragile marks and want to be fewer and thicker than a printed grid would use. The broken, speckled texture on the type is fine on fabric — it is a solid shape with holes in it, not a soft gradient, and it survives the weave. Washed grey suits it; so would ecru or a pale blue.
How do I get one made?
Describe the allocation at JustOG — the four jobs, the two initials, and which two lines got traded. Pick a direction, drag the crop frame, see it composited on the real garment, and it's made to order and shipped.
Designs other people have published are in the shop.
Somebody is sweeping tonight. The sheet on the door says otherwise.