The Rise and Fall of the Gold Standard in the United States by George Selgin
https://www.cato.org/sites/cato.org/files/pubs/pdf/pa729_web.pdf
In a genuine gold standard, the basic
monetary unit is a specific weight of gold alloy of some specific purity, or its equivalent
in fine gold, and prices are expressed in the
unit or in some fractional units based upon
it. Assuming that coinage is a government
monopoly, the government offers to convert
gold bullion into “full-bodied” gold coins,
representing either the standard unit itself
or multiples or fractions thereof, in unlimited amounts. This policy of providing for the
unlimited minting of gold bullion is known
as “free” coinage. Money is created through
public demand to convert bullion to coin.
The emergence of redeemable substitutes for gold coin, backed only by fractional gold reserves and consisting either of circulating notes or transferable deposit credits, appears to have been both an inevitable occurrence as well as one that, despite setting the stage for occasional crises, has also contributed greatly to economic prosperity.
In general, if there is no government restriction or regulation of the freedom to form credit/debt contracts, then banks or even non-bank firms can issue paper notes or deposit liabilities in any ratio to the supply of gold coins. This credit expansion would drive the economy during the prosperous economic boom periods. Conversion of liabilities to gold would be suspended during economic bust periods. A run to withdraw gold from the gold windows of banks or other financial firms would be resolved via systemic debt default and the temporary closing of the gold window of an affected bank or firm.