What is the relationship between Bitcoin's purchasing power and global real interest rates, in the eventual steady-state equilibrium?

We are likely still decades away from Bitcoin's equilibrium point, with respect to its relationship vs. other financial assets, but this day will one day come, and there will exist some relationship between real interest rates and Bitcoin's purchasing power in real terms.

I'd like to present the following hypothesis, and I'd appreciate people's feedback:

The intuition behind (1) is straightforward. Real interest rates reflect the opportunity cost of capital. When the opportunity cost of capital falls (because there are fewer attractive investment opportunities), Bitcoin's value will rise. Likewise, when the opportunity cost of capital rises, Bitcoin's value will fall.

(2) is also fairly straightforward. In equilibrium, Bitcoin appreciates at the same rate as broad economic growth.

In the distant future, I expect Bitcoin to form the basis for the global monetary system. It will likely be the primary store of value, but I do not expect BTC to be the unit of account on which economic activity is based. A good unit of account should be a good standard of deferred payment, specifically for transactions where payment is due in the future (wages, subscriptions, purchases made on credit, etc.), and this requires a unit of account that reflects a consistent amount of purchasing power in real terms.

If, however, there exists a direct relationship between bitcoin's purchasing power and real interest rates, we merely need an accurate approximation of the global real interest rate to define a unit of account in terms of BTC that reflects a consistent amount of purchasing power in real terms. This would require some type of decentralized mechanism to continuously update the approximation, but the result would be a unit of account that can truly compete with fiat as the global standard for deferred payment.

I've written about this idea at https://github.com/joshdoman/util-solidity and recently deployed a prototype of what this mechanism could look like on the RSK testnet. Check it out at https://testnet.theutil.org if you're interested (Chrome and Metamask required).