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The alternative is no reconstruction at all on one hand, and adding fake detail on another hand

And if one wants to add fake detail, why should archeologists be involved? Just have AI generate them

The archeologists are already adding fake detail, just at a different level of abstraction. Did they constrain themselves to only painting in the places where they find remnants of pigment? No, otherwise there would be gaps, cracks, and random interruptions of other colors in the painted figures. And there's the guesswork involved in going from spectral analysis (+ other tools) of a pigment sample to an actual paint that could have been plausibly available to the artist.

Reconstruction, (similar to translation) is an art that combines carefuly study of evidence and craftfully filling in gaps and adding in detail where necessary (or leaving details unfilled and ambiguous to communicate the impossibility of total translation or reconstruction!) to present some communicable form of the original that gives the viewer some closer but imperfect access to it.

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