Hartwick's rule postulates that an economy is sustainable if all rents obtained from the extraction of non-renewable resources are re-invested in produced capital (Source). A typical example would be the Norwegian Sovereign Wealth Fund that invests the resource rents obtained from oil into equity, real estate and fixed income. (Source)
In generic terms the investments that the fund makes will be in capital (e.g. machinery) or land and other rent-generating assets (e.g. land, patents, etc.). However, the produced capital will depreciate over time and the rent-generating assets do not involve the production of a new asset but the purchase of the rent attributable to the rights over an existing asset.
How then would weak sustainability (Hartwick's rule) be possible on a global scale? Presumably this would have to involve investing every cent of resource rent into capital investments with a lifespan that is at least as long as the lifespan of the resource that it substituted?