Is there a particular place in code that forbids exceeding this market cap? Should we be constantly keeping an eye on it after IOHK hands off the project to the community? Or is it somehow imbued in the chain's cryptography?
ADA can not be minted due to the parameter name of ADA in ledger and minting transaction validation being followed in Cardano.
Assets in Cardano is called as "Values" in eUTXO. Values can be ADA or any other Native tokens. In this respect, other user minted tokens also have equal status. Tokens can be minted. Minting of ADA is not possible due to cleaver name settings. ADA was only minted in Genisis transaction and any additional minting is not possible. The reason is as follows.
Value is a Map of CurrencySymbol to a Map of Token Name to Integer. Every asset class is represented by Currency Symbol and Token Name. We cal also say that Asset Class is represented as a combination of CurrencySymbol and Token Name. The ADA has a Currency Symbol and Token Symbol as empty Byte strings in the Ledger.
Transactions cannot create new assets. In the transaction, the input value has to be equal to the output value plus transaction fees.
We need a minting policy script to mint or burn tokens. The Hash of the minting script is the Currency Symbol. Since no script Hashes to empty byte string, there is no way a minting transaction that mints ADA can be created. The implementation in the Plutus repository and has been explained in a much better way in Plutus Pioneer Lecture #5 at around 15 minutes. https://youtu.be/6VbhY162GQA