Keep in mind ideally there is an isomorphism:

• money to battery
• proof-of-work to energy

Suppose the amount of proof-of-work of a money is P. Suppose a goods needs amount of N energy to produce one unit.

If the price S is greater than N/P, one person can

1. spend N energy to produce one unit goods
2. sell the produced goods in the market to get S money
3. give a miner N/P unit of money to get energy N

Netting S-N/P money in hand for free.

If the price S is less than N/P, one person can

1. buy one unit goods by spending S money
2. give one unit goods to some producer by getting N energy from the producer
3. help a miner to get N/P unit of money by contributing energy N

Netting N/P-S money in hand for free.

In short, the price level of energy-only goods is irrelevant to the money volume and is always N/P.

Definition of base material is the goods that can not be produced by energy. We might need less and less base materials by technology advance, by Einstein's m=e/c^2, it is possible in a future there is no need for the definition of base materials. Land is a typical base material example today, however.

A typical goods requires base materials and energy to produce; a skillful profession requires a lot of training or experience consuming base materials or energy beforehand. The production of any goods can be eventually decomposed into the necessary energy part and base materials part. We know the pricing of any energy-only goods as above energy arbitrage argument. What about the price level of base materials? Without loss of conceptual generality, assume there are only two goods, one is the energy-only goods and the other is the base-materials-only goods with total amount K. Suppose the money volume is V. Suppose the ratio for saving is A, ratio for transaction of energy-only goods is B, therefore ratio of currency volume for transaction of base materials goods must be 1-A-B. Simplify to have V(1-A-B)/K as the price level of base materials which will be increasing assuming constant A and B, examples like indefinite volume increasing of ETH or fiat currency.

Let one unit goods be eventually produced by N energy and M unit of base materials then what is the price ? we have N/P + MV(1-A-B)/K for its price. When base materials are abundant or the required base material is tiny, this number is around N/P which is irrelevant to money volume as long as P remains the same. When the required energy for the goods production is tiny (such as land), this number is around MV(1-A-B)/K which is linear with money volume and irrelevant to P. No matter the money in question is battery or gold or BTC or ETH, the conclusion remains. Therefore, in order to avoid weird real gain of holding base materials or holding money, the money volume V and the amount of proof-of-work of the money P shall be constant. Fictionally, if the radius of Earth happens to be 2 times larger, then the energy influx from the Sun and the land size become 4 times larger, so we can have V to be 4 times larger and the old battery money can still function fairly by creating 4 times battery volume, no previous land/money holder can have a real gain.