For another expensive approach, I suspect gold, like the gold voyager record would surpass it.
I imagine you could encode a lot of data in something like a QR code stamped in clay.
In other words, clay tablets get re-purposed too.
Bronze tablets will not break. Unlike stone or ceramic, they are slowly corroded, but we have well preserved bronze tablets which have survived at least 2200 years.
A bronze tablet, or better a stainless steel sheet, can be engraved with text using a computer-controlled mill.
Then again, selecting a physical carrier isn't going to ensure the longevity of data stored.
Far more poignant are questions whether data on those stone tables will be readable, let alone understandable. Ultimately, those tables will contain marks that - to us - signify 1's and 0's. If you want data to outlive us for just a couple of millennia, anyone far down the future will need to figure out which numerical system is used first. Then they have to understand the concept of binary representation of information. And then they have to understand the encoding.
Ironically, a JPEG picture of a cave painting stored on a stone tablet, is still far more brittle compared to actual cave paintings which lasted for tens of thousands of years.
Of course, other concerns such as curation and relevance of cultural objects stored as a digital representation also need to be factored in. Some stuff simply doesn't survive because later generations simply lose interest. The more time passes, the more longevity of objects solely hinges on simple happenstance and chance.
https://en.wikipedia.org/wiki/Long-term_nuclear_waste_warnin...
In which you end up with these types of proposals:
> The linguist Thomas Sebeok was a member of the Bechtel working group. Building on earlier suggestions made by Alvin Weinberg and Arsen Darnay he proposed the creation of an atomic priesthood, a panel of experts where members would be replaced through nominations by a council. Similar to the Catholic church — which has preserved and authorized its message for almost 2,000 years — the atomic priesthood would have to preserve the knowledge about locations and dangers of radioactive waste by creating rituals and myths. The priesthood would indicate off-limits areas and the consequences of disobedience
Meanwhile, there's Github's Archive Program which as this nice tidbit on it's roadmap:
> The GitHub Archive Program is partnering with Microsoft’s Project Silica to ultimately archive all active public repositories for over 10,000 years, by writing them into quartz glass platters using a femtosecond laser.
https://archiveprogram.github.com/approach/
Which sounds nice. But also unrealistic since technology alone isn't enough to ensure longevity. Embedding the longevity of data into culture could also involve founding a "digital priesthood" analoguous to Sebeok's "atomic priesthood". A group of people who safeguard and pass on the knowledge required to read and interpret artefacts containing digital representations of information.
This question could have an answer by now, but it looks like everybody is optimizing for cost/GB.